Ex. 1: Last year, the price of a lawnmower was $358.99. The same model sells
for $329.99 this year. What is the percent change in the price of the
over the 2 years? Round your answer to the nearest tenth.
lawnmower

The table that represents the function y =1/3 x + 4 is the second table. This can be seen by comparing the input and output values of the given tables.

A function defines the relationship between two variables, wherein one variable depends on the other. In other words, a function is a rule or mapping from one set of values, known as the domain, to another set of values, known as the range.

The table that represents the function y =1/3 x + 4 is the second table. This can be seen by comparing the input and output values of the given tables.

The second table's input values are (6, 9, 12) and the output values are (6, 9, 12). This is equal to the equation y = 1/3 x + 4, where 1/3 x + 4 = x.

The other tables do not represent the function y = 1/3 x + 4. For example, the first table has input values of (0, -3, -6) and output values of (4, 3, 2), which do not match the equation y = 1/3 x + 4.

The third table has input values of (0, 3, 6) and output values of (4, 6, 8), which also do not match the equation y = 1/3 x + 4.

Finally, the fourth table has input values of (3, 6, 9) and output values of (5, 7, 9). This does not match the equation y = 1/3 x + 4 either.

Therefore, the table that represents the function y =1/3 x + 4 is the second table.

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The wallpaper cost $40 to John.

To find the amount of wallpaper John purchased, we have to solve for x in the cost function equation.

First, let's write down the cost function c(x) using the given information.Cost function equationc(x) = 12x + 20.

Here, x is the amount of wallpaper needed in square meters, and c(x) is the total cost John has to pay, including the cost of wallpaper and delivery.

Now, let's use the given total cost of $500 and solve for x.c(x) = 12x + 20Since the total cost John paid is $500, we can write the following equation:12x + 20 = 500

To solve for x, we can isolate x on one side by subtracting 20 from both sides.12x = 480x = 40Therefore, John purchased 40 square meters of wallpaper.

Answer: 40

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[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{k=0}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 0 )}{3} \right)\right][/tex]

[tex]\sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o }{3} \right) +i \sin\left( \cfrac{ 219^o }{3} \right)\right]\implies \boxed{4[\cos(73^o)+i\sin(73^o)]} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=1}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 1 )}{3} \right)\right][/tex]

[tex]\sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 579^o }{3} \right) +i \sin\left( \cfrac{ 579^o }{3} \right)\right]\implies \boxed{4[\cos(193^o)+i\sin(193^o)]} \\\\[-0.35em] ~\dotfill\\\\ \boxed{k=2}\hspace{5em} \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 219^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 219^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 3 ]{64} \left[ \cos\left( \cfrac{ 939^o }{3} \right) +i \sin\left( \cfrac{ 939^o }{3} \right)\right]\implies \boxed{4[\cos(313^o)+i\sin(313^o)]}[/tex]

If Lucinda used a random selection method, made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

what are perpendicular lines?

Perpendicular lines are two lines that intersect at a 90-degree angle, forming four right angles at the point of intersection. In other words, if you were to draw a perpendicular line from one of the lines to the other at their point of intersection, it would form a right angle with each of the original lines.

Without having access to more information about how Lucinda selected the sample of students, it's difficult to determine whether or not the sample is truly random.

However, there are a few things that we can consider when trying to determine whether or not the sample is random. For example:

Did Lucinda use a random selection method to choose the students? If she simply surveyed her friends or classmates, for example, the sample would not be random.

Did Lucinda make any effort to ensure that the sample is representative of the larger population of students? For example, did she make sure to include students from a variety of grades, genders, and ethnic backgrounds.

Therefore, if Lucinda used a random selection method, and made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.

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Answer:

a) 22/50

b) 24/50

c) 8/50

d) 18/50

Step-by-step explanation:

Total students= 18 + 8  + 14 + 10 = 50

students who play instruments = 14 + 8 = 22

--

students who play a sport = 18 + 8 = 26

students who  dont play a sport = 50 - 26 = 24

--

c) students who play both instrument and sport = 8

--

d) students who play sports only = 18

Students who play instruments from Venn diagram is 22, students who play both instrument and sport is 8 and students who play sports only is 18.

A set is a collection of well defined objects.

