13. The front wheels of a toy truck are 9 cm in circumference. The back wheels are 12 cm in circumference. If the truck travels down a long slope, in a straight line and without slipping, how far will the truck have travelled when the front wheels have made 10 more revolutions than the back wheels?

The three options of exterior angles are m∠5 + m∠6 =180°,

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

The angles that are created οutside οf a triangle are its exteriοr angles. In οther wοrds, the angle fοrmed between οne οf a triangle's sides and its adjacent extended side is the triangle's exteriοr angle.

Given that the exteriοr angles are m∠1, m∠4, and m∠6.

The interiοr angles οf the triangle are angles m∠2, m∠3, and m∠5.

The sum οf all angles οf a triangle is 180°.

Thus m∠2 + m∠3 + m∠5 = 180°

The interiοr angle and the cοrrespοnding exteriοr angle in a triangle make up a linear pair. Exteriοr Angle plus Interiοr Angle equals 180°, sο.

The exteriοr angle at angle 5 is angle 6.

Thus m∠5 + m∠6 =180°

The interiοr and exteriοr angles that make up a triangle are always added tοgether tο fοrm the exteriοr angle. The term "exteriοr angle prοperty" refers tο this feature. If twο triangles' cοrrespοnding angles tend tο be cοngruent and their side lengths are prοpοrtiοnal, any twο triangles will be similar tο οne anοther.

The οppοsite interiοr angles οf m∠6 are m∠2,  m∠3.

Thus m∠2 + m∠3 = m∠6

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The probability that exactly 11 raindrops fall on the picnic table the next time it sprinkles is 0.066, rounded to three decimal places.

We can model the number of raindrops that fall on the picnic table as a Poisson distribution with parameter a, where a is the expected number of raindrops that fall on a 1 square meter area during a rainstorm. Since 462 raindrops fell over an area of 55 square meters, the average number of raindrops per square meter is:

a = 462/55 ≈ 8.4

Therefore, the probability that exactly 11 raindrops fall on the picnic table during a rainstorm is:

P(X = 11) = (eᵃ * a¹¹) / 11!

= (e⁻⁸ ⁴ * 8.4¹¹) / 11!

≈ 0.066

Rounding to three decimal places, we get the probability that exactly 11 raindrops fall on the picnic table as 0.066.

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Answer:

Step-by-step explanation:

x = 4 or x = -2

The equation given is an instance of a linear equation in two variables, which can be solved by using the process of substitution to find the value of one of the variables.Therefore, the solution to the given equation is y = 4√(3).

Equation is a mathematical statement that states the equality of two expressions. It is usually expressed as a numerical equation with an equal sign (=) between the two expressions. Equations are used to express relationships between various quantities and can be used to solve problems in many areas of mathematics, science, and engineering. In addition, equations are often used to describe physical laws and chemical reactions.

In this case, the equation is y = 8/x, and we want to solve for y.

To do this, we need to first find the value of x. We can do this by using the side lengths of the triangle given, which are 2 and x. We can use the Pythagorean theorem to calculate the value of x. The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side. So, we can use this equation to find the value of x: 2²+ x²= (8/x)². Solving for x, we get x = 2√(3).

Now that we have the value of x, we can substitute it into the original equation and solve for y. So, y = 8/2√(3), which simplifies to y = 4√(3). Therefore, the solution to the given equation is y = 4√(3).

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Answer:

Step-by-step explanation:

If a father's age is four times the age of his daughter.. After 5 more years , his age would be 5 times his daughter's age at that time.

Let's use D to represent the daughter's current age and F to represent the father's current age.

