Which fraction is equivalent ?

Yes, it is worth the extra drive, going to the further store is cheaper.

The cheaper option saves you $0.09.

Given:

Price or sale = $3.19 a pound

1.) Neighborhood store

Distance = 2.1 miles away

As, the car averages about 19 miles per gallon,

=2.1 miles / (19 miles/gallon)

= 0.1105 gallons of gas < 17 gallons

The gas is about $3.83/gallon, then the cost be

=0.1105 gallons x ($3.83/gallon)

= $0.42

The chicken is sold for $3.59 a pound, and you need 3 pounds, then you would pay:

= 3 pounds x ($3.59/pound)

= $10.77

So, the total is

= $0.42 (gas) + $10.77 (chiken)

= $11.19

2.) Store across town

Distance = 8.5 miles away

The car averages about 19 miles per gallon, then you would need:

=8.5 miles / (19 miles/gallon)

= 0.447 gallons of gas < 17 gallons

The gas is about $3.83/gallon, then the gas would cost:

=0.447 gallons x ($3.83/gallon)

= $1.71

The chicken is sold for $3.19 a pound, and you need 3 pounds, then you would pay:

= 3 pounds x ($3.19/pound)

= $9.57

The total cost

= $1.71 (gas) + $9.57

= $11.28

Thus, $11.19 < $11.28, then it is worth the extra drive.

Hence, cheaper option saves you= $11.28 - $11.19 = $0.09

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The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.

A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.

Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.

Sodium contains in a can of soup is 300mg

Sodium contains in a can of frozen dinners is 450mg

Let the number of cans of soup purchased be x

Then, the number of frozen dinners purchased=x+5

Total sodium purchased=6000mg

So, 300x+450(x+5)=6000mg

Therefore, the system is 300x+450(x+5)=6000mg

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Answer:

Step-by-step explanation:

B.

Answer:

x = 3

and

y = 2

Step-by-step explanation:

Check the picture below.

[tex] \Large{\boxed{\sf d = \sqrt{40} }} [/tex]

[tex] \\ [/tex]

The distance between two points is given by the following formula:

[tex] \Large{\sf d = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}} [/tex]

Where:

[tex] \\ [/tex]

First, let's identify our values:

[tex] \sf (\underbrace{\sf -3}_{\sf x_A} \: , \: \overbrace{\sf 2}^{\sf y_A}) \: \: and \: \: (\underbrace{\sf 3}_{\sf x_B} \: , \: \overbrace{\sf 0}^{\sf y_B}) [/tex]

[tex] \\ [/tex]

Now, substitute these values into our formula:

[tex] \sf d = \sqrt{\sf (3 - (-3))^2 + (0 - 2)^2} \\ \\ \sf d = \sqrt{\sf 6^2 + (-2)^2} \\ \\ \sf d = \sqrt{\sf 36 + 4 } \\ \\ \boxed{\boxed{\sf d = \sqrt{40} }} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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A graph to model the proportional relationship between cost and number of songs is shown in the image attached below.

Mathematically, a proportional relationship and the constant of proportionality can be represented or modeled with the following equation or mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for a song as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 10/20

Constant of proportionality (k) = 0.2

Therefore, an equation for any number of song for this karaoke is given by:

y = 0.2x.

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Answer:

Step-by-step explanation:

B because that is the letter of my first name!

The relationship is not proportional because the number of used bottles increases more. Option B

A relationship is said to be proportional when the two variables that are in question are either increasing or decreasing at the same rate. It could also be that one one quantity is increasing and the other is  decreasing.

If we look at the proportionality in the proper sense of it, there appears to be no relationship between the two variables as the number of used bottles is increasing at a much higher rate than the number of bottles that is recycled.

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The slope of the equation and y- intercept​ is 320 and 1500 respectively.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

Given that the total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking.

To find the slope and y- intercept​.

y=320x+1500

Therefore, the slope of the line is;

m =320

Then the y- intercept is 1500

Hence, The slope of the equation and y- intercept​ is 320 and 1500 respectively.

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Answer:

Below

Step-by-step explanation:

You didn't include the picture......

each cube has a volume of  1/4 * 1/4 * 1/4 = 1/64 cm^3

     count the total number of cubes and multiply by  1/64

                                         to get volume in cm^3

Groups not counted as unemployed in the official unemployment statistics are the underemployed and discouraged workers.

A discouraged worker is someone who can work and is qualified for employment but is not already working and has not looked for work in the past four weeks. Discouraged workers typically have given up looking for work because they have discovered no relevant employment possibilities or have not been successful in getting a job after applying.

Discouragement among employees has a wide range and complex root causes. Because they lack the skills to deal with technological change at work, workers occasionally leave the workforce. During the Great Recession, the manufacturing industry let go of senior workers who were unable to operate the modern computer numeric control (CNC) equipment, which was used to cut wood and other hard materials.

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The probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

The formula for z-score is z = (x -μ)/σ

Where,

Z is standard score.

x is observed value.

μ is mean of the sample.

σ is standard deviation of the sample.

According to the given question.

The mean of the distribution is μ = 44

The standard deviation of the distribution is σ = 6

The observed value is x = 38

Therefore, z-score = (38 -44)/6 = -1

So, the are P(z > -1) = 15.87%

Hence, the probability that a randomly selected student has a typing speed of less than 38 words per minute is 15.87%.

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The standard deviation of the sampling w would be 0.06.

What is a standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

Population proportion

                         [tex]p=\frac{2756}{5500} \\\\\\p=0.501091\\\\p=0.501[/tex]

The mean of the sampling distribution for samples of size n=70 customers = 0.501

The standard deviation of the sampling distribution for samples of size n=70 customers is

                         [tex]=\sqrt{\frac{p* (1-P)}{n}} \\\\=\sqrt{\frac{ 501091(1-0.501091) }{2}}\\\\ = 0.059761 \\\\=0.06[/tex]

Hence, the standard deviation of the sampling w would be 0.06.

