How long would it take to drive 1km at a speed of 1.71km/h (with working)

Answer:

x = -1, y = -1

Step-by-step explanation:

[tex]4x + 3 = - 8x - 9[/tex]

[tex]12x + 3 = - 9[/tex]

[tex]12x = - 12[/tex]

[tex]x = - 1[/tex]

[tex]y = 4( - 1) + 3 = - 4 + 3 = - 1[/tex]

As per the terms from the two sequences given in tables as attachment hereby along with the question statement, the following statements from the provided options are true.

(i) [(a₁) > (g₂)]

(iv) Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ).

As per the question statement and the reference tables attached thereby along with the question, we are provided with terms from the two sequences in table format, and five statements based on the sequences.

We are required to determine which statements among the five, are true.

To solve this question, we will use the trial-and-error method, where we will consider individual statement and assess it's honesty.

First statement is [(a₁) > (g₂)], which is true. As we can see from the table, that, [(a₁) = 10] and [(g₂) = 4], i.e., (10 > 4), or, [(a₁) > (g₂)].

Second statement is that, "The constant difference for (aₙ) is 10" which is False. We can clearly see from the table that, (a₁ = 10), (a₂ = 15), (a₃ = 20), (a₄ = 25) and so on, and [(25 - 20) = (20 - 15) = (15 - 10) = 5], i.e.,

[(a₄ - a₃) = (a₃ - a₂) = (a₂ - a₁) = 5]. Hence, the common difference for (aₙ) is 5, and not 10.

Third statement is that, "(aₙ) can be modelled by a linear function, and (gₙ) can be modelled by an exponential function" which is true for the first part, but false for the second, making the complete statement false as whole.
From the left hand side table, we can see that, (a₂ = 15) and (a₁ = 10),

Or, [a₂ = (10 + 5)]

Or, [a₂ = (a₁ + 5)]

Similarly, (a₃ = 20),

Or, [a₃ = (15 + 5)]

Or, [a₃ = (a₂ + 5)]

That is, we can generalise (aₙ) as

[aₙ = {(aₙ₋₁) + 5}] where, (n = 2, 3, 4, 5...) and (a₁ = 10).

Hence, (aₙ) can be modelled by a linear function.

But from the right hand side table, we can see that, (g₂ = 4) and (g₁ = 2),

Or, [g₂ = (2 * 2)]

Or, [g₂ = 2g₁]

Similarly, (g₃ = 8),

Or, [g3 = (2 * 4)]

Or, [g₃ = 2g₂], it goes on for (gₙ).

Therefore, we can generalise (gₙ) as

[gₙ = 2*(gₙ₋₁)] where, (n = 2, 3, 4, 5...) and (g₁ = 2).

Here, (gₙ) can also modelled as a linear function and not as a exponential function (which goes in the form of "xⁿ").

Coming to the fourth statement, "Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ)" is true, as from both the tables,

For (n = 5), [aₙ = a₅ = (a₄ + 5) = (25 + 5) = 30],

And [gₙ = g₅ = (2 * g₄) = (2 * 16) = 32], which is greater than 30,

Or, [(g₅) > (a₅)].

Similarly, for (n = 6), (a₆ = 35) while (g₆ = 64), i.e., [(g₆) > (a₆)], and it continues for greater values of "n".

Coming to the last statement, that [a₁₀ > g₆], is false. As we can observe from the both the tables and their sequence,

For (n = 5), (aₙ = 50), for (n = 6), (aₙ = 35), for (n = 7), (aₙ = 40), for (n = 8), (aₙ = 45), for (n = 9), (aₙ = 50) and for (n = 10), (aₙ = 55),

While on the other hand, for (n = 5), (gₙ = 32) and for (n = 6), (gₙ = 64).

Since (64 > 55), therefore, [(g₆) > (a₁₀)].

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 ∠O  ≅  ∠U is third statement which is congruent .

