The scale of a model train is 1 inch to 16.48 feet. One of the cars of the model train is $6$ inches long. What is the length, in feet, of the actual train car? Round to the nearest whole number.

Answer:

x = 3

Step-by-step explanation:

[tex] {2}^{(2x - 3)} \ast {5}^{(x - 1)} = 200 \\ \\ \implies \: {2}^{(2x - 3)} \ast {5}^{(x - 1)} =8 \ast \: 25 \\ \\\implies \: {2}^{(2x - 3)} \ast {5}^{(x - 1)} = {2}^{3} \ast {5}^{2} [/tex]

Comparing like terms on both sides, we find:

[tex]{2}^{(2x - 3)}= {2}^{3}\: \: or \:\:{5}^{(x - 1)} = {5}^{2} [/tex]

[tex]\implies \:2x - 3 = 3 \: \: or \: \:x - 1 = 2 \\ \\ \implies \:2x = 3 + 3 \: \: or \: \: x = 1 + 2\\ \\ \implies \:2x = 6 \: \: or \: \: x = 3 \\ \\ \implies \:x = \frac{6}{3} \: \: or \: \: x = 3 \\ \\ \implies \:x = 3 \: \: or \: \: x = 3 \\ \\ \implies \huge \:x = 3 [/tex]

To find the lengths of a right triangle, we can use what is called Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse.

13^2 + b^2 = 17^2

169 + b^2 = 289

b^2 = 120

b = 11.0 cm

The length of the other leg of the triangle is 11.0 cm (rounded).

Hope this helps!

The length of the other leg of the triangle is 11.0 cm rounded to the nearest tenth.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

[tex]a^2 + b^2 = c^2[/tex]

Given that One of the legs of a right triangle measures 13 cm and its hypotenuse measures 17 cm.

To find the lengths of a right triangle, we can use Pythagorean Theorem:

[tex]a^2 + b^2 = c^2[/tex],

where; a and b are the legs of the triangle and c is the hypotenuse.

[tex]13^2 + b^2 = 17^2\\169 + b^2 = 289\\b^2 = 120[/tex]

b = 11.0 cm

Therefore, The length of the other leg of the triangle is 11.0 cm rounded to the nearest tenth.

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Answer:

∠ BCD = 44°

Step-by-step explanation:

the secant- tangent angle BCD is half the difference of the intercepted arcs, so

∠ BCD = [tex]\frac{1}{2}[/tex] (EB - BD) = [tex]\frac{1}{2}[/tex] (171 - 83)° = [tex]\frac{1}{2}[/tex] × 88° = 44°

Answer:

2

Step-by-step explanation:

2⁹ ÷ (4^x) = 32^x × 32^(-1)

2⁹ ÷ 32^(-1) = 32^x × 4^x

16384 = 128^x

Kalau kamu dah belajar logaritma,

[tex]x = log_{128}(16384) \\ x = 2[/tex]

Jika belum,

2¹⁴ = 2^(7x)

Bandingkan kuasa persamaan tersebut,

7x = 14

x = 2

Answer:

Point W is [tex](-5,-4)[/tex]

Point Z is [tex](-5,6)[/tex]

Hope This Helps! :) Please Give Brainliest if you can!

Answer: Point W is (5, -4 Point Z is (-5,6)

Answer:

refer to this image here:

hope this helps :)

We will use graphical way to solve it

Graph it

Solution is

Answer:

6 times means 6 multiplied by

The sum of a number and 2 means x + 2

x = number

(2+x) × 6

The equation C -7 - 3/4 = 0 is an algebraic equation

To solve the equation we (a) add 7 and 3/4 to both sides of the equation

The equation is given as:

C -7 - 3/4 = 0

Make C the subject of formula by adding 7 and 3/4 to both sides of equation

C = 7 + 3/4

Now, we can solve for C

Hence, to solve the equation we (a) add 7 and 3/4 to both sides of the equation

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The appropraite statistical test that would be used to measure the difference  in the variability of the mean scores among the three schools is mean absolute deviation.

Mean absolute deviation is the average of the absolute difference between the data set and its mean. Mean absolute deviation is used to measure spread.

