consider the set of numbers $\{1, 10, 10^2, 10^3, \dots, 10^{10}\}$. the ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer?

The team that is more consistent because its range is the smallest.

The term "consistency" refers to the measure of how close or spread out the values are within a dataset. In this context, we can compare the consistency of the teams based on their ranges.

The range of a dataset is the difference between the maximum and minimum values. A smaller range indicates that the values within the dataset are closer together and less spread out, suggesting greater consistency.

Given the information provided:

Team A: Mean = 21, Range = 8

Team B: Mean = 27, Range = 6

Team C: Mean = 23, Range = 10

Comparing the ranges of the teams, we can see that Team B has the smallest range of 6, indicating that the ages of the team members are relatively closer together and less spread out compared to the other teams. Therefore, we can conclude that Team B is more consistent in terms of the age distribution of its members.

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Answer:

In January

she used 3/5 of what she used in February.

In February she used 2/3 litres of oil.

So it is 3/5 of 2/3 to find what amount she used in January.

3/5 × 2/3 = 6/15

If we simplify 6/15 we find 2/5 as our answer.

So our answer is 2/5 litres.

Answer:

x=\(\sqrt{220}\)

Step-by-step explanation:

Since this is a right angle triangle, and we have two lengths already found, we can use pythagoras to find x.

We know that  

a²+b²=c²

Where a, and b are the smaller lengths (the adjacent and opposite), and C is always the longest one (the hypotenuse).

In this case,

x=a

b=6

c=16

So to plug these into the equation, we get:

x²+6²=16²

To isolate x,

we get:

x²=16²-6²

x=\(\sqrt{16^2-6^2}\)

\(x=\sqrt[]{220}\)

_________

\( \: \)

x² = 16² - 6²

x² = 256 - 36

x² = 220

x = √220

x ≈ 14.9cm

To find the horsepower of the motor, we can use the conversion factor that equates 1 horsepower to 550 foot-pounds per second.The horsepower of the motor is approximately 13. The correct option is D) 13.

Given that the motor has a power of 7,150 foot-pounds per second, we can divide this value by 550 to convert it to horsepower:

Horsepower = Power (in foot-pounds per second) / 550

Horsepower = 7,150 / 550

Horsepower ≈ 13

Therefore, the horsepower of the motor is approximately 13. The correct option is D) 13.

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The area of the triangle by the given points i.e. P(1,1,1) , Q(-2,-7,-1) and R(-7,-1,4) is √4773/2. The area of the triangle is \(\frac{1}{2}\)  |PQ × PR|.

From the points that is  given in the question with the adjacent sides,

P(1,1,1) , Q(-2,-7,-1) and R(-7,-1,4)

Area of the triangle = \(\frac{1}{2}\)  |PQ × PR|

then, from the above points,

PQ = <-3,-8,-2>

and PR = <-8,-2,3>

now, The matrices can be written as,

PQ × PR = \(\left[\begin{array}{ccc}i&j&k\\-3&-8&-2\\-8&-2&3\end{array}\right]\)  

by calculating the above matrices we get,

= -28i + 25j - 58k

| PQ × PR | = \(\sqrt{28^{2} + 25^{2} + 58^{2}\)

=√4773

However, the Area of the triangle = √4773 / 2

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The question is-

Find the area of the triangle determined by the points P(1,1,1) , Q(-2,-7,-1) and R(-7,-1,4).

Answer:

B, A, D, C

Step-by-step explanation:

Covert all units into grams.

540 g = 540 g

180,000 mg = 180g

0.8 tonnes = 800000 g

2.3 kg = 2300 g

Arrange in ascending order.

180,000 mg, 540 g, 2.3 kg, 0.8 tonnes

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

correct on eduinity

Answer:

h = 7

Step-by-step explanation:

-3h + 6 = -15

Get rid of the 6 by subtracting it from both sides.

-3h + 6 - 6 = -15 - 6

-3h = -21

Get rid of the -3 by dividing it from both sides.

