What is the simplified form of [tex]\sqrt{400x ^{100}[/tex]

(i)  If Jane's assumption is correct, she will not get 15 tomatoes.

(ii) If Jane's supposition about the body mass of the each tomato is wrong, she could not obtain 15 tomatoes to 1 kg of tomatoes.

What types of things are assumptions?

An presumption is something you believe to be true despite the lack of evidence. People might presume, for instance, that you are a geek if you wear spectacles, even though that is untrue.

(b) (i) If Jane's assumption is correct, then the weight of 15 tomatoes would be:

15 tomatoes × 75 g/tomato = 1125 g

Since 1 kg is equal to 1000 g, Jane would need to buy at least:

1125 g / 1000 g/kg = 1.125 kg of tomatoes

Therefore, Jane would need to ask for at least 1.125 kg of tomatoes to get 15 tomatoes if her assumption about the weight of each tomato is correct.

(b) (ii) If Jane's assumption about the weight of each tomato is not correct, it is possible that she could get 15 tomatoes with 1 kg of tomatoes, depending on the actual weight of each tomato.

For example, if each tomato actually weighs 67 g, then 15 tomatoes would weigh:

15 tomatoes × 67 g/tomato = 1005 g

This is less than 1 kg, so Jane would get 15 tomatoes with 1 kg of tomatoes.

On the other hand, if each tomato actually weighs 100 g, then 15 tomatoes would weigh:

15 tomatoes × 100 g/tomato = 1500 g

This is more than 1 kg, so Jane would not get 15 tomatoes with 1 kg of tomatoes if her assumption about the weight of each tomato is incorrect.

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Trigoometric function

1) To find a value of theta that satisfies the statement, we can rearrange the equation and use the double angle formula for cosine:

cos(π/2-theta)=1/7

cos(π/2)cos(theta)+sin(π/2)sin(theta)=1/7

0cos(theta)+1sin(theta)=1/7

sin(theta)=1/7

theta=sin^-1(1/7)

theta=8.213 degrees or 0.143 radians

Therefore, a value of theta that satisfies the statement is 0.143 radians.

2) To find all values of theta that satisfy the statement, we can use the fact that sin(theta) is negative in the third and fourth quadrants:

sin(theta)=-√3/2

theta=sin^-1(-√3/2)

theta=4π/3 or 5π/3

Therefore, the values of theta that satisfy the statement are 4π/3 and 5π/3.

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4.61 x 10¹⁷ atoms of radon means that is the total number of atoms in the  element and is dependent on the number of mole.

This is referred to as the proportionality factor that relates the number of constituent particles in a sample with the amount of substance in that sample.

One mole of a substance is equal to 6.022 × 10²³ units of that substance (such as atoms, molecules, or ions). The number 6.022 × 10²³ is known as Avogadro's number or Avogadro's constant. The concept of the mole can be used to convert between mass and number of particles.

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The measurement of variability that would be best to use for the distribution is Interquartile Range, the correct option is (b).

The best measurement of variability to use depends on the distribution of the data and the purpose of the analysis.

If the distribution is skewed or contains outliers, the median and interquartile range would be better measures of variability than the mean and standard deviation.

The median is less affected by extreme values, and

The interquartile range is a robust measure of spread that is not influenced by outliers.

The mean and mean absolute deviation may be appropriate if the data are approximately symmetric and do not contain outliers.

Therefore, The best measurement of variability is (b) Interquartile range.

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The image after the rotation would be X(2, 1) Y(0,-2) and Z(-2, 1) according to the graph below.

An ordered graphical depiction of numbers or variables is how this is described.

180 degrees in each direction results in (x,y) becoming (-x,-y). The coordinates are thus inverted to either positive or negative values depending on their respective signs.

A graph is a mathematical structure made up of a set of lines linking some pairs of VERTICES that may or may not be empty and a collection of points called VERTICES. Graphs are a common method for displaying the relationships between data. Although taking up less space, a graph accomplishes the goal of presenting data that are either too many or complex to be adequately described in the text.

There are eight different types: linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal.

Hence, it means  X(−2, −1), Y(0, 2), and Z(2, −1) = X(2, 1) Y(0,-2) and Z(-2, 1).

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Complete question -

31, 87, 90 are the numbers which are considered possible outliers.

An outlier is an observation or data point that is significantly different from other observations in a dataset. In other words, it is an unusual or extreme value that is much higher or lower than most other values in the data.

A box and whisker plot is used to easily detect outliers. In this figure, the outliers are shown as black circles or dots. These are the data points that are distant from other observations.

Therefore, the numbers which are considered possible outliers are 31, 87, and 90.

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The ratio of the amount Joe saved the money against Keith is 1:2.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

Ratios contrast two figures by ordinarily dividing them.

A/B would be your formula if you were comparing one data point (A) to another data point (B).

