i need help with this problem it says

one less than triple a number is the same as six times a number reduced by 7

15 points

Sample 1: Mean=10.01, Standard deviation=13.90 Sample 2: Mean

=11.43, Standard deviation

=14.10

Sample size of 1st year = n1

= 1012Mean of 1st year sample

= X1 = 10.01Standard deviation of 1st year sample

= s1

= 13.90Sample size of 2nd year

= n2

= 1012Mean of 2nd year sample

= X2

= 11.43

Standard deviation of 2nd year sample = s2

= 14.10 Let us assume a significance level of α = 0.05, which implies that the critical region consists of 2.5% in both tails (since it is a two-tailed test).

Therefore, we do not have sufficient evidence to conclude that the mean number of hours per week spent on the Internet differs between 2010 and another year.

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Answer:

Step-by-step explanation:

If we subtract 7 from both sides, we get -2 on the right.  This is not possible, since absolute values are always 0 or greater.

a) Simplest function g(n) such that f(n) ∈ Θ(g(n)) is g(n) = n2 .

Justification:

To prove this we have to prove both the upper and lower bounds of f(n).

For the upper bound , 3n 2 + 5n lg n ≤ cn2 + dn2 where c and d are constants.

So, 3 + 5 lg n/n ≤ c + d which holds for c = 4 and d = 1.

For the lower bound, 3n 2 + 5n lg n ≥ en2 .where e is a constant.

This holds true because for n ≥ 2, lg n ≤ (n/2).

Therefore, 3n 2 + 5n lg n ≥ 3n 2 + 5n (n/2) = en2 for some constant e.

b) The ratio f(2n)/f(n) approaches the constant 36 from above.

The proof is as follows:

f(2n) = 3(2n) 2 + 5(2n) lg(2n) = 12n 2 + 10n lg n

f(n) = 3n 2 + 5n lg n f(2n)/f(n)

= (12n 2 + 10n lg n)/(3n 2 + 5n lg n)

= 4(2n 2 /n 2 ) + 10(lg n/lg n) / (n 2 /n 2 ) + 5(lg n/lg n)

which simplifies to 4(2) + 10/1 + 5/1 = 36

Therefore, the constant is 36 and it approaches this constant from above.

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Answer:

Probability ≈ 0.0714

Step-by-step explanation:

Consider permutation and combination;

\(Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714\)

Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.

Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.

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The perimeter is the sum of the lengths of the sides of a closed plane figure.

The total distance from the outside of the closed figure is called the perimeter. Sum of all sides of a closed figure. The formula is: perimeter = sum of all sides

The units for the perimeter of a polygon remain the same as the units for each side. If the sides have different units, convert them to the same units and then find the perimeter.

A regular polygon has all equal sides. So if the polygon has 'n' sides, add the same length 'n' times. Perimeter of regular polygon = (length of one side) × number of sides

Example: Perimeter of regular hexagon is 6 × length of side

Total distance around polygon is. It can be found by summing all the sides of the polygon. Rectangle perimeter = 2( length + width)

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Answer:

Alrighty so number one is 5 z (x + 2y), and number two is 13x + 19y - 34z

Step-by-step explanation:

no real number.

no negative number has a real number square root.

just think : what number multiplied by itself creates a negative number ?

positive multiplied with positive is positive.

negative multiplied with negative is positive.

so, it is not possible.

only positive numbers can have real number square roots.

The principal square root of a negative number is not a real number. Therefore, the principal square root of -25 is "no real number"......

U⁠ ⁠´⁠꓃⁠ ⁠`⁠ ⁠U

Tthe height of the building is approximately 321.86 feet.

Using the given information, we can find the height of the building using trigonometry.

Let's assume that the height of the building is represented by "h". Then, we can create a right triangle with the height of the building as the opposite side, the distance from the base of the building as the adjacent side, and the angle of elevation as the angle between them.

We know that the tangent of an angle is equal to the opposite side divided by the adjacent side. Therefore, we can write the equation:

tan(9°) = h/2000

To solve for "h", we can multiply both sides of the equation by 2000:

2000 * tan(9°) = h

Using a calculator, we can evaluate the right-hand side of the equation:

2000 * tan(9°) ≈ 321.86

Therefore, the height of the building is approximately 321.86 feet.