We know that the father's age is four times the age of his daughter, so we can write an equation to represent this relationship:

F = 4D

We also know that after 5 years, the father's age would be three times his daughter's age, so we can write another equation to represent this:

F + 5 = 3(D + 5)

Now we can substitute the first equation into the second equation to get an equation with only one variable:

4D + 5 = 3(D + 5)

Simplifying the equation, we get:

4D + 5 = 3D + 15

Subtracting 3D and 5 from both sides, we get:

D = 10

Therefore, the daughter's current age is 10 years old. We can use the first equation to find out the father's current age:

F = 4D = 4(10) = 40

After 5 more years, the father's age would be:

F + 5 + 5 = 40 + 10 = 50

In summary, after 5 more years, the father's age would be 50 and his daughter's age would be 10, which is 5 times younger than the father.

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Water fills a tank at a rate of 150 liters during the first hour, 125 liters during the second, 150 liters during the third, and so on. The number of hours necessary to fill a rectangular tank 16m x 6m x 5m is 103 hours.

The volume of the rectangular tank can be found by multiplying its length, width, and height:

The volume of the tank = Length x Width x Height

Volume of tank = 16m x 6m x 5m

The volume of the tank = 480 cubic meters

We need to convert this volume to liters in order to compare it to the flow rate of water. Since 1 cubic meter is equal to 1,000 liters, we have:

Volume of tank = 480 x 1,000 = 480,000 liters

Now we can add up the flow rate of water over time until it exceeds the volume of the tank. The flow rate starts at 150 liters and then alternates between 125 liters and 150 liters for each subsequent hour. We can express this pattern as:

[tex]150 + 125 + 150 + 125 + 150 + ...[/tex]

This is an arithmetic sequence with a first term of 150, a common difference of -25 (since each subsequent term is 25 less than the previous one), and an unknown number of terms. We can use the formula for the sum of an arithmetic sequence to find the number of terms:

Sum = (n/2)(first term + last term)

where n is the number of terms.

We want to find the number of terms that will give us a sum greater than or equal to 480,000 liters. We can set up an inequality:

(n/2)(150 + (150 + (n-1)(-25))) ≥ 480,000

Simplifying and solving for n, we get:

n ≥ 102.4

Since we need a whole number of terms, we can round up to 103 terms. This means it will take 103 hours to fill the tank.

Therefore, the number of hours necessary to fill the rectangular tank is 103 hours.

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The given data in this problem allows for the creation of a system with three variables, that represent the earnings from the sales in the three days, by solving this system we can obtain these following sale prices:

The sale price for each sweater is obtained solving a system of equations.

The variables of the system of equations are given as follows:

Considering the profits for each day, along with the amounts of each sweater sold, the equations that compose the system are given as follows:

Inserting these three equations into a calculator, the solution to the system of equations is given as follows:

x = 15, y = 20, z = 45.

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By answering the presented question, we may conclude that  For slope example, if a figure's measures are in metros, the volume will be in cubic metros (m3).

The slope of a line determines how steep it is. The gradient is expressed mathematically as gradient overflow. The slope is computed by dividing the vertical difference (run) between two locations by the height difference (rise). The curve form of an expression is used to describe the straight line equation, which is written as y = mx + b. The y-intercept of the line is located where the inclination is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7. (0, 7). The y-intercept is placed where the slope of the path is m, b is b, and (0, b).  

When we calculate the volume of a 3D figure, we call our solution "units 3 (cubed)".

The term "cubed" is used since volume is calculated by multiplying three dimensions (length, breadth, and height), resulting in a unit raised to the power of three. For example, if a figure's measures are in metres, the volume will be in cubic metros (m3).

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The mass of Raymond's favorite book is 1273 grams.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

Let x be the mass of Raymond's favorite book in grams. According to the problem, we have:

2702 = x + 1429

To solve for x, we can isolate it on one side of the equation by subtracting 1429 from both sides:

x = 2702 - 1429

x = 1273

Therefore, the mass of Raymond's favorite book is 1273 grams.

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Hence, in answering the stated question, we may say that Therefore, the simplified expression is [tex]1/(4a^6).[/tex]

In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.

To simplify this expression, we can use the laws of exponents:

[tex]a^-4/4a^6 = 1/(4a^4 * a^2) = 1/(4a^6)[/tex]

Therefore, the simplified expression is [tex]1/(4a^6).[/tex]

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B. Both the mean and median will decrease, but the mean will decrease by more than the median.