This indicates that you are multiplying information A by information B.

For instance, your ratio will be 5/10 if A is 5 and B is 10.

So, the total money saved is $45.

Joey saved $15.

Then, Keith saved:
45 - 15 = 30

The ratio would be:

15/30

1/2

1:2

Therefore, the ratio of the amount Joe saved the money against Keith is 1:2.

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Answer:

Yes they are similar since it is a regular shape

Yes, the red outer shape is a regular hexagon. the hexagons are similar. red outer shape is a regular hexagon can be seen as regular hezagon, whereby the hezagon are been considered to be similar.

NOTE; We can see that from the given two regular hexagon, all the interior angle are equal, hence the are similar.

A regular hexagon is a polygon with six equal sides and six equal angles. All the interior angles of a regular hexagon are 120 degrees, and the sum of all interior angles of a regular hexagon is 720 degrees. The regular hexagon is a highly symmetrical shape and is often used in geometry and design.

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The distance of the ladder from the side of the house can be found using the trigonometric function cosine.

Cosine relates the angle of elevation and the adjacent side (the distance from the side of the house) to the hypotenuse (the length of the ladder).

Cos(55 degrees) = adjacent/hypotenuse

Cos(55 degrees) = adjacent/16

Adjacent = 16 * cos(55 degrees)

Adjacent = 9.2 feet

Therefore, the distance of the ladder from the side of the house is 9.2 feet to the nearest tenth.

Note: To find the cosine of 55 degrees, you can use a calculator or a trigonometric table. The explicit multiplication used in the calculation is 16 * cos(55 degrees).

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If F(-9,-4), E(-7, a) G(-2,5), and H(-6,-1) then the value of a is equal to -1, then EF is parallel to GH.

What are the parallel lines?

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.

To determine if EF is parallel to GH, we need to compare the slopes of the two lines.

The slope of line EF can be found using the coordinates of points E and F:

slope of EF = (y2 - y1)/(x2 - x1) = (a - (-4))/(-7 - (-9)) = (a + 4)/2

The slope of line GH can be found using the coordinates of points G and H:

slope of GH = (y2 - y1)/(x2 - x1) = (5 - (-1))/(-2 - (-6)) = 6/4 = 3/2

For EF to be parallel to GH, their slopes must be equal. Therefore, we can set the slope of EF equal to the slope of GH and solve for a:

(a + 4)/2 = 3/2

Multiplying both sides by 2, we get:

a + 4 = 3

Subtracting 4 from both sides, we get:

a = -1

Therefore, if a is equal to -1, then EF is parallel to GH.

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The probability that this really contains a letter just after an odd number is one-half. D's likelihood of being in the program but not at the first place is 1/4.

A possibility which deals with the possibility of random occurrences is referred to as probability. All occurrences must have a chance of occuring at least once, or 1.

The possibility or possibility of an incident occurrence is known as probability. For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of coin flipping and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

You can choose from among four letters, A, B, C, and D, and two numbers, 5 and 6.

The size of the sample space is (8, 16, 20, and 24)

If a code is chosen at random,

The probability that it has a letter that immediately follows an odd number (1/8, 1/6, 1/3, 2/5, 2/3)

= 1/2

If a code is chosen at random,

The probability that D is in the code but is not in the first position (1/8, 1/6, 1/3, 2/5, 2/3)

= 1/4

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Answer:

First Option, (A) $29,922.

Step-by-step explanation:

To calculate the future value of Heather's savings account after 5 years, we can use the formula for compound interest:

FV = P((1+i)^n - 1)/i

where:

FV = future value

P = principal (the initial amount Heather deposits)

i = interest rate per period (monthly in this case)

n = number of periods (months in this case)

P = $75 (the amount of Heather's monthly payments)

i = 3.6% / 12 = 0.003 (the monthly interest rate, calculated by dividing the annual interest rate by 12)

n = 5 x 12 = 60 (the total number of months in 5 years)

Substituting these values into the formula, we get:

FV = $75((1+0.003)^60 - 1)/0.003

FV = $75(1.21879)/0.003

FV = $29,922.02 (rounded to the nearest cent)

Therefore, Heather will have approximately $29,922.02 in her savings account after the 5 year period. The answer is option A: $29,922.

Answer: 1rubber band + 15,736.50 rubber bands

Step-by-step explanation:

Well I'm not sure how advanced you wanted this but you could say that it equals to 15,737.50x1

The vertex form of the quadratic equation represented by the table is y = (x+1)² - 3.

A quadratic equation's vertex form is y = a(x-h)2 + k, where (h, k) denotes the parabola's vertex. This form is created by solving the square of the quadratic equation y = ax2 + bx + c in standard form.

