A farmer plants five apple trees in 25 minutes. If he continues to work at a constant rate, how long will it take him to plant 200 trees?

Answer:

[tex]x=45 \sqrt{5}[/tex]

Step-by-step explanation:

[tex]2 \log_3x+\log_35=4\log_315[/tex]

[tex]\textsf{Apply power log law}\quad n\log_ab=\log_ab^n:[/tex]

[tex]\implies \log_3x^2+\log_35=\log_315^4[/tex]

[tex]\textsf{Apply product log law}\quad \log_ab+\log_ac=\log_abc:[/tex]

[tex]\implies \log_35x^2=\log_315^4[/tex]

[tex]\textsf{Apply equality log law}\quad \log_ab=\log_ac \implies b=c:[/tex]

[tex]\implies 5x^2=15^4[/tex]

[tex]\implies x^2=10125[/tex]

[tex]\implies x=\pm \sqrt{10125}[/tex]

[tex]\implies x=\pm \sqrt{2025 \cdot 5}[/tex]

[tex]\implies x=\pm \sqrt{2025} \sqrt{5}[/tex]

[tex]\implies x=\pm 45 \sqrt{5}[/tex]

As we cannot take logs of negative numbers,

[tex]\implies x=45 \sqrt{5}\quad \sf only[/tex]

Answer:

247.29 ft

Step-by-step explanation:

Need to find the opposite side, so use sine

4725sin 3 = 247.29

Answer:

its this symbol

Step-by-step explanation:

Answer:

85 ft^2

Step-by-step explanation:

Base = 5 x 5 = 25 ft^2

FOUR triangles   4  *   1/2 * b * h  = 4 * 1/2 * 5 * 6 = 60 ft^2

added together = 85 ft^2

Answer:

[tex] - 60[/tex]

Dynamic pricing is typically used to increase ticket sales on low attendance days, offer fans discounts on concessions.

Dynamic pricing is used to set the price of tickets based on the situation of the demand and reduce the number of unsold tickets.

It is used to adjust the prices that tickets are sold during sports which can be based on such variables as demand, weather, team performance and even pitching match-ups.

Therefore, Dynamic pricing is typically used to increase ticket sales on low attendance days, offer fans discounts on concessions.

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Answer:

$8.95

Step-by-step explanation:

If Ari spent $35.80 for 4 posters and each of the poster price was the same therefore if we want the price for one poster we have to divide $35.80 by four to see the cost for one poster which will be $8.95. If you want to know if the price of each poster was the same you can just multiply $8.95 by 4 and you'll actually see that you got back the same money that Ari used to spend for the four posters .

Answer:

simultaneous equations are used to solve for 2 variable

Answer:

y = 2

Step-by-step explanation:

Given table:

[tex]\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\\underline{| \ \ \text{x} \ \ | \ \ \text{y} \ \ | } \\ \underline{| \ \text{-6} \ \ | \ \text{-3} \ \ |} \\ | \underline{\ \text{-4} \ \ | \ \text{-2} \ \ | }\\ \underline{| \ \text{-2} \ \ | \ \text{-1} \ \ |} \\ \underline{| \ \ \text{0} \ \ | \ \ 0 \ \ |}[/tex]

To determine the value of y when "x" is 4, we need to determine the equation of the line that represents the table given. Then, we can substitute the value of "x" in the equation to determine the value of y.

Determining the equation of the line that represents the table:

Y-intercept:

Since the coordinate (0, 0) is included in the table, we can tell that the equation of the line that represents the table passes through the origin. Therefore, we can tell that the y-intercept is 0 as the y-intercept is the point on the line that intersects the y-axis.

Slope:

The slope of the line can be determined by picking any two points in the table and substituting the coordinates of the chosen points in the slope formula. Let our chosen points be (-6, -3) and (0, 0).

[tex]\implies \text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]\implies \text{Slope} = \dfrac{0 - (-3) }{0 - (-6) }[/tex]

[tex]\implies \text{Slope} = \dfrac{0 + 3 }{0 + 6 }[/tex]

[tex]\implies \text{Slope} = \dfrac{3}{6} = \dfrac{1}{2}[/tex]

Equation of line:

The equation of the line represented by the table in slope intercept form is y = mx + b, where "m" is the slope and "b" is the y-intercept.

Obtained slope and y-intercept:

⇒ y = (1/2)x + 0

⇒ y = x/2

Therefore, the equation of the line is y = x/2.

Determining the value of y when "x" is 4:

Obtained equation of line that represents the table:

Given value:

Therefore,

Thus, the value of "y" when "x" is 4 is 2.