Since the wheel of cheese has a much higher cost than the other 11 items, removing it will decrease the overall mean cost of the items purchased. However, the median, which is the middle value when the items are arranged in order, will also decrease but not by as much as the mean since it is not as affected by outliers like the wheel of cheese.

The mean is calculated by taking the sum of all the prices and dividing it by the number of items, so removing the most expensive item (the wheel of cheese) will decrease the sum of prices and thus decrease the mean.

The median is the middle value when all the prices are arranged in order. Since the wheel of cheese is the most expensive item, it will be the last item on the ordered list. Removing it will not change the position of any other items, so the median will simply be the middle value of the remaining 11 items. The value of the median is not affected by the price of the wheel of cheese, so the median will also decrease but only by a small amount. T

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The correct question should be:

Chucky grabbed 12 items in the grocery store that each had a different price and had a mean cost of about $7.41. One of the items was an entire wheel of cheese that cost $39.99. Chucky then decided to put the wheel of cheese back and only buy the other 11 items. How will removing the wheel of cheese affect the mean and median?

A. Both the mean and median will decrease, but the median will decrease by more than the mean.

B. Both the mean and median will decrease, but the mean will decrease by more than the median.

C. Both the mean and median will increase, but the median will increase by more than the mean.

D. Both the mean and median will increase, but the mean will increase by more than the median.

Answer:

Step-by-step explanatB Convection caused hot air to rise to the top of your house is the best explanation for why you may feel very hot when you go up to your attic on a summer day.

Convection is the transfer of heat by the movement of a fluid, such as air. On a hot summer day, the air inside your attic can become very hot, and because hot air rises, it will accumulate at the top of your house. When you go up to your attic, you will feel the heat from this accumulated hot air.

Conduction, on the other hand, is the transfer of heat through a material, such as the roof or walls of your house. While some heat may be conducted through the roof, it is unlikely to be the primary cause of the heat in your attic.

Insulation (option C) can help to keep the heat from the attic from escaping into the cooler temperatures below, but it is not the primary cause of the heat in the attic.

ion:

There are multiple ways to find the center and radius of a circle, depending on what information your provided.

Method 1: Reading the standard equation of a circle

Equation of a circle: [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]

where h is the center's x-coordinate, k is the center's y-coordinate, and r is the radius. Here's an example:

[tex](x-5)^{2} +(y+2)^{2} =25[/tex]

In this case, the center would be (5,-2) and the radius is 5

Method 2: Reading a graph

In the attached graph, there is a circle with a labeled center point. The radius can be found by finding the distance from the center to a different point on the circle.

Distance Formula:

[tex]D = \sqrt{ (x_{2}-x_{1}) ^{2} + (y_{2}-y_{1}) ^{2}}\\[/tex]

The first point we use will be the center ( 5 , -2 ), and the second point will be a point on the circle, (10,-2).

[tex]r = D = \sqrt{ ((10)-(5)) ^{2} + ((-2)-(-2) )^{2}}\\r = D = \sqrt{ (5 ^{2} + 0)^{2}}\\r = D = \sqrt{25}\\r = 5[/tex]

Next, plug in the values into the standard equation of a circle formula

[tex](x-5)^{2} +(y+2)^{2} =5^2[/tex]

Simplify

[tex](x-5)^{2} +(y+2)^{2} =25[/tex]

Answer:

[tex]x=\frac{b-a}{ab}[/tex]

Step-by-step explanation:

[tex]\frac{1}{ax} -\frac{1}{bx} =1\\\frac{1}{ax} *\frac{b}{b} -\frac{1}{bx} *\frac{a}{a} =1\\\frac{b}{abx} -\frac{a}{abx}=1\\\frac{b-a}{abx}=1\\b-a=abx\\x=\frac{b-a}{ab}[/tex]

Answer:

x = 13

Step-by-step explanation:

To find the value of x we need to isolate it! To do this we have to get rid of any other value around it...

