Jessica rode her bicycle 128 miles in 8 weeks, riding the same distance each week. Pablo rode his bicycle 95 miles in 5 weeks, riding the same distance each week. Which statement correctly compares the number of miles per week they rode?

1/5(15+10x-5) is equivalent to 2(x+1).

What is equivalent equation?

Equivalent equations are algebraic equations with the same roots or solutions.

1/5(15+10x-5) can be simplified as follows:

1/5(15+10x-5) = 1/5(10x + 10)

Factor out 10 from the expression in the parentheses:

1/5(10x + 10) = 1/5 * 10 * (x + 1)

Simplify:

1/5 * 10 * (x + 1) = 2(x + 1)

Therefore, 1/5(15+10x-5) is equivalent to 2(x+1).

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Answer:

The combined volume of 9cm, 7cm, and 6cm is 378cm³ if a rectangular prism or cube

Step-by-step explanation:

To find the volume of a 3-dimensional prism or cube you need to find the Area of the Base and Height and multiply them.
Equation = Bh
Since there are only 3 different numbers you just need to multiply them together.

I hope this was helpful!

Lanthanum, a chemical element with the atomic number 57, has the symbol La in the Periodic Table.

Density is calculated by comparing an object's mass to its volume.

In this question the density of lanthanum is given in grams per mililitre.

For lanthanum density, the appropriate response is 6.15 grammes per millilitre.

To convert grams into kilograms, we do

Since\s1g=.001kg

Hence, the formula to determine the density of lanthanum in kilogrammes is 0.001*6.15g/ml, or 0.00615kg/ml.

Hence, 0.001*6.15g/ml, or 0.00615kg/ml, is the formula for computing the density of lanthanum in kilogrammes. Therefore,

The density will then be 0.00615/0.454 lbs/ml, or 0.0135462555066 lbs/ml, which is the equivalent in pounds.

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The reasonable value of the range would depend on a variety of factors, such as the difficulty of the exam, the amount of material covered, and the level of preparation of the students. However, as a general guideline, a reasonable range for the number of hours studied for an exam might be around 10 to 20 hours. This would suggest that students are putting in a reasonable amount of effort and time to prepare for the exam, without overdoing it or under-preparing.

If the tens digit of a two-digit number is one more than the units digit and the number itself is 6 times the sum of the digits, then the solution is a two-digit number 54.

Let's assume that the units digit of the two-digit number is x. According to the problem statement, the tens digit is one more than the units digit, which means that the tens digit is x + 1. Therefore, the two-digit number can be expressed as 10(x+1) + x, which simplifies to 11x + 10.

The problem also states that the number is 6 times the sum of its digits. The sum of the digits is x + (x + 1) = 2x + 1. Therefore, we can set up an equation:

11x + 10 = 6(2x + 1)

Simplifying the equation, we get:

11x + 10 = 12x + 6

Subtracting 11x from both sides, we get:

10 = x + 6

Subtracting 6 from both sides, we get:

x = 4

Therefore, the units digit is 4, and the tens digit is one more than that, which is 5. The two-digit number is 54. We can check that this is indeed 6 times the sum of its digits:

54 = 6(4 + 5)

54 = 6(9)

54 = 54

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Answer:

1/10

Step-by-step explanation:

Puppy food portions.

Unish Baskota

Kennedi is feeding her 5 puppies. She has half a bag of dog food left. How much of the bag

will each puppy receive?

If Kennedi has half a bag of dog food left and she has 5 puppies to feed, then each puppy will receive 1/5th of the remaining dog food.

To calculate this, you can divide the remaining dog food (which is half a bag) by the number of puppies (which is 5):

1/2 bag of dog food ÷ 5 puppies = 1/10 bag of dog food per puppy

So each puppy will receive 1/10th of the bag of dog food.

Each puppy would receive 1/10 of food

The percentage of full marks was obtained by D is (d) 60%.

What is percentage  ?

Let's start by using the given information to find out how many marks B, C, and D got in the exam.