Answer:

-24/16, -√2, 21/51, 0.42

Step-by-step explanation:

Look at the signs of the numbers. Negative numbers will be on the left, while positive numbers will be on the right. That means -√2 and -24/16 will be on the left, while 0.42 and 21/51 will be on the right.

Part 1:

We can change the negative numbers to decimals to compare them.

-√2 ≈ -1.41

-24/16 = -1.5

-1.5 is smaller, which means the first number in the sequence will be -24/16 and then -√2.

Part 2:

We can also change the positive numbers to decimals to compare them.

0.42 = 0.42

21/51 ≈ 0.41

21/51 is a bit smaller, so the third number in the sequence will be 21/51 and then 0.42.

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Answer:

490 miles

Step-by-step explanation:

7/1.4 = 5

98*5 = 490

Answer:

Step-by-step explanation:

x + 4 = 2x + 1 -x -x 4 = 1x + 1 -1 -1 3 = 1x -- -- 1 1 3 = x

Check: 3 + 4 = 2(3) + 1 7 = 6 + 1 7 = 7

Answer:

[tex]\frac{4}{3}[/tex] miles

Step-by-step explanation:

Check the attachment.

Answer:

X intercepts: (0,12)

Y intercepts: (-32,88)

Answer:

  add the areas of the parts

Step-by-step explanation:

The area of an unusual shape is often easily found by decomposing it into shapes that you have formulas for. Divide the shape into parts, and add the areas of those parts.

__

Alternatively, some shapes are conveniently described by "missing" parts, For example, your "plus shaped" figure may be described as an overall rectangle with rectangles removed from the corners. Then the area of the shape is found by subtracting the missing area from that of the overall rectangle.

__

As a rule, you want the parts to be non-overlapping. That way, you can add the areas of the parts without counting any area twice (or more times). If you have overlapping parts, you need to subtract the area(s) that may be counted multiple times.

__

Sometimes you can take advantage of symmetry, so that you only need to compute part of the total area, then multiply by a factor that takes the symmetry into account.

__

In the attached figure, the dimensions of rectangle A are 6 m wide by 7 m high. The dimensions of rectangle B must be found by adding the width dimensions shown across the top of the figure: 5 m +6 m +6 m = 16 m. It is marked as 4 m high. Then the total area is ...

  area of A + area of B

  = (6 m)(7 m) +(16 m)(4 m)

  = 42 m² +64 m² = 106 m²

This can also be found as the area of the 16 m by 11 m enclosing rectangle, less the two 5 m by 7 m corner cut-outs.

  (16 m)(11 m) -2(5 m)(7 m) = 176 m² -2(35 m²) = 106 m²

Answer:

[tex]\frac{x}{2} *\sqrt{x^{2} +4}[/tex] +[tex]\frac{1}{2}[/tex]*LN(|[tex]\frac{x+\sqrt{x^{2} +4} }{2}[/tex]|) +C

Step-by-step explanation:

we will have to do a trig sub for this

use x=a*tanθ for sqrt(x^2 +a^2) where a=2

x=2tanθ, dx= 2 sec^2 (θ) dθ

this turns [tex]\int\limits {\sqrt{x^{2}+4 } } \, dx[/tex] into integral(sqrt( [2tanθ]^2 +4) * 2sec^2 (θ) )dθ

the sqrt( [2tanθ]^2 +4) will condense into 2sec^2 (θ) after converting tan^2(θ) into sec^2(θ) -1

then it simplifies into integral(4*sec^3 (θ)) dθ

you will need to do integration by parts to work out the integral of sec^3(θ) but it will turn into (1/2)sec(θ)tan(θ) + (1/2) LN(|sec(θ)+tan(θ)|) +C

then you will need to rework your functions of θ back into functions of x

tanθ will resolve back into [tex]\frac{x}{2}[/tex] (see substitutions) while secθ will resolve into [tex]\frac{\sqrt{x^{2} +4} }{2}[/tex]

sec(θ)=[tex]\frac{\sqrt{x^{2} +4} }{2}[/tex]  is from its ratio identity of hyp/adj where the hyp. is [tex]\sqrt{x^{2} +4}[/tex]  and adj is 2 (see tan(θ) ratio)

after resolving back into functions of x, substitute ratios for trig functions:

= [tex]\frac{x}{2} *\sqrt{x^{2} +4}[/tex] + [tex]\frac{1}{2}[/tex]*LN(|[tex]\frac{x+\sqrt{x^{2} +4} }{2}[/tex]|) +C

Answer:

500 is the answer

Step-by-step explanation:

hope it helps....