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Answer:

44

Step-by-step explanation:

25dided by 4 is 6.25

multiply 6.25 and 7 and you'll get 43.75

round that to the nearest whole and you get 44

Answer:

Your correct answer is 3,000

Step-by-step explanation:

                 25

             x 120

             -------------

                3,000

25 * 12 = 300

Now, you add an extra zero to get your answer.

Answer:

3000

Step-by-step explanation:

25 * 120

120

25

-------

600

240

3000

25 * 12 = 300

then add zero to end

3000

Using the diagram of the circle given above, the value of the parts of the circle is as follows:

1.) Minor arc = Arc AB

2.) Major arc = Arc ACB

3.) Semicircle = AC

4.) Two central angles = 40° and 320°

5.) Arc AB = < 180°

6.) Arc ACB = > 180°

The minor arc of a circle is defined as part of the circle that is less than 180° that connects two points on the circumference of a circle.

The major arc of a circle is defined as the part of the circle that is greater than 180° that connects two points on the circle of a circle.

A semi circle is defined as exactly half of a circle which has a total of 180°.

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Answer:

Step-by-step explanation:

Combine like terms

7x^6

2x^5+5x^5= 7x^5

8x^3

-3x^2-6x^2= -9x^2

9x+2x= 11x

-5

Put back into order

7x^6+7x^5+8x^3-9x^2+11x-5

Answer:

The slope of f(x) will be positive

Step-by-step explanation:

the slope of f(x) will be positive sign the coefficient in front of the x, 2, is positive.

Answer:

Let (2a + 1) be an odd number. Let (2b + 1) be another odd number. The product 2(2ab + a + b) + 1 is a multiple of 2 plus 1, which is an odd number.

Step-by-step explanation:

To dilute 40 quarts of 5% acid solution to a 2% solution, you need to add x quarts of water. To find x, we can use the following formula: Initial amount of acid × initial concentration = final amount of acid × final concentration We know the initial amount of acid is 5% of 40 quarts, which is 2 quarts.

So the formula becomes: 2 quarts × 5% = (40 + x) / 50 quarts × 2%Now we can solve for x:2 × 40 × 5% = (40 + x) / 50 × 2%400% / 2% = 40 + xx = 400 - 40x = 360 quarts Therefore, you need to add 360 quarts of water to 40 quarts of 5% acid solution to dilute it to a 2% solution.

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We can use the normal distribution to determine the value that is larger than roughly 55% of the population. So the value that is closest to the value larger than roughly 55% of the population is 89.24.

We can use a standard normal distribution table or a calculator to find that the z-score is approximately -0.1257.

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation.

x = z * σ + μ

x = (-0.1257) * 6 + 90

x ≈ 89.24

So the value that is closest to the value larger than roughly 55% of the population is 89.24.

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Answer:

-15$

30 ft

6*c

I hope this helps

Answer:

Step-by-step explanation:

a. → Mary had a debt of $30. She earned $15 more now she has _x = $30 + $15_______.

b.→ A diver was at the depth of 10ft . Then he sank 5ft. then he sank 15ft more . now he is at depth of _x = 10 + 5 + 15 ft.

c.→ The temperature was 2*c and feel 7* . Then it rose 4*. Now the Temperature is _x = 2 + 4__________ *c.

Answer:

11a. >

11b.<

12. 88 people

60% of 220 are in favor, so that means 40% aren't

40%, or 0.4 times 220 = 88 people

Option D, the math scores of current 9th-grade students compared with their 8th-grade math scores, would be considered an example of a matched pair or paired data.

This is because the data is collected from the same group of individuals at two different points in time, allowing for a comparison of the change in math scores. The other options involve comparing different groups or populations, which would not be considered paired data. Additionally, the terms "mean" and "percentage" are not relevant in this context as the question is asking about the type of data comparison, not the specific used.

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Total amount she earn is $558

Given that;

Payment per hour on weekdays = $15.50

Payment per hour on Sunday = 2($15.50) = $31

Hour work on Sunday = 8 hour

Hour work on weekdays = 20 hour

Find:

Total amount she earn

Computation:

Total amount she earn = (20)(15.50) + (8)(31)

Total amount she earn = $310 + 248

Total amount she earn = $558

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We have to show that the set of numbers of the form a + b√2, where a and b are rational numbers, forms a field with respect to addition and multiplication.

To start, we need to show that the set of numbers is closed under addition and multiplication. This means that if we add or multiply two numbers in the set, the result must also be in the set.