The axis of symmetry is given by the formula:

x = -b/2a.

x = (-1 + 1) / 2 = -0.5

Substitute x = -0.5 into the given table and find the corresponding value of y:

f(-0.5) = (-0.5+1)² - 3 = -2.25

The vertex of the parabola is (-0.5, -2.25).

The vertex form of a quadratic equation is:

y = a(x-h)² + k

Find the value of a by using any of the given points on the parabola.

Substitute (1, 4):

4 = a(1 + 0.5)² - 2.25

6.25 = a(1.5)²

a = 2.78

Substituting the values of a, h, and k, we get:

y = 2.78(x+0.5)² - 2.25

y = (x+1)² - 3

Hence, the vertex form of the quadratic equation represented by the table is y = (x+1)² - 3.

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So, the final answers are:

a.) f(g(-2)) = 1/3

b.) g(f(1)) = 8

Question 1: Use the following functions to evaluate each expression f(x) = 1/(x + 2) and g(x) = 3x + 7.

a.) f(g(-2)) = f(3(-2) + 7) = f(1) = 1/(1 + 2) = 1/3

b.) g(f(1)) = g(1/(1 + 2)) = g(1/3) = 3(1/3) + 7 = 1 + 7 = 8

So, the final answers are:

a.) f(g(-2)) = 1/3

b.) g(f(1)) = 8

In summary, to evaluate the expression f(g(x)) or g(f(x)), we need to first find the value of the inner function and then substitute it into the outer function. This process is called function composition. It is important to follow the order of operations and simplify the expression as much as possible.

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Subtraction of  the polynomials using the horizontal format (3x³ + x² + 2) from 7x³- x - 8 is 4x³ - x² - x - 10.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

To subtract the polynomials using the horizontal format, we will first write the two polynomials next to each other with the subtraction sign in between, then subtract the corresponding terms.

7x³- x - 8 - (3x³ + x² + 2)

Next, we will distribute the negative sign to each term inside the parentheses:

7x³ - x - 8 - 3x³- x²- 2

Now we will combine like terms:

4x³ - x² - x - 10

So, the final answer is 4x³ - x² - x - 10.

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Mr. Morris should expect around 3672 books in the collection to have minor or major damage.

What is proportion ?

Proportion is a relationship between two quantities that expresses the fraction of one quantity in terms of the other. In other words, a proportion is a statement that two ratios are equal.

To estimate the number of books in the collection that have minor or major damage, we first need to find the proportion of books in the sample that have such damage. We can then use this proportion to estimate the number of damaged books in the entire collection.

The total number of books in the sample is:

Total number of books = 737 + 67 + 31 = 835

The proportion of books in the sample that have minor or major damage is:

Proportion of damaged books = (67 + 31) / 835 = 0.108

To estimate the number of damaged books in the entire collection, we can multiply the proportion of damaged books by the total number of books in the collection:

Number of damaged books in collection = 0.108 x 34,000 = 3672

Rounding this answer to the nearest whole number, we get:

Therefore, Mr. Morris should expect around 3672 books in the collection to have minor or major damage.

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The equivalent expression to the given one is:

y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²

We start with the expression:

y⁸*y³*x⁰*x⁻²

Remember the exponent rule for products of powers with the same base, it says that we can write:

xᵃ*xᵇ = xᵃ⁺ᵇ

So we just add the two exponents.

Using exponent rules, we can rewrite the product as

y⁸*y³*x⁰*x⁻² = y³⁺⁸*x⁰⁻² = y¹¹*x⁻²

That is the equivalent expression.

Then we can write:

y⁸*y³*x⁰*x⁻² = y¹¹*x⁻²

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Answer:

16,500 miles

Step-by-step explanation:

In 12 minutes, the satellite travels 3,300 miles around Earth. To find how far the satellite travels around Earth in 1 hour, we can use unit conversion:

1 hour = 60 minutes

So, the number of 12-minute intervals in 1 hour is:

1 hour / 12 minutes = 5 intervals

Therefore, in 1 hour, the satellite travels:

3,300 miles/interval × 5 intervals = 16,500 miles

So the satellite travels around Earth at a distance of 16,500 miles in 1 hour.

The equation that links x and y is [tex]y=(\frac{1}{3} )x+3[/tex] if x is 3,6,9,12,15 & y is 4,5,6,7,8.

The definition of the an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical equation is a statement that two numbers or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account together in order to comprehend or describe the whole situation, this is known as an equation.