We know that A got 10% less than B, so if A got 360 marks, then B got 10% more than that, which is:

B = 360 + 10% of 360

= 360 + 36

= 396

We also know that B got 25% more than C, so if B got 396 marks, then C got 25% less than that, which is:

C = 396 - 25% of 396

= 396 - 99

= 297

Finally, we know that C got 20% less than D, so if C got 297 marks, then D got 20% more than that, which is:

D = 297 + 20% of 297

= 297 + 59.4

= 356.4

So D got 356.4 marks out of 500. To find out what percentage of full marks D obtained, we can use the formula:

percentage = (marks obtained / full marks) x 100

Therefore, the percentage of full marks obtained by D is:

percentage = (356.4 / 500) x 100

= 71.28%

Rounded to the nearest integer, the answer is approximately 71%, which is closest to option (d) 60%. Therefore, the answer is (d) 60%.

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Step-by-step explanation:

You can choose from four main ways to detect outliers:

1.Sorting your values from low to high and checking minimum and maximum values.

2.Visualizing your data with a box plot and looking for outliers.

3.Using the interquartile range to create fences for your data.

4.Using statistical procedures to identify extreme values

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Answer:

The slope is 9.

Step-by-step explanation:

This equation is written in slope intercept form, [tex]y=mx+b[/tex] where m is the slope and b is the y intercept. Based on this equation, the slope is [tex]\frac{9}{1}[/tex] which is simplified to 9.

Answer:

[tex] \sf \: d) \: 6[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 2x + 12 = 24

Then the value of x will be,

→ 2x + 12 = 24

→ 2x = 24 - 12

→ 2x = 12

→ x = 12 ÷ 2

→ [ x = 6 ]

Hence, option (d) is correct.

The temperature in Fahrenheit that is equal to 17 degree Celsius is  62.6 Fahrenheit .

The Celsius (°C) and Fahrenheit (°F) are two common temperature scales which are used to measure the temperature. Celsius is based on the metric system, and is widely used in most countries. Fahrenheit, on the other hand, is used mostly in the United States and a few other countries.

We use the the formula "°F = (°C × 1.8) + 32" , to convert the temperature from degree Celsius to degree Fahrenheit ;  

In this case  , we have to convert 17 Celsius to Fahrenheit,

So , we can write the formula as : °F = (°C × 1.8) + 32

⇒ °F = (17 × 1.8) + 32 ;

⇒ °F = 30.6 + 32 ;

⇒ °F = 62.6  .

Therefore, 17 Celsius is equal to 62.6 Fahrenheit .

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To convert between pounds and kilogrammes, multiply the number of pounds by 0.45359237, and to do the opposite, multiply the number of kilogrammes by 2.20462.

So, 64 kg is equal to 141.095 lbs.

One pound is nearly equal to 454 grams. A kilogramme value is 2.20462 pounds.

1 pound is equal to 0.45359237 kilograms.

Use the formula below to convert kilogrammes (kg) to pounds (lbs):

For conversion of kilograms to pounds, multiply your figure by 2.20462

64 kg can be converted to pounds by multiplying by 2.20462:

96 kg X 2.20462 lbs/kg

=141.095 lbs

Therefore, 64 kg is nearly equal to 141.095 lbs.

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Answer:

D

Step-by-step explanation:

step by step... solved

The situation cannot be modeled by a linear equation. The processing fee is $42 and the daily fee is $102.With a budget of $1200maximum number of days you can rent the beach house is 6 days

a. To determine if the situation can be modeled by a linear equation, we can plot the data on a graph with days on the x-axis and total cost on the y-axis.

When we plot the data, we can see that it does not form a straight line, which means the situation cannot be modeled by a linear equation.

b. To find the processing fee and the daily fee, we can use the information given in the table.

Let's call the processing fee "p" and the daily fee "d". We can set up two equations to represent the total cost for two different numbers of days:

2d + p = 246

4d + p = 450

Subtracting the first equation from the second, we get:

2d = 204

So, d = 102.

Substituting d = 102 into the first equation, we get:

2(102) + p = 246

Solving for p, we get:

p = 42

Therefore, the processing fee is $42 and the daily fee is $102.

c. We can use the equation for the total cost with the processing fee and daily fee we found in part (b) to determine the maximum number of days we can rent the beach house for $1200.