For addition, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we add them, we get (a1 + a2) + (b1 + b2)√2. Since a1, a2, b1, and b2 are all rational numbers, their sum is also a rational number. So, the result of adding two numbers in the set is always another number in the set, which means that the set is closed under addition.

For multiplication, let's take two numbers in the set, say (a1 + b1√2) and (a2 + b2√2). When we multiply them, we get (a1a2 + 2b1b2) + (a1b2 + a2b1)√2. Again, since all the numbers involved are rational, the result is also a rational number. This means that the set is closed under multiplication as well.

Next, we need to show that the set satisfies the commutative, associative, and distributive laws for both addition and multiplication. This means that the order in which we add or multiply numbers in the set does not matter, and that addition and multiplication can be combined in a predictable way.

The commutative, associative, and distributive laws for addition and multiplication are well-known for rational numbers, and it can be easily verified that they hold for this set as well.

Finally, we need to show that the set has additive and multiplicative inverses. This means that for each number in the set, there exists another number in the set such that when added (or multiplied) to the original number, the result is 0 (or 1).

It can be shown that for any number of the form a + b√2, its additive inverse is -a - b√2, and its multiplicative inverse is (a / (a^2 + 2b^2)) - (b / (a^2 + 2b^2))√2, assuming that a^2 + 2b^2 is not equal to 0. Both of these are also rational numbers, since they are obtained by dividing rational numbers.

So, we have shown that the set of numbers of the form a + b√2, where a and b are rational numbers, is closed under addition and multiplication, satisfies the commutative, associative, and distributive laws, and has additive and multiplicative inverses. This means that the set of numbers forms a field with respect to addition and multiplication.

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Given:

The value of x = 2.

Solution:

F ( x ) = 2x⁴ - x³ + 5x - 9

=> 2 ( 2 )⁴ - ( 2 )³ + 5 × 2 - 9

=> 2 × 16 - 8 + 10 - 9

=> 32 - 8 + 10 - 9

=> 24 + 1

=> 25

A. 25

Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?

Let

x ------> students enrolled last year

we have that

100%+10%=110%=110/100=1.10

so

528=1.10x

solve for x

x=528/1.10

x=480

Aiden run and walk in 60 ​minute, then the distance = 9180 meters

Given that,

Aiden run at a constant peed of 3. 5 meter per second for 1/2 hour.

Then, he walk at a rate of 1. 6 meter per second for 1/2 hour.

(1) 3. 5 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

\(\frac{1}{2}\) hour = 1800 seconds

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

So,

We can write,

Distance = speed * time

3.5 * 1800 = 6300 meters    (Equation-1)

(2) 1. 6 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

\(\frac{1}{2}\) hour = 1800 seconds

So,

We can write,

Distance = speed * time

1.6 * 1800 = 2880 meters       (Equation-2)

Then,

We can add the equation - 1 and 2,

= 6300 meters + 2880 meters  

= 9180 meters

Therefore,

Aiden run and walk in 60 ​minute, then the distance = 9180 meters

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The probability of having high volume two weeks from now given that the volume is high this week is 0.64. The probability of having high volume for three consecutive weeks is 0.512 or 51.2%.

(1) The transition matrix for this Markov process can be represented as:

P = | 0.8 0.2 |

| 0.5 0.5 |

Where Pij represents the probability of transitioning from state i to state j.

(2) If the volume this week is high, we can find the probability that the volume will be high two weeks from now by multiplying the probabilities of transitioning from state 1 to state 1 twice:

P(High volume two weeks from now | High volume this week) = P11 x P11 = 0.8 x 0.8 = 0.64

So, the probability of having high volume two weeks from now given that the volume is high this week is 0.64.

(3) To find the probability that volume will be high for three consecutive weeks, we can multiply the probabilities of transitioning from state 1 to state 1 three times:

P(High volume for three consecutive weeks) = P11 x P11 x P11 = 0.8 x 0.8 x 0.8 = 0.512

Therefore, the probability of having high volume for three consecutive weeks is 0.512 or 51.2%.

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70% of the population prefers coca-cola over pepsi, the probability that both prefer coca-cola is 0.49.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

70% of the population prefers Coca-Cola over Pepsi,

that is 0.7

The probability of the Pepsi is 30% = 0.3

The probability that both prefers coca cola is 0.7 x 0.7 = 0.49.

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