What is congruent triangle?

ΔONP and ΔUTV are congruent .

By using ASA Theorem ,

                 NP ≅ TV

                ∠P  ≅  ∠V

                ∠O  ≅  ∠U

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Answer:

∠O  ≅  ∠U is third statement which is congruent .

Step-by-step explanation:

What is congruent triangle?

Two figures are said to be "congruent" if they can be placed perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other.

Congruent refers to having precisely the same form and size.

If all three sides of two triangles are the same, they are said to be congruent.

If we have a side, an angle between the sides, and then a second side that is congruent, we know they are congruent. In other words, side, angle, side.

ΔONP and ΔUTV are congruent .

By using ASA Theorem ,

                NP ≅ TV

               ∠P  ≅  ∠V

               ∠O  ≅  ∠U

BRAINLIST??

11 miles he run per day, Monday-Friday.

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.

Given:

Total distance travelled = 60 miles.

On Saturday= 5 miles

Sunday was off

So, from Monday to Friday he travelled

=60 - 5

= 55 miles.

and, per day he run

= 55/5

= 11 miles

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Answer:

C.

Step-by-step explanation:

The solution to a system of equations is the point where the two lines intersect. In this case, the lines intersect at Point C.

Answer:  The answer is 5 shirts

Step-by-step explanation:

8x + 6 = 50

subtract 6 from each side:

8x +6 (-6) = 50 (-6)

8x=44

divide by 8:

8x/8=44/8

x=5.5

round to single shirts:

x=5 shirts

Answer:

Step-by-step explanation: you have to divide 50 by 8 then get your answer of 6.25, but you also have to consider two things; the extra $6.00 flat fee, and you cant buy 6.25 shirts, so what we do is multiply 8 times 6 to get 48, but we have to consider the extra $6.00, so you take away 8 which gives you 5 shirts, plus the shipping fee so in all he can buy 5 shirts.

Answer:

13 sec

Step-by-step explanation:

Prius' acceleration

  60 mi/hr = 88 ft s

accel = change  in v / change in time =  88 f/s  / 10.3 s = 8.54 ft / s^2

F = ma     =    2903 * 8.54 = 24802  lb ft/s^2

Now increase the mass to 4903 by adding a 2000 lb trailer  (which, by the way is way past the towing capacity of an anemic Prius !)

    F = ma

   24802 = 4903 a    shows a = 5.06 ft/s^2

  45 mi/hr = 66 ft/s

      a = change in v / change in time

      5.06 = 66 / 5.06 = 13 sec

Mark has 35 unique combinations to choose from, so can he co go 5 weeks with this set of clothes

Number of pants in Mark's closet = 5

Number of shirts in Mark's closet = 7

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

He can choose amongst the pants in 5 ways, similarly, he can choose among the shirts in 7 ways

Total number of combinations = 5*7 = 35 unique combinations

So, if he wears one combination each day he can last 35 days or 5 weeks, without buying new clothes

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Answer: the slope=0

Step-by-step explanation:

[tex]\displaystyle\\(-6,4)\ \ \ \ \ (-15,4)\\\\\boxed {The\ slope=\frac{y_2-y_1}{x_2-y_1} }\\\\The\ slope=\frac{4-4}{-15-(-6)} \\The\ slope=\frac{0}{-15+6} \\\\The\ slope=0[/tex]

The exponents are solved below\

What are exponents?

Exponentiation is a mathematical process denoted by the symbol bn that involves two integers, the base b and the exponent or power n, and is spoken as "b (raised) to the (power of) n." Exponentiation corresponds to repeated multiplication of the base when n is a positive integer: bn is the product of multiplying n bases. Typically, the exponent is displayed as a superscript to the right of the base. In such scenario, bn is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, more succinctly, "b to nth." In other words, when a base raised to one exponent is multiplied by the same base raised to another exponent, the exponents accumulate.

