Jackie made a poster for the school advertising
the Science Olympiad. She included sample
statistics on the speed of the mousetrap cars
from the previous years. A. If one car raced 8 meters in 1. 5 seconds,
what was its speed?
b. How does this compare to the record time of
10 meters in 2. 32 seconds?

There are 3 adults in the family by using the method of substitution and elimination.

Substitution is a method used in mathematics to replace one or more variables in an equation or expression with a value or expression that is equivalent to the variable(s). This is done in order to simplify an equation or expression or to solve for a variable.

Elimination is a method used in mathematics to solve a system of equations by eliminating one variable. This method involves manipulating the equations in such a way that one of the variables is eliminated, leaving a simpler equation with only one variable that can be solved easily.

In the given question,

Here's how we can solve for x, the number of adults:

Multiply the first equation by 2 to get rid of the coefficient of x in the second equation:

12x + 10y = 56

10x + 14y = 58

Subtract the first equation from the second equation to eliminate y:

10x + 14y - (12x + 10y) = 58 - 56

-2x + 4y = 2

Divide both sides by -2 to isolate x:

x - 2y = -1

x = 2y - 1

Substitute x = 2y - 1 into one of the original equations (let's use the first one) and solve for y:

6x + 5y = 28

6(2y - 1) + 5y = 28

12y - 6 + 5y = 28

17y = 34

y = 2

Substitute y = 2 into the equation x = 2y - 1 to solve for x:

x = 2(2) - 1

x = 3

Therefore, there are 3 adults in the family.

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Answer:

Sure, here are the numbers arranged from greatest to least

Step-by-step explanation:

Order from greatest to least

1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%

Answer:

From the greatest to least

Step-by-step explanation:

1.3, 4.5%, 1/3, -4/5, -0.04, -21.5%

You can identify which number is greater than other by using a number line.

What is a number line?

A number line is what a math student can use to find the answer to addition and subtraction questions. A straight line, theoretically extending to infinity in both positive and negative directions from zero, that shows the relative order of the real numbers.

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Answer:

x > 8

Step-by-step explanation:

-6x + 18 < 2 - 4x

-2x + 18 < 2

-2x < -16

x > 8

Answer:9%

Step-by-step explanation:

Sorry for taking so long i didn't understand it at first

Yes, we can say the shape of the sampling distribution for the sample mean if we know the population distribution.

However, if we do not know the population distribution, we cannot determine the exact shape of the sampling distribution for the sample mean. In this case, we can make use of the Central Limit Theorem (CLT) to make some assumptions about the shape of the sampling distribution. According to CLT, as the sample size increases, the sampling distribution of the sample mean becomes approximately normal, regardless of the shape of the population distribution, provided that the sample size is sufficiently large. Therefore, if the sample size is 19 and the population distribution is unknown, we can assume that the sampling distribution of the sample mean is approximately normal if the sample data is not heavily skewed or contains extreme outliers.

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The best type of inspection to use depends on the nature of the purchase. Each type of inspection has its own advantages and disadvantages, and should be chosen based on the requirements of the product and the level of risk associated with the inspection.

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The bottom of the ladder is moving at a rate of 4/3 ft per second.

To solve the problem, we can use the Pythagorean Theorem:[tex]$x^2 + y^2 = 64$[/tex], where x is the distance from the wall to the bottom of the ladder and y is the length of the ladder. We differentiate this equation with respect to time t and use the chain rule to get [tex]$\frac{d}{dt} (x^2 + y^2) = \frac{d}{dt} 64$[/tex]

Simplifying, we get

[tex]$2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0$[/tex]

When the bottom of the ladder is 4 feet from the wall, we have x = 4 and y = 8, so we can substitute these values into our equation and solve for [tex]$\frac{dx}{dt}$[/tex]:

[tex]$2(4)\frac{dx}{dt} + 2(8)(-2) = 0$[/tex]

[tex]$\frac{dx}{dt} = \frac{16}{8} = \frac{4}{3}$[/tex]

Therefore, the bottom of the ladder is moving at a rate of [tex]$\frac{4}{3}$[/tex] ft/s.

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Answer:

6 and 10

Step-by-step explanation:

first find what 1 min is in meters

1/3 is 8 so 8x3 = 1m which is 24

now divide based on the next two numbers

1/4 of 24 = 6

6x 1 = 6

now the next

24/12 = 2

2x5 = 10

these two results, 6 and 10, are the answers to the missing meter values

The option that would result in the smallest margin of error in estimating the mean salt content, u, is 95% confidence, n = 50. The correct answer is Option D.