Firstly we need to get rid of the ' -2 '. We have to add 2 to both sides!

Now we are left with 3x = 39 so we have to get rid of the 3. We have to divide 3 from both sides!

x = 13!

Hope this helps, have a lovely day! :)

The probability that the sample proportion of customers who are happy with the food quality is between 70% and 77% is 0.693

Andy is a restaurant owner who believes that 72% of his customers are happy with the food quality of his restaurant. What are the probabilities for the following questions, given a random sample of 78 customers? Probability that less than 57 customers are satisfied with the food quality:To find the probability that less than 57 customers are happy with the food quality, we'll first compute the z-score.Z = (x - µ) / σZ = (56.5 - 72.84) / 4.392 Z = -3.7 Using the table, we can find that the probability of a z-score less than -3.7 is 0.0001. Thus, the probability that less than 57 customers are happy with the food quality is 0.0001.

Probability that at least 57 customers are satisfied with the food quality:The probability that at least 57 customers are satisfied with the food quality is the complement of the probability that less than 57 customers are satisfied with the food quality. Hence, the answer is: 1 - 0.0001 = 0.9999 Probability that the sample proportion of customers who are satisfied with the food quality is between 70% and 77%:To calculate the probability that the sample proportion of customers who are happy with the food quality is between 70% and 77%, we'll need to compute the z-scores for both values.

The z-score is given by Z = (p - P) / sqrt(PQ/n), where P is the true proportion (0.72), Q is 1 - P (0.28), and n is the sample size (78).Z1 = (0.70 - 0.72) / sqrt(0.72*0.28/78) = -0.85Z2 = (0.77 - 0.72) / sqrt(0.72*0.28/78) = 1.24The probability is the difference between the two probabilities of the standard normal distribution, which is 0.8907 - 0.1977 = 0.693. Hence, the probability that the sample proportion of customers who are happy with the food quality is between 70% and 77% is 0.693.

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According to the question, if the blocks are 11" x 10" x 6" and the blocks are in a stack at the store that is 60" x 55" x 54" then there are 270 blocks in the store.

Given that dimensions of the blocks and the store :-

Block :- 11" x 10" x 6"

Store :- 60" x 55" x 54"

To find the number of blocks in a stack we need to first calculate the volume of the block as well as the store.

This, Volume of block = 11 x 10 x 6 = 660

and, Volume of the store = 60 x 55 x 54 = 178200

Therefore, the number of blocks would be = Volume of the store / Volume of block

No. of block = 178200/660

No. of block = 270

Hence Number of blocks stored in the stack at the storeroom is 270 blocks.

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Answer:

A should be 180 - 68 which is 112 degrees

Step-by-step explanation:

Answer:a=108

Step-by-step explanation:

140+(180-60)+(180-84)+(180-68)=140+120+96+112=260+208=468

sum of angles are 540, so,

540-468=180-a

72=180-a

a=108

For the plotted point P on the given number line, the number represented by point P is 5.80⁻³.

A number line is a linear visual representation of numbers and integers. This line is used to compare equally spaced numbers on an infinite line that extends horizontally or vertically on either side. A number line shows point values ​​and equal divisions on the line.

There are 10 points at equal intervals that falls between point 5.10⁻³ and point 6.10⁻³.

Counting from the very left the points are as follows:

5.10⁻³, 5.20⁻³, 5.30⁻³, 5.40⁻³, 5.50⁻³, 5.60⁻³, 5.70⁻³, 5.80⁻³, 5.90⁻³, 6.00⁻³, 6.10⁻³.

Point P falls on 5.80⁻³, therefore the value of point P is 5.80⁻³.

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The complete question is as follows:

The value for f(-5), f(-1), f(0), f(2), f(4) are 12, 0, -3, -9, -15.

What is a function?

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of outputs (called the range) with the property that each input is related to exactly one output. A function is usually denoted by a symbol such as f(x), where x is the input variable and f(x) is the output variable. The value of the output variable depends on the value of the input variable and the rule that defines the function.