The exponents are solved as follows

(10⁻²)⁹ = 10⁻¹⁸ = 1/10¹⁸

10⁻³ - 10⁻⁸ = 1/10³ - 1/10⁸ = (10⁵ - 10⁸)/10⁸ = 9.9999x10⁻⁴

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Answer: 2080

Step-by-step explanation:

62² −42²

3844−42²

3844−1764

2080

Since the scale utilized in the draw is 1 inch : 9 feet and the diving board is 2 inches, we need to multiply the 2 inches by the scale:

The actual diving board is 18ft long

Given: Pair of parallel lines and a transversal with angles x and y.

Required: To determine which type of angles are formed by x and y.

Explanation: Consider the following figure below showing a pair of parallel lines and a transversal

In the figure, line l is parallel to line m, and line n is the transversal.

Further alternate angles are the pair:

The angles lying inside the parallel lines are alternate interior, while the angles lying outside the parallel lines are the alternate exterior.

While the corresponding angles are the pair:

Finally, the consecutive interior angles are the pair of non-adjacent angles that lie on the same side of the transversal. In the figure above, the consecutive interior angles are:

Hence the given pair of angles x and y are consecutive interior angles.

Final Answer: Option D is correct.

Answer:

0.044444 = 11111/250000

Step-by-step explanation:

[tex]=\frac{44444}{1000000} =\frac{22222}{500000} =\frac{11111}{250000}[/tex]

Hope this helps

The probability of all XY in a group of four siblings is 1/16 (6.5%), and also the probability of all XX offspring is 1/16 (6.5%).

Let us first know how do chromosomes work?

Long DNA molecules called chromosomes contain all or a portion of an organism's genetic code. Males receive one X and one Y chromosome from each parent, whereas females receive two X chromosomes from each parent.

For females, the likelihood or probability of inheriting two X chromosomes is 1/2 (50%) while for men, the probaility of receiving one X chromosome and one Y chromosome is similarly 1/2.

Therefore, the probability that all XY siblings are present in a group of 4 siblings is:

[tex]1/2 * 1/2 * 1/2 * 1/2 = 1/16[/tex]

Also the probability that a family of four siblings or offspring includes all XX is

[tex]1/2 * 1/2 * 1/2 * 1/2 = 1/16[/tex]

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The probability of all XY in a group of four siblings is 1/16 (6.5%), and also the probability of all XX offspring is 1/16 (6.5%).

For females, the likelihood or probability of inheriting two X chromosomes is 1/2 (50%) while for men, the probability of receiving one X chromosome and one Y chromosome is similarly 1/2.

Therefore, the probability that all XY siblings are present in a group of 4 siblings is:

1/2*1/2*1/2*1/2=1/16

Also the probability that a family of four siblings or offspring includes all XX is

1/2*1/2*1/2*1/2=1/16

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The statement that The cube root of zero is zero is true .

The number that results in the original number after being multiplied three times is known as the cube root of a number.[tex]\sqrt[3]{}[/tex] The sign is used to represent a number's cube root in radical form.

The cube root of 0 will be calculated and explained here. First, observe that the mathematical symbol for the cube root of O is as follows:

[tex]\sqrt[3]{0}[/tex]

The number (n), which you can multiply twice by itself to get the number zero, is the cube root of zero. Alternatively, n×n×n should equal 0. Consequently, the following equation can be used to address the issue:

[tex]n^{3}[/tex] = 0

The answer to the cube root of 0 is as follows when the aforementioned equation is solved:

[tex]\sqrt[3]{0}[/tex]= 0

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The pink ribbon is shortest.

Purple > yellow > silver > pink

These work out to 60,466,176 case insensitive combinations of letters.

There are 10 digits 0–9.

The are 26 letters in the modern alphabets.

However, you didn’t specify whether capital and lowercase letters count as the same letter or separate. In the former case, there are 26 letters, in the latter, there are 52.