A group of students were asked if they play a sport or play an instrument

Total number of students= 18 + 8  + 14 + 10 = 50

students who play instruments from venn diagram

= 14 + 8

= 22

students who play a sport = 18 + 8

= 26

students who dont play a sport = 50 - 26 = 24

c) students who play both instrument and sport = 8

d) students who play sports only = 18

Hence, students who play instruments from venn diagram is 22, students who play both instrument and sport is 8 and students who play sports only is 18.

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the coordinates of P on the given diagram is (0.6, -0.8).

the Pythagoras theorem is defined as, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides.

The formula for the Pythagoras theorem is written as c² = a² + b², where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, the Pythagoras equation may be used to any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.

Using the Pythagoras trigonometric identity to determine sine based on cos(Θ) = 0.6

Sin²Θ+Cos²Θ=1

SIn²Θ=1-Cos²(0.6)

Sin²Θ=1-.36

SinΘ=-0.8

Since , CosΘ=0.6 and SinΘ=-0.8 the location of point P is (0.6, -0.8)

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The vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

To determine if the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly independent, we need to find the scalars a, b, and c that satisfy the equation:

a * [-5 4 5] + b * [2 -1 5] + c * [-17 16 45] = [0 0 0]

If the only solution is a = b = c = 0, the vectors are linearly independent. If there are other solutions where a, b, and c are not all zero, the vectors are linearly dependent.

Let's form a matrix with these vectors as columns:

|-5  2 -17|
| 4 -1  16|
| 5  5  45|

Now, we can row reduce this matrix to its reduced row echelon form (RREF):

| 1 -2  5|
| 0  1 -3|
| 0  0  0|

From the RREF, we can write the system of linear equations:

x - 2y + 5z = 0
y - 3z = 0

Solving this system, we get:

y = 3z
x = 2y - 5z = 6z - 5z = z

Since z can be any scalar, we have infinitely many solutions where not all of a, b, and c are zero. For example, when z = 1, we get x = 1 and y = 3. So, the scalars (1, 3, 1) make the equation true.

Thus, the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

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Answer:

Step-by-step explanation:

 square pyramid. Calculate the unknown defining height, slant height, surface area, side length and volume of a square pyrami

the missing dimension of the triangle is the base, which has a length of 21 feet. To find the missing dimension of the triangle, we will use the formula for the area of a triangle, which is:

Area = 1/2 x base x height

We know that the area of the triangle is 14 ft squared and the height is 6 ft. We can substitute these values into the formula and solve for the base:

14 = 1/2 x base x 6

Multiplying both sides by 2/6 (or simplifying to 1/3) gives:

14 x 3/2 = base

21 = base

Therefore, the missing dimension of the triangle is the base, which has a length of 21 feet.

This means that the triangle has a height of 6 feet and a base of 21 feet, and its area is 14 square feet. The height of a triangle is the perpendicular distance from the base to the opposite vertex, and in this case, it is given as 6 feet. The base of a triangle is the side opposite the height, and we have found that it has a length of 21 feet.

In summary, we can find the missing dimension of a triangle by using the formula for the area of a triangle and the given dimensions. In this case, we found that the missing dimension is the base, which has a length of 21 feet, and we know that the height is 6 feet.

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Answer:

Let's say the number of visits to the pool is represented by the variable 'x'.

If a person chooses to pay per visit, the cost will be 4x dollars.

If a person chooses to buy a membership, the cost will be a one-time payment of $100.

We want to find out when the cost of buying a membership becomes less expensive than paying per visit. In other words, we want to solve the inequality:

4x > 100

To solve for x, we need to isolate the variable. We can do this by dividing both sides by 4:

x > 25

So, if a person plans to visit the pool more than 25 times, it's more cost-effective to buy a membership instead of paying per visit.

Step-by-step explanation:

Insects can show three types of development. One of them, holometaboly (complete development), consists of the stages of egg, larva, pupa and sexually mature adult, which occupy different habitats. Insects with holometaboly belong to the most numerous orders in terms of known species. This type of development is related to a greater number of species due to the a) protection in the pupa stage, favoring the survival of fertile adults. b) production of many eggs, larvae and pupae, increasing the number of adults. c) exploration of different niches, avoiding competition between life stages. d) food intake at all stages of life, ensuring the emergence of adults. e) use of the same food in all stages, optimizing the body's nutrition.

The monthly percentage rate is 1.45%, and the APR is 17.4%.