8d + p = 858

Substituting p = 42 and d = 102, we get:

8(102) + 42 = 858

Simplifying, we get:

840 + 42 = 882

So, we can rent the beach house for a maximum of 6 days with a budget of $1200

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Linear Equation and It's Application in Real Life

In the given problem, it is an application of linear equation and solving word problem about mathematical operation. It is a combination of general mathematics and algebra.

In word problem about time and work, the equation is 1/x + 1/y + 1/z + ... = 1/t, where

x is the amount of time consume by first person

y is the amount of time consume by second person

z is the amount of time consume by third person

t is the amount of time they consume working together.  

In this case, to solve for the amount of work that Rizal can finish the school project alone.

1/x + 1/y + 1/z + ... = 1/t

It can be derived as 1/x = 1/t - (1/y + 1/z + ... ), where x is the amount of work done by Joseph, and y for Maria.

Given

Joseph can finish the chores in 2 hours

Maria can finish the same chores in 4 hours.

Create  mathematical equation using the given formula for work problem.

1/x + 1/y = 1/t, where x = 2 hours, and y = 4 hours

½ + ¼ = 1/t, solve for t

The LCD of 2, 4 and t is 4t, the new equation will be

4t(1/2) + 4t(1/4) = 4t(1/t)

2t + t = 4

3t = 4

t = 4/3

t = 1 1/3 hours

Final Answer

1 1/3 hours to complete the task when they work together.  

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Answer:

x = -3

Step-by-step explanation:

A vertical line has an undefined slope and its equation can be written as x = a, where 'a' is the x-coordinate of any point lying on the line. This is because all points on a vertical line have the same x-coordinate.

In this case, we are looking for the equation of the vertical line that passes through the point (-3, 8). Since this line is vertical, its equation will be of the form x = a, where a is the x-coordinate of any point on the line.

We can see that the x-coordinate of the point (-3, 8) is -3, so the equation of the vertical line passing through this point will be:

x = -3

And that's the answer. The equation of the vertical line passing through the point (-3, 8) is x = -3.

The value of phone B is [tex]\omega = 840[/tex].

Any equation with a maximum degree of 1 is said to be linear. In a linear equation, no variable has an exponent bigger than 1, thus. There is always a straight line on the graph of a linear equation.

Given that each term in a linear equation has an exponent of 1, graphing an algebraic equation always yields a straight line.  For this reason, it is referred to as a "linear equation." There are both one-variable and two-variable linear equations.

[tex]v= 1000[/tex]

[tex](\frac{4}{5})^d[/tex] is the value of phone A and

[tex]\omega = 840[/tex] is the value of phone B.

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Complete Question;

For each cell phone, write an equation that relates the value of the phone in dollars to the years since release, t. Use v for the value of Phone A and w for the value of Phone B.

The value of x in the right triangle is 8.7 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The side of a right angle triangle can be found using trigonometric ratios or Pythagoras's theorem.

Hence, let's use Pythagoras's theorem,

c² = a² + b²

where

Therefore,

x² = 10² - 5²

x² = 100 - 25

x = √75

x = 8.66025403784

Therefore,

x = 8.7 units

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Based on the information, it can be inferred that Susan can receive a 100% refund of the taxes that were erroneously charged to her.

According to the previous information we can infer that the government can refund 100% of the money that she wrongly contributed to her taxes. This is because this return does not have a %, but is equivalent to the excess contributions that she made. Due to the above, we can affirm that she can receive all the surpluses that she contributed without any type of withholding or percentage.

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To convert 511 inches into centimeters by using the conversion factor of 2.54 cm/inch.

Conversions play a crucial role in our daily lives. Whether it's converting the temperature from Fahrenheit to Celsius, converting currency when traveling to another country, or converting units of measurements, it's essential to know how to convert between different values. In this article, we'll explain how to convert 511 inches into centimeters.

To convert 511 inches into centimeters, we need to use a conversion factor. The conversion factor for converting inches to centimeters is 2.54. This means that one inch is equal to 2.54 centimeters. To convert 511 inches to centimeters, we need to multiply 511 by 2.54.

511 inches x 2.54 cm/inch = 1298.94 cm

Therefore, 511 inches is equivalent to 1298.94 centimeters. It's important to note that when converting between different units of measurements, it's crucial to use the correct conversion factor. In this case, we used the conversion factor of 2.54 cm/inch to convert inches into centimeters.