-3h/-3 = -21/-3

h = 7

\(\huge\textsf{Hey there!}\)

\(\textsf{-3h + 6 = -15}\)

\(\large\text{SUBTRACT 6 to BOTH SIDES}\)

\(\textsf{-3h + 6 - 6= -15 - 6}\\\\\\\large\text{CANCEL out: 6 - 6 because that gives you 0}\\\\\large\text{KEEP: -15 - 6 because that helps you solve for the h-value}\\\\\textsf{-15 - 6 = \bf -21}\)

\(\large\text{New equation: -3h = -21}\)

\(\large\text{DIVIDE -3 to BOTH SIDES}\\\\\mathsf{\dfrac{-3h}{-3}=\dfrac{-21}{-3}}\\\\\\\large\text{CANCEL out: }\mathsf{\dfrac{-3}{-3}}\large\text{ because that gives you 1}\\\\\\\large\text{KEEP: }\mathsf{\dfrac{-21}{-3}}\large\text{ because that solves for your h-value}\)

\(\mathsf{h = \dfrac{-21}{-3}}\\\\\\\mathsf{\dfrac{-21}{-3}=\bf 7}\\\\\\\\\mathsf{h = \bf 7}\)

\(\boxed{\boxed{\large\textsf{Answer: \huge\bf h = 7}}}\huge\checkmark\)

\(\large\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The sample size of only 5, it's difficult to make strong conclusions about the differences in pricing between the two stores.

To compare the textbook prices for two online bookstores, we can calculate the mean and standard deviation of the textbook prices for each store.

For store A:

Mean = (115 + 43 + 99 + 80 + 119) / 5 = $91.20

Standard deviation = 34.48

For store B:

Mean = (110 + 40 + 99 + 69 + 109) / 5 = $85.40

Standard deviation = 29.80

From this, we can see that the mean textbook price for store A is higher than that of store B, but store A also has a higher standard deviation, indicating greater variability in prices.

However,

With a sample size of only 5, it's difficult to make strong conclusions about the differences in pricing between the two stores.

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Answer:

the cost of a quart of oil and a gallon of gas is $2 and $2.25 respectively

Step-by-step explanation:

The computation of the cost of the quart of oil and the gallon of gas is as follows:

Let us assume the gallons of gasoline be x

And, the quart of oil be y

Now

As per the question

10x + y = $24.50 ......... (i)

8x + 2y = $22 ..............(ii)

Now divide by 2 in equation 2

4x + y = $11

y = $11 - 4x

Now put the value of y in any of the equation

10x + $11 - 4x = $24.50

6x = $24.50 - $11

6x = $13.5

x = $2.25

And, y

= $11 - 4(2.25)

= $2

Hence, the cost of a quart of oil and a gallon of gas is $2 and $2.25 respectively

The logarithm of a number raised to a power is  the product of the power. The logarithm of a quotient of two numbers is the difference of the logarithms. The logarithm of a product of two numbers is the sum.

In the given statements, logarithms are used to express relationships between exponentiation, division, and multiplication.

For the first statement, log(4) = 6 implies that 4 raised to the power of 6 is equal to 4. This demonstrates the property that the logarithm of a number raised to a power is equivalent to the power multiplied by the logarithm of the number.

In the second statement, log(2) = log(4) - 8 indicates that the logarithm of 2 is equal to the difference between the logarithms of 4 and 8. This illustrates the property that the logarithm of a quotient of two numbers is equal to the difference of their logarithms.

Lastly, in the third statement, log(4.8) = log(4) + 3 shows that the logarithm of the product 4.8 is equal to the sum of the logarithms of 4 and 3. This property signifies that the logarithm of a product of two numbers is equal to the sum of their logarithms.

These properties of logarithms are fundamental in simplifying calculations involving exponentiation, division, and multiplication.

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Answer:

A. Sample space = 6

B. 0.17

C. No

D. Yes

Step-by-step explanation:

A. The sample space of an experiment is the set of all possible outcomes of that experiment.

since there are three colours and 2 outcomes for a coin toss,

sample space = 3 * 2 = 6

B. Probability of picking a green first = 4/12 = 1/3

probability of a tail = 1/2

Probability of a green and a tail, P(A) = 1/3 * 1/2 = 0.17

C. No.

Considering the two events;

A; green card is picked first

C ; a green or red card is picked

There is an intersection point for the two events.  Therefore, they are not mutually exclusive.