To calculate the monthly percentage rate, we can divide the finance charge by the average daily balance, then multiply by 100 to convert to a percentage

Monthly percentage rate = (finance charge / average daily balance) x 100

Monthly percentage rate = ($8.12 / $560) x 100

Monthly percentage rate = 0.0145 x 100

Monthly percentage rate = 1.45%

To calculate the APR (annual percentage rate), we need to multiply the monthly percentage rate by the number of months in a year:

APR = Monthly percentage rate x 12

APR = 1.45% x 12

APR = 17.4%

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Answer: 200

Step-by-step explanation: x = 90 ÷ 0.45

x = 200

Based on the information, we can infer that the whole number equivalent to this fraction is 285.

To clear the fraction and obtain an integer we must perform all the mathematical operations that are in the fraction, in this case it is a division and seven multiplications. Here we show you the result:

As evidenced in the procedure, the multiplications were cleared and later the fraction was divided. In this case the result would be the integer 285.

Note: This question is incomplete. Here is the complete information:

How to express this fraction in whole numbers?

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The probability that a randomly chosen person is actually lying given that the polygraph test concluded that they were lying is 0.05.

The probability that a random person taking a polygraph test is actually lying can be calculated using Bayes' Theorem. In this case, the population consists of 5% liars, so the probability of a randomly chosen person being a liar is 0.05. The reliability of the polygraph test is said to be 90%, meaning that the probability of a person telling the truth passing the test is 0.90, and the probability of a person telling a lie failing the test is also 0.90. Therefore, using Bayes' Theorem, the probability that a randomly chosen person is actually lying given that the polygraph test concluded that they were lying is:

P(Lying | Polygraph) = P(Polygraph | Lying) * P(Lying) / P(Polygraph)

= (0.90 * 0.05) / 0.90

= 0.05

Therefore, the probability that a randomly chosen person is actually lying given that the polygraph test concluded that they were lying is 0.05.

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Answer:

12 feet by 10 feet

Step-by-step explanation:

Let length = x + 2 and breadth = x

[tex]2(x+2+x)=44[/tex]

[tex]2(2x+2)=44[/tex]

[tex]2x+2= 44\div2[/tex]

[tex]2x=22-2[/tex]

[tex]2x=20[/tex]

[tex]x=20\div2= 10 \ \text{feet}[/tex]

Thus, breadth = 10 feet

length = 10 + 2 = 12 feet

After answering the prοvided questiοn, we can cοnclude that PS = circle (QR(NQ - NR))/NR, which is nοt οne οf the given οptiοns.

A circle seems tο be a twο-dimensiοnal cοmpοnent defined as such cοllectiοn οf the all pοints in a jet that becοme equidistant frοm the hub. A circle is cοmmοnly pοrtrayed with the capital "O" fοr centre and the lοwer sectiοn "r" fοr the radius, which is the distance frοm the οrigin tο any pοint οn the circle.

Girth (the distance frοm arοund circle) is given by the fοrmula 2r, where (pi) is a prοpοrtiοnality cοnstant rοughly equal tο 3.14159. The fοrmula r² calculates the circle's circumference, which refers tο the amοunt οf rοοm inside οf the circle.

Nοne οf the given οptiοns represent PS directly. Hοwever, we can use the intersecting secant theοrem tο find PS.

(NQ)(NQ+QR) = (NR)(NR+PR)

We can sοlve fοr PR tο get:

PR = (NR)(NR+PR)/(NQ+QR)

PR(NQ+QR) = (NR)(NR+PR)

PRNQ + PRQR = NR² + PRNR

PRNQ = NR² + PRNR - PRQR

PRNQ = NR(NR + PR - QR)

PR = NR(NR + PR - QR)/NQ

PR(NQ) = NR(NR + PR - QR)

PRNQ = NR(NR + PR - QR)

PRNQ - NR(PR - NR - QR) = 0

PR(NQ - NR) = NR(NR + QR)

PR = (NR(NR + QR))/(NQ - NR)

PS(PR + NR) = QR(NR + QR)

PS = (QR(NR + QR))/(PR + NR)

PS = (QR(NR + QR))/((NR(NR + QR))/(NQ - NR) + NR)

PS = (QR(NQ - NR))/NR

Therefοre, the cοrrect expressiοn representing PS is:

PS = (QR(NQ - NR))/NR, which is nοt οne οf the given οptiοns.

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Answer:

Let's denote the first term of the sequence as a, and the common difference between consecutive terms as d.