Given function:

f(x) = -3x -3

Now, we will substitute values of x in f(x) as follows:

when x =-5,

f(-5) = -3 (-5) - 3

      = 15 -3 = 12.

when x =-1,

f(-5) = -3 (-1) - 3

      = 3 -3 = 0.

 when x = 0,

f(-5) = -3 (0) - 3

      = 0 -3 = -3.

when x = 2,

f(-5) = -3 (2) - 3

      = -6 -3 = -9.

when x = 4,

f(-5) = -3 (4) - 3

      = -12 -3 = -15.    

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Answer:

Its the 3rd one

Step-by-step explanation:

I had this question twice

Answer:

number 3 i did this 2 days ago

Step-by-step explanation:

From the given data, we can see that only one condition is violated, which is the sample size being less than 10% of the population size. The other conditions, such as the population distribution being approximately normal, np > 10, and n(1-p) > 10, are all satisfied. Therefore, the statement "more than one condition is violated" is incorrect.

Only one condition is violated in the given data, which is the sample size being less than 10% of the population size. The other conditions are all satisfied and do not violate any of the conditions for a representative sample.

It is important to note that in order for a sample to be representative of the population, the sample size should be at least 10% of the population size. If the sample size is less than 10% of the population size, the sample may not accurately represent the population and the results may be biased.

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The length of the remaining piece of beam as polynomial is 6y²⁺⁷⁺¹¹

An algebraic expression with two or more algebraic terms is known as a polynomial.It has exponents, operators, coefficients, coefficients, variables, and constants.  A polynomial is a mathematical expression that solely uses the operations addition, subtraction, multiplication, and non-negative integer powers of variables. It is made up of indeterminates (also known as variables) and coefficients.

The length of the wooden beam is (7y²⁺⁷⁺¹) meters long and a piece of length (y²⁻¹⁰) meters is cut off ¹.

Therefore, the length of the remaining piece of beam can be expressed as follows:

(7y²⁺⁷⁺¹)-(y²⁻¹⁰) = 6y²⁺⁷⁺¹¹

So, the length of the remaining piece of beam is 6y²⁺⁷⁺¹¹

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Answer:

sum of 5 and 7

Step-by-step explanation:

5+7

sum means an adding equetion

Answer:

The answer is 2.5

Step-by-step explanation:

° The sum of 5 and 7 is 5 + 7 = 12

° The quotient of means "the result got from dividing one variable by another", so, 30/12 = 2.5

Answer:

a. The x-values are equally spaced, and the y-values change by equal differences, so the function is linear.

Step-by-step explanation:

A linear function is categorized by a function which has a constant factor separating all coordinates. In this table, each x-value increases by 1 while each y-value increases by 2. So, it is linear.

To convert the salary data from different countries into US dollars, the industrial/organizational psychologist would need to use the exchange rates between each country's currency and the US dollar. Exchange rates are the value of one currency in terms of another currency.

For example, if the exchange rate between the US dollar and the British pound is 1.38, this means that one US dollar is worth 1.38 British pounds. So, to convert the average monthly salary of an accountant in the UK into US dollars, the psychologist would divide the salary in pounds by the exchange rate.
Once the psychologist has converted all of the salary data into US dollars, she can then compare the average monthly salaries of accountants across the five different countries and analyze the relationships between job satisfaction, job performance, and job compensation.

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Therefore, the total cost to make 100 wind chimes is 14,000$.

In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables (unknowns) and specifies a relationship between those variables. Equations are used to model real-world phenomena, solve problems, and make predictions. There are many types of equations in mathematics, including linear equations, quadratic equations, polynomial equations, exponential equations, trigonometric equations, and many more. Each type of equation has its own set of methods and techniques for solving it.

Here,

The cost of making one wind chime is 10 + 130 = 140$.

To make 100 wind chimes, the total cost would be:

100 x 140 = 14,000$.

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