The margin of error is the amount by which a statistic is expected to differ from the true value of the population parameter. The interval estimate is calculated with the help of a margin of error. The margin of error and the interval estimate are inversely related to each other. If we want a small margin of error, we must increase the sample size.

The confidence level is the likelihood that a population parameter will fall within a specified range of values. The confidence level is determined by the sample size and margin of error. The sample size and margin of error are directly related to each other. When the sample size is smaller, the margin of error is larger. When the sample size is larger, the margin of error is smaller.

The margin of error is the highest at a confidence level of 50%. In general, as the confidence level increases, the margin of error decreases, and vice versa. As the sample size increases, the margin of error decreases. It follows that a 95% confidence level, n = 50 would yield the smallest margin of error in estimating the mean salt content, u. Hence, option D) 95% confidence, n = 50 would result in the smallest margin of error in estimating the mean salt content, u.

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The x-intercept is (4.5, 0) and  y-intercept is (0, -1) for the given function.

What are intercepts ?

Intercepts are the points at which a curve intersects with the x-axis and y-axis on a coordinate plane. The x-intercept is the point where the curve intersects with the x-axis, and its y-coordinate is zero. The y-intercept is the point where the curve intersects with the y-axis, and its x-coordinate is zero. The intercepts provide useful information about the behavior and properties of a curve, such as its roots and symmetry.

According to the question:

To find the x-intercept, we need to set y = 0 and solve for x:

[tex]0 = log(2x + 1) - 11 = log(2x + 1)10 = 2x + 19 = 2xx = 4.5[/tex]

Therefore, the x-intercept is (4.5, 0).

To find the y-intercept, we need to set x = 0 and evaluate the function:

[tex]f(0) = log(2(0) + 1) - 1[/tex]

= 0 - 1[tex]= log(1) - 1[/tex]

= -1

Therefore, the y-intercept is (0, -1).

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Answer:

[tex]11xy - 9x + 2y[/tex]

Step-by-step explanation:

[tex]6xy - 9x + 5xy + 2y[/tex]

Add the xy terms together:

[tex]11xy - 9x + 2y[/tex]

Answer:

Step-by-step explanation:

There are 5²⁵ possible ways to select 25 cans of soda from 5 types, while there are [5¹⁸] (25 choose 7) possible ways to select 25 cans with at least 7 Dr. Peppers, and only [3²²] (25 choose 3) possible ways to select 25 cans with only 3 Dr. Peppers available.

(a) Since there are five types of soda and we are selecting 25 cans, we can choose any type of soda for each can. Therefore, the number of ways to select 25 cans of soda is 5²⁵.

(b) If we must include at least seven Dr. Peppers, then we can choose the remaining 18 cans from any of the five types of soda (including Dr. Pepper). We can choose 7 Dr. Peppers in (25 choose 7) ways. Therefore, the number of ways to select 25 cans of soda with at least seven Dr. Peppers is (25 choose 7) [5¹⁸].

(c) If there are only three Dr. Peppers available, then we must choose all three Dr. Peppers and select the remaining 22 cans from the four types of soda (excluding Dr. Pepper). We can choose the remaining 22 cans in 4²² ways. Therefore, the number of ways to select 25 cans of soda with only three Dr. Peppers available is 3 [4²²].

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Complete question:

From an unlimited selection of five types of soda, one of which is Dr. Pepper, you are putting 25 cans on a table.

(a) Determine the number of ways you can select 25 cans of soda.

(b) Determine the number of ways you can select 25 cans of soda if you must include at least seven Dr. Peppers.

(c) Determine the number of ways you can select 25 cans of soda if it turns out there are only three Dr. Peppers available.

Except than x = 1, all real numbers fall within the function's domain.

Since there are no limitations on what we can substitute for x, the domain of a function, f(x), is all real numbers because any real numbers would make f(x) a defined function. As a result, when this is not the case, the domain of a function, f(x), is not all real numbers.

The rational function r(x) = 2x/(x-1) is defined as follows.

So, we set the denominator to zero and solve for x in order to determine the domain of r(x):

x - 1 = 0

x = 1

Hence, x = 1 is the only value of x that causes the denominator to equal 0. R(x) therefore has a domain of all real numbers other than x = 1.