Then, we know that the fifth term is 5, so:

a + 4d = 5

Similarly, we know that the sixth term is 2.5, so:

a + 5d = 2.5

We can solve this system of equations by subtracting the first equation from the second:

(a + 5d) - (a + 4d) = 2.5 - 5

d = -2.5

Now, we can substitute this value of d into either equation to find the value of a:

a + 4d = 5

a + 4(-2.5) = 5

a - 10 = 5

a = 15

Therefore, the first term of the sequence is 15, and the common difference is -2.5. We can use this to find the value of the second term:

a + d = 15 + (-2.5) = 12.5

Therefore, the second term of the sequence is 12.5.

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The volume of the pyramid is 600 cubic centimeters (cm³).

The formula for the volume of a pyramid is given by

V = (1/3) × base area × height

Since the base of the pyramid is a square with sides of 10 cm, the base area can be calculated as

base area = side length × side length = 10 cm × 10 cm = 100 cm²

Substituting the given values into the formula for the volume of a pyramid, we get

V = (1/3) × base area × height

Substitute the values in the equation

= (1/3) × 100 cm² × 18 cm

Multiply the numbers

= 600 cm³

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I have solved the question in general as the given question is incomplete.

The complete question is:

What is the volume of a pyramid whose base is square? The sides of the base are 10 cm each and the height of the pyramid is 18 cm.

Answer:  -2

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

x=-3 y=7

x=-2 y=5

x=-1 y=3

x=0 y=1

x=1 y=-1

x=2 y=-3

x=3 y=-5

You can see the pattern of decreasing by 2 each time so use that if you need any more values

Answer: 6y+18

Step-by-step explanation:

6 x y=6y  

6 x 3= 18

Answer:

The product of a constant factor of six and a factor with the sum of two terms.

Step-by-step explanation:

Since we have given that

6(y+3)

It has sum of two terms i.e. y and 3.

Mathematically, it is expressed as

y+3

And the product of constant factor of six and a factor with the sum of two terms.

Mathematically, it is expressed as

6(y+3)

Hence, The product of a constant factor of six and a factor with the sum of two terms.

One figure should be rotated to match the other's alignment. Expand one figure till it is the same size as another.

A figure or object in a coordinate plane can be transformed to create a new figure or object that has been relocated, flipped, or altered in some other way. Translations, rotations, and reflections are the three primary forms of transformations. Moving a figure horizontally or vertically without altering its size or shape is known as translation. Rotation entails angling a figure around a fixed point, often known as the rotational center.

given

The subsequent transformations must be used in order to demonstrate similarity between two figures:

Translation (moving the figures to the same spot) (moving the figures to the same position)

Rotation (rotation one figure to fit the other) (rotating one figure to match the other)

Dilation (resizing the figures such that they have the same shape, but maybe different sizes) (resizing the figures so that they have the same shape, but possibly different sizes)

Consequently, the following set of transformations should be used to demonstrate that the figures abc and def are similar.

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Answer:

Step-by-step explanation:

If there are five knights and they need to divide the guard duty equally for the 24 hours in a day, each knight would spend 24/5 = 4.8 hours on guard duty in one day.

However, since it's not possible to guard for a fraction of an hour, they would need to round that number to the nearest whole number. In this case, each knight would spend 5 hours per day on guard duty.

Answer:

(a) To find the mean value, we sum up all the values and divide by the number of values:

Mean = (17 + 22 + 25 + 27 + 32 + 40 + 45 + 51 + 59 + 62) / 10 = 36.0

So, the mean value is 36.0.

To find the median value, we first need to put the data set in order from smallest to largest:

17, 22, 25, 27, 32, 40, 45, 51, 59, 62

The median is the middle value of the data set, which is 36 in this case.

So, the median value is 36.0.

(b) To find the mean absolute deviation (MAD), we first need to find the deviation of each value from the mean:

|17 - 36.0| = 19.0

|22 - 36.0| = 14.0

|25 - 36.0| = 11.0

|27 - 36.0| = 9.0

|32 - 36.0| = 4.0

|40 - 36.0| = 4.0

|45 - 36.0| = 9.0

|51 - 36.0| = 15.0

|59 - 36.0| = 23.0

|62 - 36.0| = 26.0

Next, we find the mean of these deviations:

MAD = (19.0 + 14.0 + 11.0 + 9.0 + 4.0 + 4.0 + 9.0 + 15.0 + 23.0 + 26.0) / 10

MAD = 13.0

So, the mean absolute deviation for this data set is 13.0.