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when the charged rod is brought closer to the sphere negative charges get induced on the sphere by gathering some electrons from the ground and the negative  remain on the sphere even after disconnecting it.

here the ground acts as a reservoir of electrons.a conducting sphere of radius r is connected to ground through a battery with a voltage vo as shown. a. assuming ground is at infinity, find the net charge on the sphere. the sphere is disconnected from the battery, and a thick shell of a neutral, polarizable material is placed around the sphere.

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5 radical 8 to the power of 3

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

When two pairs of corresponding sides and the corresponding angles between them are congruent, the triangles are congruent.

Side-Angle-Side (SAS) Rule

The proof by S A S congruence rule is given below.

Given from fig, JK || LM.

And JK = LM

Since JK is parallel to LM and JN is a transversal so the angle made on the same side of JN are corresponding angles which are equal to each other.

So, angle KJL = angle MLN........equation 1

Also given L is the midpoint of JN so, JL = NL.....equation 2

Now, in triangle JLK and triangle LNM

JK = LM (given)

angle KJL = angle MLN (from 1)

JL = NL (from 2)

So by S A S congruence rule, triangle JLK conguent triangle LNM proved.

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Answer:

Step-by-step explanation:

11.

Answer:

a=90°

c=45°

b=45°

Step-by-step explanation:

this triangle is a right triangle. (shown by the box in angle a) this means a must equal 90°

and by extension means the other two angles have to equal 45° each because right angles always have two angles of the same degree and the angles of a triangle always Equal 180°

Answer:

Step-by-step explanation:

Planet A has a mass of 8× 10²5 kilograms. Planet B has a mass of 6×10 kilograms. Choose which planet has the larger mass. Then fill in th blank with a number written in standard notation. Planet A has the larger mass. The mass of Planet A is times as large as the mass of Planet B. O Planet B has the larger mass. $0 times as large as the mass of Planet A.

Answer:

10

Step-by-step explanation:

im him trust

-------------------

The measure of an inscribed angle is half the measure of the intercepted arc:

Angles a and b sum to a right angle since inscribed between the tangent and diameter.

Then we have:

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{4 }{7 +3} \implies \cfrac{ 4 }{ 10 } \implies \cfrac{2 }{ 5 }[/tex]

Answer:

answer is c!

because it's domain is -7!!

The height of tree in meter is 11.5 meter after the conversion from 37.95 feet to meter.

A conversion factor is measurement value in numbers that is used in converting one unit to another unit by arithmetic operations.  

Given that a tree is 37.95 feet tall and 1 meter is 3.3 feet.

So to find 37.95 feet tree in meter we have to divide 37.95 by 3.3  

= 37.95 / 3.3

= 11.5 meter

1 meter is 3.3 feet, then 11.5 meter is 37.95 feet.

Therefore, the height of tree in meter is 11.5 meter.

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The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The points are (3, 4) and (-1, -4). Then the equation of the line is given as,

(y + 4) = [(4 + 4) / (3 + 1)](x + 1)

y + 4 = 2(x + 1)

y = 2x + 2 - 2

y = 2x - 2

The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.

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The measure of each angle are mentioned below

What is angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

The measure of each angle is

∠a = 90°

∠b = 45°

∠c = 45°

∠d = 90°

∠e = 45°

∠f = 45° {coordinate judgment angle }

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Thus, in ΔCDE the m/∠D = 130⁰, which can be calculated using angle sum property of triangle.

Triangle is derived from the Latin word triangulus, which means "three-cornered" or "having three angles," and is composed of the roots tri-, "three," and angulus, "angle or corner." Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Given that: In ΔCDE

m/∠C = (x-4)°

m/∠D = (9x + 4)°

m/∠E = (2x + 12)°

Now, to find m/∠D

So, We know that sum of internal angles of a triangle is equal to 180⁰ .Here, we are given a ΔCDE and all its three internal angles.

Putting the sum of all three equal to 180⁰:

∠C + ∠D + ∠E = 180⁰(x-4)°+ (9x + 4)°+ (2x + 12)°

= 180⁰12x +12

= 180⁰x +1 = 15⁰

x = 14⁰

Thus, Putting value of x in m/∠D = (9x + 4)°.

m/∠D = (9 × 14 +4)⁰

m/∠D = 130⁰

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The complete question is as follows:

In ΔCDE, m ∠ C = ( x − 4 ) ∘ m∠C=(x−4) ∘ , m ∠ D = ( 9 x + 4 ) ∘ m∠D=(9x+4) ∘ , and m ∠ E = ( 2 x + 12 ) ∘ m∠E=(2x+12) ∘ . Find m ∠ D.

The probability that the sum of the faces is 7 = 15/216

The value of m = 15 and the value of n = 216

In this question, we have been given three regular dice are rolled simultaneously.

We need to find the probability that the sum of the faces is 7.

When three dice are rolled simultaneously, the total number of outcomes

n(S) = 6 * 6 * 6

n(S) = 216

Let event A: sum of the faces is 7

A = {(1, 2, 4), (1, 4, 2), (4, 1, 2), (4, 2, 1), (2, 1, 4), (2, 4, 1), (1, 3, 3), (3, 3, 1), (3, 1, 3), (2, 2, 3), (2, 3, 2), (3, 2, 2), (1, 5, 1), (5, 1, 1), (1, 1, 5)}

n(A) = 15

So, the probability that the sum of the faces is 7 = 15/216

Hence, if the probability that the sum of the faces is 7 can be represented by m/n in simplest form then m = 15 and n = 216

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