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Answer:

p = 6.95 + (0.95 × t)

Step-by-step explanation:

A function rule explains how to convert an input value (x) into an output value (y) for any given function.

To get the total price (p) we need to add the cost of the pizza itself, and add each topping. The part of the equation (0.95 × t) can solve for the price of each topping, so we add that on.

The base of the triangle is 9 inches and the height is 2 inches.

Let's denote the height of the triangle as h, and the base as b.

We know that the area of a triangle is given by the formula:

Area = (1/2) * base * height

Substituting the values we have:

9 = (1/2) * b * h

Multiplying both sides by 2 gives:

18 = b * h

We also know that the base is 5 inches more than 2 times the height:

b = 2h + 5

Substituting this expression for b in terms of h in the area equation, we get:

18 = (2h + 5) * h

Expanding the right-hand side, we get:

18 = 2h^2 + 5h

Rearranging this equation, we get:

2h² + 5h - 18 = 0

We can solve for h by using the quadratic formula:

h = [-b ± [tex]\sqrt{b² - 4ac}[/tex]] / 2a

where a = 2, b = 5, and c = -18.

Plugging these values into the formula, we get:

h = [-5 ± [tex]\sqrt{5^{2} - 4(2)(-18) }[/tex]] / (2 * 2)

Simplifying:

h = [-5 ± [tex]\sqrt{169}[/tex]] / 4

Taking the positive solution:

h = [-5 + 13] / 4

h = 2

Now that we know the height is 2 inches, we can use the equation b = 2h + 5 to find the base:

b = 2(2) + 5 = 9

Therefore, the base of the triangle is 9 inches and the height is 2 inches.

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The maximum error in using the value of the radius to compute the volume of the sphere is approximately 554.86 cubic centimeters.

What is sphere ?

A sphere is a three-dimensional shape that is perfectly round, with all points on the surface at an equal distance from the center.

The formula for the volume of a sphere is given by V = (4/3)πr³, where r is the radius of the sphere.

The maximum error in the measurement of the radius is given as 0.03 cm. Therefore, the actual radius of the sphere can be anywhere between 20.97 cm (21 - 0.03) and 21.03 cm (21 + 0.03).

To find the maximum error in using this value of the radius to compute the volume of the sphere, we need to find the maximum possible difference in the volumes calculated using these two values.

So, we can calculate the volume of the sphere using the maximum and minimum values of the radius as follows:

V_max = (4/3)π(21.03)³

V_min = (4/3)π(20.97)³

Now, we can find the difference between these two values to get the maximum possible error:

Max error = V_max - V_min

Max error = (4/3)π(21.03)³ - (4/3)π(20.97)³

Max error ≈ 554.86 cubic centimeters

Therefore, the maximum error in using the value of the radius to compute the volume of the sphere is approximately 554.86 cubic centimeters.

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The volume of the solid is 342.9 sq. cm.

The volume of an object is the amount of substance that the object can contain. Th three dimensions of the object is required in order to determine its volume.

Considering the question,

volume of a cylinder = [tex]\pi[/tex]r^2h

Where r is the radius and h is the height of the cylinder.

volume of the hole = length*width*height

Thus,

The volume of a cylinder = [tex]\pi[/tex]r^2h

                   = 22/7*4^2*10

                   = 502.86

The volume of the cylinder is 502.86 sq. cm.

The volume of the hole = length*width*height

                                     = 4*4*10

                                     = 160 sq cm.

The volume of the solid = volume of a cylinder  - volume of the hole

                                         = 502.86 - 160

                                      = 342.86

The volume of the solid is 342.9 sq. cm.

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In 120 minutes, all the three boats will next meet at the starting location. The solution has been obtained by using the concept of least common multiple.

What is least common multiple?

Least Common Multiple is abbreviated as LCM. The smallest multiple shared by two or more different numbers is referred to as the least common multiple.

We are given that three boats start cruising around a small island starting at the same time and from the same location, and following the same route.

They take one full circle around the island which is 2 km.

First boat:

It covers 5 km in 60 minutes.

So, it will cover 2 km in 60/5 * 2 = 24 minutes

Second boat:

It covers 4 km in 60 minutes.