(c) To find the percentage of the data set that lies closer than the MAD to the mean, we count how many values are within one MAD of the mean. We have:

17, 22, 25, 27, 32, 40, 45, 51, 59, 62

The values within one MAD of the mean (36.0 +/- 13.0) are:

17, 22, 25, 27, 32, 40, 45, 51

So, 8 out of 10 values are within one MAD of the mean.

The percentage of the data set that lies closer than the MAD to the mean is:

8 / 10 * 100% = 80%

(a) To find the mean value, we sum up all the values and divide by the number of values:

Mean = (7 + 7 + 7 + 8 + 8 + 9 + 10 + 32) / 8 = 9.5

So, the mean value is 9.5.

To find the mean absolute deviation (MAD), we first need to find the deviation of each value from the mean:

|7 - 9.5| = 2.5

|7 - 9.5| = 2.5

|7 - 9.5| = 2.5

|8 - 9.5| = 1.5

|8 - 9.5| = 1.5

|9 - 9.5| = 0.5

|10 - 9.5| = 0.5

|32 - 9.5| = 22.

To determine if the difference in years at the company between employees with a high school degree and those with an MBA is significant at the 95% confidence level, we can perform a hypothesis test for p-value.

We can run a hypothesis test to see if the difference in years spent at the organization between workers with a high school diploma and those with an MBA is significant at the 95% confidence level.

We must first specify our alternative hypothesis and null hypothesis. Our null hypothesis is that there is no discernible difference in the number of years that personnel with a high school diploma and those with an MBA have worked for the organization. Our alternate theory is that the two groups have significantly different average years of employment.

The probability of witnessing the data if the null hypothesis is correct can then be determined using a t-test. The null hypothesis can be rejected if the p-value is less than 0.05, and the difference in years spent at the company between workers with a high school diploma and those with an MBA is determined to be significant at the 95% level of confidence.

We can use a two-sample t-test to compare the means of the two groups if the data is normally distributed and the variances are identical.

If the t-test yields a p-value of less than 0.05, we can reject the null hypothesis and draw the conclusion that there is a significant difference in the number of years that employees with a high school diploma and those with an MBA have worked for the organisation. In contrast, if the p-value is higher than 0.05, we are unable to rule out the null hypothesis since there is insufficient data to support the existence of a significant difference.

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Answer:

9.4 meters

Step-by-step explanation:

We can use the formula for the volume of a cone:

V = (1/3) * pi * r^2 *h

where V is the volume, r is the radius of the base, and h is the height.

We know the volume and height of the cone, so we can solve for the radius:

240 = (1/3) * pi * r^2 * 5

r^2 = 240 / (pi * 5/3)

r^2 = 45.68

r = sqrt(45.68)

r = 6.76 meters (rounded to two decimal places)

Now we can use the Pythagorean theorem to find the slant height:

x^2 = r^2 + h^2

x^2 = 6.76^2 + 5^2

x^2 = 88.5276

x = sqrt(88.5276)

x = 9.4 meters

Answer:

sub in 6 into g

6^2+23

36+23

59

Answer:

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

If we have two circles with radii of 6 cm and 12 cm, respectively, their areas are:

A1 = π(6 cm)² ≈ 113.1 cm²

A2 = π(12 cm)² ≈ 452.4 cm²

Therefore, the area of the largest circle is closest to 452.4 square centimeters, which corresponds to the circle with radius 12 cm.

The probability that a flight between New York City and Chicago is less than 64 minutes is 0.28, or 28%.

Since the time to fly between New York City and Chicago is uniformly distributed between 50 and 100 minutes, we can use the formula for the uniform probability density function (PDF) to find the probability that a flight is less than 64 minutes:

f(x) = 1 / (b - a), for a ≤ x ≤ b

where a = 50 and b = 100 are the minimum and maximum times, respectively.

To find the probability that a flight is less than 64 minutes, we need to integrate the PDF from a to 64:

P(X < 64) = [tex]\int\limits^{64}_{50}[/tex] f(x) dx = [tex]\int\limits^{64}_{50}\\[/tex](1 / 50) dx = (1 / 50) * [x]|₅₀ ⁶⁴

= (1 / 50) * (64 - 50) = 0.28

This means that approximately 28% of flights will arrive in less than 64 minutes.

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