MAD =  [tex]\frac{1}{n}[/tex]∑ l x - m(x) l

Where:

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Answer:

W: (-4,5) W' -> (5,4)

X: (-1,4) X' -> (4,1)

Y: (-6,1) Y' -> (1,6)

Z: (-8,3) Z' -> (3,8)

Step-by-step explanation:

Let me give you a quick brief of how to master rotations!!

You need to understand the formula and positioning rules

The formulas shall be given by teachers or looked up!

*** BUT THE SHAPE POSITIONING RULES MATTER!!

-If the shape was in quadrant 2 which is where it is right now then a 90 degree turn clockwise would result in the shape being on quadrant 1, 180 quad 4, 270: quad 3, and 360 would be the original quad which is 2.

The formula for clockwise for this one is that you need to flip the (x,y) to (y,x)

The shape should be on quadrant 1 which is the one on the top right of the coordinate plane!

They want you to graph it by W'X'Y'Z

The ' is prime which is the new position/coordinate

W: (-4,5) W' -> (5,4)

X: (-1,4) X' -> (4,1)

Y: (-6,1) Y' -> (1,6)

Z: (-8,3) Z' -> (3,8)

That is the rotation 90 degrees clockwise coordinates!!

***REMEMBER EACH ROTATION RULE HAS A DIFFERENT FORMULA!!**

Counterclockwise is pretty similar but the opposite direction with different rules!

**POSITION OF THE SHAPE IS THE MOST IMPORTANT!!!**

Step-by-step explanation:

x is the angle.

complementary angles are adding up to 90°.

supplementary angles are adding up to 180°.

so,

90 - x = (180 - x) - 40 = 140 - x

0 = 50 ? no

there is something wrong here. this cannot work out, there is no solution. there cannot be a solution.

because due to the definitions, the supplementary measure of an angle must always be 90° larger than the complementary measure of the same angle. that is by default the difference in their definition.

so, if an angle is only 40° less than the supplementary angle, then it cannot be the complementary angle.

so, either there was a mistake in the question, or this is a trick question.

under the given circumstances, there is no solution possible.

The probability of popping a balloon is the likelihood of the balloon

The given parameters are:

There are three balloons.

So, the theoretical probability of popping a stripped balloon is:

P = 1/3

The experimental probability of not popping a polka dot is calculated as:

P = 1 - P(Polka dot)

This gives

P = 1 - 5/40

Evaluate

P = 0.875

Hence, the experimental probability of not popping a polka dot is 0.875

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Answer:

28620

Step-by-step explanation:

→ Find the multiplier

( 100 + 6 ) ÷ 100 = 1.06

→ Multiply by the original amount

27000 × 1.06 = 28620

According to the given sine function, it is found that the period of rotation is of 0.21 seconds.

Suppose a sine function modeled by:

[tex]y = A\sin{[B(x + c)]}[/tex]

The period is given by:

[tex]P = \frac{2\pi}{B}[/tex].

In this problem, the function is:

h(t)=60+45 sin (30t).

The vertical shift and the amplitude do not interfer in the period, hence B = 30 and:

[tex]P = \frac{2\pi}{30} = 0.21[/tex]

The period of rotation is of 0.21 seconds.

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Answer:

So, we can check step by step.

2x^2-7x+5=0

So, 2x^2-2x-5x+5=0 is correct

2x(x-1)=2x^2-2x, 5(x-1)=-5x + 5= 0, that step is correct

(I'll skip the next step)

2x-5=0,

2x=5

x=5/2, NOT 2/5

The other one is correct

Sorry if this seems a bit vague!

[tex]\\ \rm\Rrightarrow 2x^2-7x+5=0[/tex]

[tex]\\ \rm\Rrightarrow 2x^2-2x-5x+5=0[/tex]

[tex]\\ \rm\Rrightarrow 2x(x-1)-5(x-1)=0[/tex]

[tex]\\ \rm\Rrightarrow (2x-5)(x-1)=0[/tex]

[tex]\\ \rm\Rrightarrow x=5/2,1[/tex]

Lauren written 2/5 instead of 5/2

Let's verify once more

Answer:

OPTION C

Step-by-step explanation:

This function is odd function because it is symmetric about the origin

Note:This graph also represents the graph of tanx

I hope it helped you

Answer:

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

a proportional relationship when graphed always is a straight line that goes through the origin (0,0)

The graph shown, shows a straight line but the line doesn't go through the origin therefore the graph does not show a proportional relationship.