So, it will cover 2 km in 60/4 * 2 = 30 minutes

Third boat:

It covers 3 km in 60 minutes.

So, it will cover 2 km in 60/3 * 2 = 40 minutes

Now, taking the LCM of 24, 30 and 40, we get 120.

Hence, in 120 minutes all the three boats will next meet at the starting location.

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The height of the statue is given by the similar triangles and x = 2.667 m

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the triangles be represented as ABC and CDE

Now , the triangles ABC and CDE are similar

Let the height of the statue be = measure of AB = x

Now , the height of Patty = measure of CE = 1.6 m

Let the distance between Patty and mirror be CE = 2.4 m

Let the distance between mirror and base of statue BC = 4 m

And , corresponding sides of similar triangles are in the same ratio

Substituting the values , we get

AB / CE = BC / CE

x / 1.6 = 4 / 2.4

Multiply by 1.6 on both sides , we get

x = ( 4 x 1.6 ) / 2.4

x = 4 ( 2/3 )

x = 2.6667 m

Hence , the height of the statue is 2.6667 m

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Answer:

{32, 60, 68}

Step-by-step explanation:

If a triangle is a right triangle, the sum of the squares of the two shorter sides must equal to the square of the longest side

Only {32, 60, 68} fits this property

32² + 60² = 1,024 + 3600 = 4,624
68² = 4,624

The other options do not satisfy this requirement

Answer:{32,60,68} represents the three sides of a right triangle

Step-by-step explanation: If the given triangle is a right triangle then it must follow Pythagoras's theorem,

according to Pythagoras's theorem,

(hypotenuse)²=(base)²+(height)²

Since hypotenuse is the longest side, so here 68 is the largest

so, hypotenuse=68 ,base=32 ,height=60

putting the values in the above equation,

(68)²=(32)²+(60)²

4624=1024+3600

4624=4624

since LHS=RHS

Therefore, it is a right triangle

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Therefore, the probability that a truck drives between 92 and 144 miles in a day is 0.7454, or about 74.54% (rounded to four decimal places).

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. An event with probability 0 is impossible, while an event with probability 1 is certain. In probability theory, an event is any outcome or set of outcomes of a random process or experiment. The probability of an event is determined by calculating the ratio of the number of ways the event can occur to the total number of possible outcomes. Probability is used in a wide variety of fields, including mathematics, statistics, physics, engineering, finance, and economics, to model and analyze random phenomena and make predictions about future events.

Here,

To solve this problem, we need to standardize the given values using the formula:

z = (x - μ) / σ

where z is the standard normal random variable, x is the observed value, μ is the mean, and σ is the standard deviation.

For x = 92:

z = (92 - 110) / 25 = -0.72

For x = 144:

z = (144 - 110) / 25 = 1.36

Using a standard normal distribution table or a calculator, we can find the probability that a standard normal random variable falls between -0.72 and 1.36:

P(-0.72 < z < 1.36) = 0.7454

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333 whole cups can be filled to full capacity before the water cooler is empty.

What is volume of an object?

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms of cubic units. In other words, the volume of any object or container is the capacity of the container to hold the amount of fluid (gas or liquid).

First, we need to calculate the volume of one cone-shaped cup:

The formula for the volume of a cone is V = (1/3)πr²h, where r is the band h is the height. Since the diameter of the cup is given as 2 inches, the radius is 1 inch. Thus, the volume of one cup is:

approximately 333 whole cups can be filled to full capacity before the water cooler is empty.

Next, we need to determine how many cups can fit into the water cooler. To do this, we can divide the volume of the cooler by the volume of one cup:

          [tex]V = \frac{1}{3} \pi 1^{2} 3 \\\\V= \frac{1}{3} \pi \ cubic\ inches[/tex]

Number of cups = Volume of cooler / Volume of one cup

Number of cups = 350 cubic inches / [(1/3)π cubic inches]

Number of cups ≈ 333 whole cups

Therefore, approximately whole cups can be filled to full capacity before the water cooler is empty.

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1. Option B. A correlation exists between two variables when higher values of one variable consistently go with higher or lower values of another variable

2. Option C. Amount of smoking and lung cancer, height and weight of people, price of a good and demand of the good

Examples of pairs of variables that are correlated:

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