We can express the domain as follows in interval notation:

(-∞, 1) U (1, ∞)

Except than x = 1, all real numbers fall within the function's domain.

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Question:

Which of the following correctly describes the domain of the function shown below?

r(x) = 2x x-1

A. {x:x0}

B. {x: x = 1}

c. x all .real .numbers}

D. xx1}

Answer:

Step-by-step explanation:

First, we need to determine the cost of making one necklace.

The total cost of supplies is $46 + $30 = $76.

If she makes one necklace, that cost is divided by one, so the cost of making one necklace is $76.

To find the selling price, we need to add a markup of 75%.

Markup = 75% x Cost = 0.75 x $76 = $57

The selling price will be the cost plus the markup:

Selling price = Cost + Markup = $76 + $57 = $133.

Therefore, Layla should charge $133 for each necklace.

The answer is d) 133.04, although it should be rounded to the nearest cent, so the final answer would be $133.

The correct answer is (A) r² - 2rs +s² which is a square of a Binomial.

What exactly are binomials?

In algebra, a binomial is a polynomial which consists of two terms. The terms may be separated by a plus or minus sign. The general form of a binomial is:

ax + b

where "a" and "b" are constants and "x" is the variable. A binomial can be added, subtracted, multiplied, and divided using algebraic operations. Binomials are commonly used in algebra to represent and solve problems involving two quantities or variables.

Now,

The correct answer is (A) r² - 2rs +s².

This is a perfect square trinomial, which can be written as (r - s)².

Option (B) c² + d² is not a binomial, it is the sum of two squares.

Option (C) 16x² - 25y² is a difference of two squares, which can be written as (4x + 5y)(4x - 5y).

Option (D) d² - de + e² is also a perfect square trinomial, but it cannot be written as the square of a binomial.

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The probability of drawing a diamond from a deck of cards is 1/4. So, the odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.

A deck of cards has 52 cards in it, and there are 13 cards of diamonds in it. So, the probability of drawing a diamond is 13/52. Simplifying 13/52, we get 1/4. The odds of an event happening are the ratio of the probability of an event happening to the probability of an event not happening. It's expressed in the form of x:y.

The probability of an event happening is the probability of success. The probability of an event not happening is the probability of failure. In the current scenario, the probability of drawing a diamond is 1/4. So, the probability of not drawing a diamond is 3/4. Therefore, the odds in favor of drawing a diamond are:

=1/3

The odds in favor of drawing a diamond from an ordinary deck of cards are 1/3.

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The coordinates of point C are (4, 2), which is located in quadrant 1.

In a 30-60-90 degree triangle, the side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is √3/2 times the length of the hypotenuse. Since the side opposite the 30-degree angle is the shortest side, it must be the distance between points A and B, which is 8 units.

Let's call point C (x, y). Since angle C is 90 degrees, side AC is perpendicular to side AB, which means it is a vertical line that passes through point A. Similarly, side BC is perpendicular to side AB, which means it is a horizontal line that passes through point B.

Therefore, point C must lie on both the vertical line passing through A and the horizontal line passing through B. The equation of the vertical line passing through A is x = -4, and the equation of the horizontal line passing through B is y = -2. So we have the system of equations

x = -4

y = -2

Solving this system gives us the coordinates of point C: (-4, -2). However, this point is not in quadrant 1, as we desired.

To find a point C in quadrant 1, we need to flip the signs of the x and y coordinates of point C. So the coordinates of point C are (4, 2).

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Therefore, the correct answer is option D: "The wire is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell. "Option E, "the wire does not carry any current," is not correct because the wire is in a region with a magnetic field, and therefore will have an induced current.

we are asked to determine the position and direction of the wire that is parallel to the cylinder axis in the hollow region. The long straight cylindrical shell has an inner radius R and an outer radius Ro, and carries a current i that is uniformly distributed over its cross section. The wire is located in the hollow region, which is defined as r > R and r < Ro.

Based on this information, we can determine the position and direction of the wire.To begin, we know that the wire must be on the cylinder axis since it is parallel to the axis. This eliminates options A, B, and C. Additionally, we know that the current in the wire must be in the opposite direction to the current in the shell. This is because the magnetic field created by the current in the shell will induce a current in the wire that is opposite in direction in order to create a repulsive force.

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Answer: No

Step-by-step explanation:

Because the length of the box is shorter than the length of the club

20in<26in

The width of the box is also shorter than the width of the club

13in<16in

The height of the box is also shorter than the height of the club

11in<16in

But what about putting it at an angle?