Answer:

500 and 600

Step-by-step explanation:

Round 536 to the nearest hundred. 536 is between 500 and 600. Look at the 30 in the tens place. It is below 50, so round down to 500.

Answer:

a. no

b. no

c. no

d. yes

Step-by-step explanation:

Case I

x = -1

y = -4

7( -1) + 4 ( -4) = -23

-7 - 4 = -23

- 11 [tex]\neq[/tex] -23

Case II

x = 2

y= 6

7 (2) + 4 ( 6) = -23

14 + 24 = -23

38 [tex]\neq[/tex] -23

Case III

x = 6

y = -7

7 ( 6) + 4 (3) =- 23

42+ 12 = -23

54 [tex]\neq[/tex] -23

Case IV

x = -5

y = 3

7 (-5) + 4 ( 3) =- 23

-35 + 12 = -23

-23 = -23

The height of the triangle is 8root3 meters.

We have given that,

A tree breaks due to a storm and the broken part bends,

So that the top of the tree touches the ground making an angle of 60 degrees with the ground.

The distance between the feet of the tree to the point where the top touches the ground is 16m.

Let the Height of the Tree =AB+AD

and given that BD=8 m

Now, when it breaks a part of it will remain perpendicular to the ground (AB) and the remaining part (AD) will make an angle of 30 degrees.

Now, in △ABD

cos(30)=BD/AD=BD=root3AD/2

AD=2(8)/root3

also in the same triangle

[tex]tan(30)=AB/BD\implies 8/\sqrt{3}[/tex]

Height of the tree=AB+AD

[tex]=\frac{16}{\sqrt{3} }+\frac{8}{\sqrt{3} } }[/tex]

[tex]=\frac{24}{\sqrt{3} } \\=8\sqrt{3}m[/tex]

Therefore the height of the triangle is 8root3.

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Answer:

The answer I got was

Step-by-step explanation:

[7, 4, 3]

You use the matrix calculator and then select a*b

Answer: 97 degrees

Step-by-step explanation:

First, find the mode, median, and mean of the given set of numbers.

Mode

The mode is the number that shows up frequently within the given set. In this case, it will be 10, as it shows up 4 times, 3 times more than any other number.

Mode: 10

~

Median

The median is the number that is in the middle of the given set. In this case, there are 9 numbers, and so the 5th given number is your median:

10 , 10 , 10 , 10 , 11 , 12 , 13 , 15 , 17

Median: 11

~

Mean

The mean is combining all numbers within the given set and dividing by the amount of numbers in that said set:

(10 + 10 + 10 + 10 + 11 + 12 + 13 + 15 + 17)/9 = 108/9 = 12

Mean: 12

Using it's concept, it is found that there is a 0.004 = 0.4% probability of a game console buyer buying a defective Suny Playcom.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, 40% of the consoles bought are of the Suny Playcom series, and of those, 1% are defective, hence the probability is given by:

p = 0.4 x 0.01 = 0.004

0.004 = 0.4% probability of a game console buyer buying a defective Suny Playcom.

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Step-by-step explanation:

Answer:

[tex]1\frac{1}{2}[/tex] or 1.5

Step-by-step explanation:

Now we know it's a dilation.  So we can use any two points.  I chose V and V'.

V: (3,6)

V': (2,4)

So how we get from 6 to 4?

[tex]4(x)=6\\x=\frac{6}{4} \\x=1.5[/tex]

You can tell it's 1.5 aswell because 4 times 1 is 4 and 4 times 0.5 is 2.  Add them to get 6.  

Therefore, the dilation factor is 1.5.

We will see that the probability of x taking on a value between 75 to 90 is P = 0.5

We know that x is a continuous random variable uniformly distributed between 65 and 85.

This means that the probability that x value y in the range is such that:

1 = P(y)*(85 - 65) = P(y)*20

1/20 = P(y).

Now, the probability of x taking a value between 75 and 85 is:

P(75 to 85) = (1/20)*(85 - 75) = 10/20 = 0.5

And the probability between 85 and 90 is zero (because the maximum value that x can take is 85, so this part does not affect).

Then we conclude that the probability of x taking a value between 75 to 90 is:

P(75 to 90) = P(75 to 85) + P(85 to 90) = 0.5 + 0 = 0.5

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Answer:

Step-by-step explanation:

Could you show two points need to be calculated? A and D are the same in this case

Answer:

23°

Step-by-step explanation:

Let the measure of the required angle be [tex]\theta[/tex]

[tex] \implies \: \theta = { \cos}^{ - 1} \: \bigg(\frac{35}{38} \bigg) \\ \\ \implies \: \theta =22.9195421516\\\\ \implies \: \theta =23\degree[/tex]