Note that the origin is where the x and y axis cross , or the bottom right corner of the graph in this case

Answer:

by using bodmas rule

to solve this problem

Step-by-step explanation:

=3^-6/3^-4

=3-2-4

=-3

Answer:

I believe D is the correct answer

let's recall that d = rt, namely distance = rate * time.

d = distance from one pier to another

c = speed of the current

b = speed of the boat

now, let's notice something, on the way over the boat travelled "d" kilometers in 4 hrs, and back the same "d" kilometers in 5 hours.

when going with the current, the boat is not really going at "b" km/s, is really going faster, at "b + c" km/s, because the current is adding to it.

now, when going against the current, the boat is not really going "b" fast, is really going slower, at "b - c", because the current is subtracting from it.

from the above, we can conclude that the 4hrs trip was with the current, since it took less time, and the 5hrs trip was against the current, and we also know that the boat does 70 km with the current in 3.5 hrs, ok hmmm let's put all that in a table.

[tex]\begin{array}{lcccl} &\stackrel{km}{distance}&\stackrel{km/h}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{on the way over}&d&b+c&4\\ \textit{on the way back}&d&b-c&5\\\cline{1-4} \textit{we also know}&70&b+c&3.5 \end{array}~\hfill \begin{cases} d=(b+c)4\\\\ d = (b-c)5 \end{cases} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{(b+c)4~~ = ~~(b-c)5}\implies 4b+4c=5b-5c \\\\\\ 4c=b-5c\implies \boxed{9c=b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{we know that}}{70~~ = ~~(b+c)3.5}\implies 70=(b+c)\cfrac{7}{2}\implies \stackrel{\textit{substituting "b"}}{70=(9c+c)\cfrac{7}{2}} \\\\\\ 70=10c\cdot \cfrac{7}{2}\implies 70=\cfrac{70c}{2}\implies 140=70c\implies \cfrac{140}{70}=c\implies \blacktriangleright 2=c \blacktriangleleft \\\\\\ \stackrel{\textit{the speed of the boat in still water is then}}{9c=b\implies 9(2)=b}\implies \blacktriangleright 18=b\blacktriangleleft[/tex]

Answer:

i dunno'

Step-by-step explanatio i dont know how to explain diss this

Answer:

Step-by-step explanation:

10/5: not part of the answer. This gives 2. The original ratio gives 5.

120 / 36 is not part of the answer. This gives 3 1/3 which is not 5

The last 3 are the only ones you should choose.

Answer:

4th option

Step-by-step explanation:

Remember the Quotient Rule:

[tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex]

6-2 = 4

So it is the last option

Answer:

The answer would be 2000

Step-by-step explanation:

Knowing that there are 1000 milliliters in 1 liter, you can multiply that by 2 to get 2000. I hope this helps! :)

Answer:

5/8

Step-by-step explanation:

Just gonna fill up the required space here lol

Answer:

c

Step-by-step explanation:

the distance between a to b is

| 15 - (- 7) | = | 15 + 7 | = | 22 | = 22

or

| - 7 - 15 | = | - 22 | = 22

The amount of money Adam should save now in order to accomplish his goal is $13,470.30.

In order to determine the amount Adam should save now, the present valaue of $19,000 has to be determined. Present value is the sum of discounted cash flows.

Present value = future value / (1 + interest)^time

Interest = 1.92/2 = 0.96%

Time = 18 x 2 = 36

$19,000 / (1.0096^36) = $13,470.30

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Answer:

Isocoles (I can't spell)

Step-by-step explanation:

180-70=110. 110-40=70.

Two angles are 70

Time drew the isosceles triangle because the two angles are equal.

Given that,
Tim drew a triangle with one angle of measure 40 degrees and the other 70 degrees. which triangle Tim drew is to be determined.

A triangle with two sides and two congruent angles is called an isosceles triangle.

Here,
Let one of the angles be x
Sum of angles = 180
40 + 70 + x = 180
x = 70
As two of the angle become equal the triangle becomes an isosceles triangle.

Thus, Time drew the isosceles triangle because the two angles are equal.

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