There is also such a thing as lowercase numbers, but since they aren’t in common standard usage, I won’t count those.

You also didn’t specify that characters couldn’t be repeated, so I am going to assume that the same character can appear multiple times in a 5 character combination.

Also, since the combinations are an alphanumeric string of characters rather than a number, I will assume that leading zeroes are allowed.

So, there are either 36 (10 digits and 26 letters).

To find the number of combinations you multiply the number of possibilities for each character;

36 x 36 x 36 x 36 x 36

These work out to 60,466,176 case insensitive combinations of letters.

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Answer: 8602 is the answer to 253 x 34, do you want the other parts solved too?

Step-by-step explanation:

Answer: 8.75

Step-by-step explanation:

3 1/8 into a decimal is 3.125

3 1/2 into a decimal in 3.5 or 3.50

4/5 into a decimal is 0.8 or .8

Then just multiply 3.125 and 3.5 and you get 10.9375

Next, multiply 10.9375 by 0.8 and you get 8.75

Therefore your answer is 8.75

The ordered pairs lie on the graph of the exponential equation is

Exponents are used in exponential functions, as the name indicates. But take note that an exponential function does not have a constant as its base and a variable as its exponent (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). One of the following forms can be used for an exponential function.

According to its definition, a fundamental exponential function has the formula f(x) = [tex]b^x[/tex], where b is a constant and x is a variable. The exponential function f(x) = [tex]e^x[/tex], where "e" is "Euler's number," and e = 2.718, is one of the most well-known ones. An exponential function may incorporate a constant if we expand the potential of various exponential functions.

Given function:

f(x) = 25 [tex](2.2)^x[/tex]

Now, taking x=0

y = f(x) = 25

and, x=0.5

y= f(x) = 37.08

and, x = 1

y = 55  

and, x=2

y = 121

So, the ordered pairs lie on the graph of the exponential equation is

2. The given function is [tex]f(x)= (3/8)^x[/tex]

Now, as per the graph As x decreases without bound, the graph of f(x) approaches y = 1.

Or,  As x decreases without bound, the graph of f(x) increases without bound.

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The length of the park not counting the path is 98 yards

The formula for determining the area of a rectangle is expressed as;

Area = lw

Where;

From the information given, we have that;

The dimensions of the path having a width of 1 yard path around it are

(L+2) x (W+2)

We have to add 2 to the length and width because there will be a 1 yard path on all 4 sides of the rectangle

Given that the area is 4200 square yards; the original width is 40 yards

Now, substitute the values into the formula, we have;

Since Area = LW

4200 = (L+2)(W+2)

4200 = (L+2)(40+2)

Add the values

4200 = (L+2)(42)

expand the bracket

4200 = 42L + 84

collect like terms

4116 = 42L

Make 'L' the subject of formula

L = 98 yards

Hence, the length is 98 yards

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Answer:

98 yards

Step-by-step explanation:

Given the points A(3,4) and B(-1,10), we can find the distance between them using the following function:

then, we have the following:

Answer:

1.4522 x [tex]10^{3}[/tex]

Answer:

To get the answer for X we have to subtract 16 from 4 which gives us 12

X=12

Hope this helps.

Answer:

4+X= 16

X=16-4

X=12

*To find X , you need to minus 16 by four. That is because you have to move (+4) to the other side (change sides,change signs). So (+4) becomes (-4) so 16-4 =12

Answer:

5 inches

Step-by-step explanation:

Hello!

The volume of a cube is simply the side length cubed, or the side lengthed multiplied by itself 3 times.

So, to find the edge, we can find the cube root of 125 to find that measure.

The edge is 5 inches.

Answer:

x² + 4x - 12

Step-by-step explanation:

Roots: -6 and 2

Leading coefficient: x²

(x + 6)(x - 2)

x(x - 2) + 6(x - 2)

x² - 2x + 6x - 12

x² + 4x - 12

I hope this helps!