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Therefore, the answers are:
a. 0.0498
b. 0.8008
c. 0.7745

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

a. The probability that none is sold on a particular day can be calculated using the formula:
P(X = 0) = (e^-λ)(λ^0) / 0!
Where λ is the mean and e is the base of the natural logarithm.
Substituting the values, we get:
P(X = 0) = (e^-3)(3^0) / 0!
P(X = 0) = (0.0498)(1) / 1
P(X = 0) = 0.0498

b. The probability that at least 2 automobiles are sold on a particular day can be calculated using the formula:
P(X ≥ 2) = 1 - P(X < 2)
P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1))
P(X ≥ 2) = 1 - ((e^-3)(3^0) / 0! + (e^-3)(3^1) / 1!)
P(X ≥ 2) = 1 - (0.0498 + 0.1494)
P(X ≥ 2) = 1 - 0.1992
P(X ≥ 2) = 0.8008

c. The probability that for five consecutive days at least one automobile is sold can be calculated using the formula:
P(X ≥ 1) = 1 - P(X = 0)
P(X ≥ 1) = 1 - (e^-3)(3^0) / 0!
P(X ≥ 1) = 1 - 0.0498
P(X ≥ 1) = 0.9502
The probability that for five consecutive days at least one automobile is sold is:
P(X ≥ 1)^5 = 0.9502^5 = 0.7745

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Mrs. Nelson waited 14 minutes in line at the grocery store.

Mrs. Nelson had to wait 4 minutes in line at her bank's automated teller machine. This was 3 minutes less than one-half of the time she waited in line at the grocery store. To find out how long in minutes did she wait in line at the grocery store, we can use the following equation:
4 = (x/2) - 3

Where x is the time she waited in line at the grocery store. To solve for x, we can first add 3 to both sides of the equation:
4 + 3 = (x/2) - 3 + 3
7 = x/2

Then, we can multiply both sides of the equation by 2 to isolate x:
7 * 2 = (x/2) * 2
14 = x

Therefore, Mrs. Nelson waited 14 minutes in line at the grocery store.

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The soap from Seventh Generation brand cost less than Method brand.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

The Method brand that is $5. 49 for 36 oz

So, the unit rate of soap

= 5.49 / 36

= $ 0.1525

and, The Seventh Generation brand that is $3. 39 for 25 oz

So, the unit rate of soap

= 3.39/ 25

= $0.1356

So, the soap from Seventh Generation brand is cheaper.

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Answer:

y = 0.8x

Step-by-step explanation:

y = x-0.2x

y=x(1-0.2)

y=x(0.8)

hence y = 0.8x

With these informations you can now do a graph !

The values of x and y in the right triangle are 4√2

The attached right triangle represents the given parameter

The given triangle is a special triangle with an angle of 45 degrees

This means that the legs of the triangles are

legs = Hypotenuse/√2

From the question, the value of the hypotenuse to be 8 units

i.e. Hypotenuse = 8

So, the above equation becomes

x and y = 8/√2

Rationalize the equation

This gives

x and y = 8/√2 * √2/√2

So, we have the final values to be

x and y = 4√2

Hence, the values are 4√2

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The diameter of the circle is 28 inches.

Formula for the area of a circle is:

A = πr²

Where A represents the area, r denotes the radius, and π is a mathematical constant approximately equal to 3.14.

To find the diameter of the circle, we can use the formula:

D = 2r

in the given formula D is the diameter and r is the radius.

We know that the area of the circle is 615.44 sq. inches. So, we can use the area formula to find the radius:

615.44 = πr²

615.44 = 3.14r²

r² = 615.44/3.14

r² = 196

r = √196

r = 14

Now that we know the radius is 14 inches, we can use the diameter formula to find the diameter:

D = 2r

D = 2(14)

D = 28

Therefore, the diameter of the given circle is 28 inches.

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Answer:

a) 0.32 = 32/100 = 8/25

b) 3.003 = 3 + 3/1000 = 3000/1000 + 3/1000 = 3003/1000

c) 13.134 = 13 + 134/1000 = 13000/1000 + 134/1000 = 13134/1000

d) 5.2303 = 5 + 2303/10000

The solution of the radical expression will be y⁴√(39y).

Algebraic expressions involving radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root can be an nth root, a square root, or a cube root.

The given expression is √39y⁹. The radical expression can be simplified as below,

E = √39y⁹

E = √( 39 x y² x y² x y² x y² x y )

E = y⁴√39y

Therefore, the expression will have the simplified solution as E = y⁴√39y.

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Answer: 73,752 crates/ week

We can get to the answer by multiplying 439 by 24 by 7

Hope this helps!!

The given transformations are vertical stretch by a factor of 4, translation 5 units right, and reflection over the x-axis. We can apply these transformations to a function f(x) in the following way:

1. Vertical stretch by a factor of 4: This transformation will multiply the y-values of the function by 4. The new function will be g(x) = 4f(x).

2. Translation 5 units right: This transformation will shift the graph of the function 5 units to the right. The new function will be h(x) = g(x - 5) = 4f(x - 5).

3. Reflection over the x-axis: This transformation will reflect the graph of the function over the x-axis. The new function will be k(x) = -h(x) = -4f(x - 5).

Therefore, the final transformed function will be k(x) = -4f(x - 5).

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