So we know  [tex]a^{2} +b^{2} =c^{2}[/tex]

so let's try [tex]20^{2} +13^{2} =x^{2}[/tex]

                               [tex]x^{2}[/tex]=569

                               [tex]x=\sqrt{159}[/tex]

x is near 23.85 in, but 23.85<26. So no.

The most specific conclusion that can be drawn from the given series is that it is convergent.

The Ratio Test is a common way of determining the convergence or divergence of an infinite series. It states that if the ratio of successive terms of a series converges to a limit less than one in absolute value, then the series is convergent.

In the case of the given series, it meets the conditions to use the ratio test, which means that the most specific conclusion that can be drawn is that the series is convergent. To explain this further, we need to examine what is meant by the condition that the series meets the ratio test.

First, we need to understand the definition of an infinite series. An infinite series is an expression of the form ∑an, where an is a sequence of numbers that has no upper bound. The limit of the sequence, as n tends to infinity, is referred to as the sum of the series. The ratio test states that the ratio of successive terms of a series converges to a limit less than one in absolute value.

In other words, if the ratio of successive terms of a series approaches zero as n tends to infinity, then the series is said to be convergent. This means that the most specific conclusion that can be drawn from the given series is that it is convergent. This is because the ratio of successive terms of the series converges to a limit less than one in absolute value, as required by the ratio test.

In conclusion, the most specific conclusion that can be drawn from the given series is that it is convergent. This is due to the fact that the ratio of successive terms of the series converges to a limit less than one in absolute value, which is the condition required by the ratio test for a series to be convergent.

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Answer:  y = 2x + 8

Step-by-step explanation:

3y - 6x = 24

      3y = 6x + 24

        y = (6x + 24) / 3

        y = 2x + 8

A candidate's final multiple score main answer can have a maximum of three cumulative Pass Not Advanced (PNA) points applied to it.

PNA points are a form of assessment for a candidate's answers to multiple-choice questions.

They are awarded when the candidate selects an answer that is not necessarily wrong, but does not go into sufficient depth or demonstrate the required level of understanding.

Each PNA point is worth a fraction of a mark, with a total of three PNA points making up one mark of the candidate's final multiple score main answer.

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The expression given as 11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq when simplified is 3 +13pq - 12p²q²

Given that

11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq

The given expression 11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq contains several terms with different variables and exponents.

To simplify the expression, we need to combine the like terms.

So, we have

11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq = 11 - 9pq - 8 - 12p²q² + 22pq

Similarly, we can combine the other terms

So, we have

11 + 8p²q² - 9pq - 8 - 20p²q² + 22pq = 3 +13pq - 12p²q²

So, the solution is 3 +13pq - 12p²q²

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Answer:

What is the probability of rolling an odd product? 1/4

What is the probability of rolling a product that is greater than or equal to 20? 2/9

What is the probability of rolling a product that is less than 10? 17/36

What is the probability of rolling a product that is a multiple of 10? 1/6

Answer: It should be -1,7

Step-by-step explanation: x=1-2=-1

y=8-1=7

Answer:

(-1, 7)

Step-by-step explanation:

A left translation is a negative number affecting the x-coordinate.

1 - 2 = -1

A down translation is a negative number affecting the y-coordinate.

8 - 1 = 7

(1, 8) --------> (-1, 7)

Answer:76904685 ways

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Answer:

(x^2−2xy+y^2)−z^2

⇒[x(x−y)−y(x−y)]−z^2

⇒(x−y)(x−y)−z^2

⇒(x−y)^2−z^2

⇒[(x−y)+z][(x−y)−z]

⇒(x−y+z)(x−y−z)

Ronaldo's family drove a total of 6.90 kilometres to get from their house to the store.

To determine the total distance Ronaldo's family drove, we need to add the distance from their house to the gas station and the distance from the gas station to the store. We can write this as:

[tex]4 6/10 km + 2 30/100 km[/tex]

To add these two distances, we need to find a common denominator for the fractions. The smallest common denominator for 10 and 100 is 100, so we can convert the first distance to an equivalent fraction with a denominator of 100:

[tex]4 6/10 km = 4 60/100 km = 4.60 km[/tex]

Then we can add the two distances:

[tex]4.60 km + 2.30 km = 6.90 km[/tex]

Therefore, Ronaldo's family drove a total of 6.90 kilometres to get from their house to the store.

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