D. Yes.

Considering the two events;

A; green card is picked first

B ; a blue or red card is picked

There is no intersection point for the two events. Therefore, they are mutually exclusive.

Answer: 1/2

Step-by-step explanation:

f(x) = A sin (Bx - C) + D

amplitude = |A|

period =

phase shift =

vertical shift = D

A

amplitude of 3 is given so  3 = |A| → A = ± 3, since it is stated that this is a positive function, then A = 3

B

period of 6π is given so

C

D

vertical shift of -1 is given so -1 = D

Now, substitute the values of A, B, C, and D into the formula (above):

Next, solve when x = 2π

The x.length is the number of rows, which is 4. x[2].length is the number of columns in the 3rd row, which is 5. The expression "new double[4][5]" creates a 2D array of doubles with 4 rows and 5 columns. The correct answer is (b) 4 and 5.

The expression double[][] x = new double[4][5] creates a 2D array x with 4 rows and 5 columns. Therefore, x.length gives the number of rows, which is 4. And x[2].length gives the number of columns in the 3rd row (since array indices start at 0), which is 5. Therefore, the correct option is (b) 4 and 5.

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Answer:

B = 10

I hope this helps!

Answer:

The sum of measures of angles in a triangle is 180. So if you take the three angles, add them, and set it to 180, you will get the answer. (39 + 3x + 7 + 5x - 2 = 180)

Step-by-step explanation:

Answer:

\(x = 17\)

Step-by-step explanation:

\(m < a + m < b + m < c = 180 \\ \\ 39 + (3x + 7) + (5x - 2) = 180 \\ 39 + 8x + 5 = 180 \\ 44 + 8x = 180 \\ 8x = 180 - 44 \\ 8x = 136 \\ x = \frac{136}{8} \\ \\ x = 17\)

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

The probability that Walmart's quality standard will be satisfied by average weight of a random sample of 10 bags of the Frito-Lay Fiery Mix Variety Pack is calculated using the properties of normal distribution.

The average weight of a random sample of 10 bags from the Frito-Lay Fiery Mix Variety Pack follows a normal distribution with the same mean as the individual bags (556.8g) but with a standard deviation equal to the original standard deviation divided by the square root of the sample size \(\(\frac{{1.2g}}{{\sqrt{10}}}\)\). To find the probability that the average weight falls within Walmart's demanded range (556g to 558g), we need to calculate the area under the normal curve between these two values.

To do this, we can standardize the values by subtracting the mean from each limit and dividing by the standard deviation of the sample mean. This will give us the z-scores for each limit. Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities for each z-score. The probability between these two limits represents the chance that Walmart's quality standard will be satisfied.

Please note that the specific decimal value for the probability may vary depending on the z-table or calculator used, but it will typically be a small probability since the demanded range is relatively narrow.

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Answer:

x = 0, y = -2

Step-by-step explanation:

\(\left \{ {{-10x-6y=12} \atop {4x+7y=-14}} \right. = \left \{ {{-10x=12+6y} \atop {4x+7y=-14}} \right. = \left \{ {{x=\frac{12+6y}{-10} }(1) \atop {4x+7y=-14}} \right\)

Replace x from formula (1) to formula (2), we got:

\(4*\frac{12+6x}{-10}=-14 <=> \frac{-2}{5}(12+6y)+7y=-14 <=> \frac{-24}{5} + \frac{-12}{5}y+7y=-14 <=> \frac{23}{5}y = \frac{-46}{5} <=> y = -2\\=> x= \frac{12+6*(-2)}{-10} = 0\)

Answer:

y = (19 - x) / -9

Step-by-step explanation:

Subtract x from both sides.

-9y = 19 - x

Divide both sides by -9

y = (19 - x) / -9

Answer:

Yes it's true

Step-by-step explanation:

Answer:Function to be graphed is,

h(x) = 2(x - 3)²

Function 'h' is a quadratic function.

Since, the coefficient of the leading term (term with the highest power) is positive, parabola will open upwards.

Both the ends of the parabola will be upwards (towards positive infinity).

As x approaches to negative infinity, h(x) approaches to positive infinity.

As x approaches to positive infinity, h(x) approaches to positive infinity.

Step-by-step explanation:

The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.

The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.

Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.

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The length of the new ballroom (in reality, the ballroom is designed according to scale drawing) is given by: Option D: 77 m

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

\(\rm 1\: ft : \dfrac{s}{k}\: in.\)

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

We're given that:

Since in the drawing, 11 inches was representing 44 m length of the ballroom when 1 inch: 4 metre scale was being used (as 11×4=44), so when the scale is 1 inch: 7 meters, then the new length of the ballroom in reality would be: 7 metre 11 times (since there is 11 inches as length of ballroom in the scale drawing)

This evaluates to \(7 \times 11 = 77 \: \rm metre\)

Thus, the length of the new ballroom (in reality, the ballroom is designed according to scale drawing) is given by: Option D: 77 m

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The length or the longer side of the new ballroom is 77m.

Dimensions of the model = 11 inches*4 inches

1 inch = 4m

A scale factor is a factor by which the dimension of an object is enlarged.

So, the dimensions of the ballroom will be:

Length = 11*4 = 44m

Width = 4*4 =16m

But, Mika decides to change the scale to 1 inch: 7metres

So, the length of the new ballroom = 11*7 =77m

So, the length of the new ballroom =77m

Hence, the length of the new ballroom is 77m.

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The answers to all parts sre whicn below.

1. Since there are two theaters each showing three different movies, the total number of possible movie choices is the product of the number of choices at each theater, which is 3 in this case. Therefore, the total number of possible movie choices is 3 x 3 = 9.

Answer: 9 choices

2. The tree diagram is most likely to go with the scenario of "two types of cake in two different shapes with two different types of frosting". The two boxes in the tree diagram represent the two types of cake, the five lines coming out of each box represent the two different shapes of cake and the two types of frosting, and the five boxes at the end of each line represent the different combinations of cake shapes and frosting types.

3. The correct organized list that represents the outcomes for choosing gloves (G) or mittens (M) in red (R), tan (T), or black (B) is:

GR, GT, GB, MR, MT, MB

4. HH, HT, TH, TT

5. There are 4 different cell phone models, each of which has 3 different plans. To find the total number of possible outcomes, we need to multiply the number of options for each choice. Using the multiplication principle, the total number of possible outcomes is:

4 (cell phone models) × 3 (plans for each model) = 12 outcomes

Therefore, the total number of possible outcomes is 12.

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Answer:

Hya there!!

_______________________

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x  >  4 /3

Interval Notation:

( 4 /3 , ∞ )

_______________________

“Sleep my little baby-oh

Sleep until you waken

When you wake you'll see the world

If I'm not mistaken...

Kiss a lover

Dance a measure,

Find your name

And buried treasure...

Face your life

Its pain,

Its pleasure,

Leave no path untaken.”

― Neil Gaiman, The Graveyard Book

_______________________

Think of life as a mytery because well it sort of is! You don't know what may happen may be good or bad but be a little curious and get ready for whatever comes your way!! ~Ashlynn

Answer:

x

Step-by-step explanation:

\(\sqrt{\frac{2x^2 +4x +2}{2} } -1\\\\= \sqrt{x^2 + 2x + 1} -1\\ \\=\sqrt{x^2 + x+x+1} -1\\\\=\sqrt{x(x+1)+(x+1)} -1\\\\=\sqrt{(x+1)(x+1)} -1\\\\=\sqrt{(x+1)^2} -1\\\\=x+1 - 1\\\\= x\)

Answer:

(5, -7)

Step-by-step explanation:

A reflection across the y axis changes the sign of the x coordinate but nothing else.

Answer:

(5,-7)

Step-by-step explanation:

Answer:

310

Step-by-step explanation:

Multiply the l/w/h x 2