Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?
The pool must have been empty for the entire interval.
The pool must have been the same depth at the start of the interval as it was at the end of the interval.
The pool must have been deeper at the end of the interval than it was at the start of the interval.
The pool must have been more shallow at the end of the interval than it was at the start of the interval.

Answer:

The answer is c because of how the equation is set and made

The radical equation is √x+3=13. Therefore, option C is the correct answer.

A radical equation is an equation in which a variable is under a radical. To solve a radical equation: Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

In option C, x is under radical, so it is radical equation.

Here, √x+3=13

√x=13-3

√x=10

Therefore, option C is the correct answer.

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Answer:

little falls has more

Step-by-step explanation:

show your work: little falls total rainfall is 1 6/8 and riverside is 1 5/8

use that to explain :) your welcome

Answer:

  Riverside had the greatest rainfall total

Step-by-step explanation:

The total amount of rain in a city will be the sum of products of rain amount and days that got that amount. The city with the largest sum got the most rain. The difference in rainfall can be found by subtracting the lesser amount from the greater.

__

Total rainfall in Riverside was ...

  (1/8)×1 +(2/8)×3 +(3/8)×3 +(4/8)×1 +(5/8)×1

  = (1 +6 +9 +4 +5)/8 = 25/8 = 3 1/8 . . . . inches

__

Total rainfall in Little Falls was ...

  (1/8)×1 +(3/8)×1 +(4/8)×1 +(6/8)×2

  = (1 +3 +4 +12)/8 = 20/8 = 2 1/2 . . . . inches

__

Riverside had more rainfall, because 3 1/8 is more than 2 1/2.

__

You can "cancel" dots that are in the same place on each plot. Doing so leaves Riverside with 3 dots at 2/8, 2 dots at 3/8, and 1 dot at 5/8. The remaining dots on the Little Falls plot are the 2 dots at 6/8.

The 3 dots at 2/8 add up to 6/8, as do the 2 dots at 3/8 on the Riverside plot. These two 6/8 values cancel the two 6/8 dots on the Little Falls plot. That leaves one uncancelled dot at 5/8 on the Riverside plot, indicating more rain fell at Riverside.

Answer:

x = 6

Step-by-step explanation:

Taking the sides in proportion :

Step-by-step explanation:

If you have any question about the sollution, ask me

The zoo is 12 inches from the school on the map

The given parameters can be represented using the following ratio:

Ratio = 1 inch : 3 miles

For 12 miles, we have:

Distance :12 miles = 1 inch : 3 miles

Multiply by 4

Distance :12 miles = 4 inches : 12 miles

By comparison, we have:

Distance = 12 miles

Hence, the zoo is 12 inches from the school on the map

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Answer:

radius 4

center (3,6)

Step-by-step explanation:

(x - h)^2 + (y - k)^2 = r^2

coordinates of the center (h, k) and the radius is (r)

x² + y²- 6x - 12y +29=0

x² - 6x + y²- 12y +29=0

(x² - 6x) + (y²- 12y) +29=0

complete the square

(x² - 6x) + 9 + (y²- 12y) +36 +29=  + 9  +36

(x² - 6x + 9) + (y²- 12y + 36) = + 9  +36 -29

(x-3)^2 + (y-6)^2 = 16

(x - h)^2 + (y - k)^2 = r^2

coordinates of the center (h, k) and the radius is (r)

center (3,6)

radius 4

cuemathcom

varsitytutors

Answer: Center: (3,2)                Radius: 5

Step-by-step explanation:#x^2 - 6x +y^2 - 4y = 12

Then take 1/2 of the 'b' term for both quadratic expressions, square those values and add them to both sides.

#x^2 -6x + 9 + y^2 - 4y + 4 = 12 + 9 + 4

(x - 3)^2 + (y -2)^2 = 25

Circle centered at (3,2) with radius = 5

Answer:

sin Θ = 11/19

Step-by-step explanation:

19 is the hypotenuse.

The legs are 11 and 4√15.

sin Θ = opp/hyp

For angle Θ, 11 is the opposite leg.

sin Θ = 11/19

Answer:

11/19 the other guys is correct

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Basically, when you have a product to two factors set equal to 0, you can use the Zero Product Property and make two separate equations, both set equal to 0, to find the roots for each factor:

[tex]2x+10=0\\2x=-10\\x=-5[/tex]

[tex]x-7=0\\x=7[/tex]

Notice that by plugging these roots back into the equation, either factor will be 0, making the whole expression 0:

[tex](2x+10)(x-7)=0\\(2(7)+10)(7-7)=0\\(24)(0)=0\\0=0[/tex]

[tex](2x+10)(x-7)=0\\(2(-5)+10)(-5-7)=0\\(0)(-12)=0\\0=0[/tex]

Answer:

Step-by-step explanation:

1. 150 * π/180

= 150π/180

= 5π/6

=2.62

2. π/2

π/2 * 180/π

= 90 degrees

Step-by-step explanation:

1)150° 's radian measure

[tex] \rm \implies150 \: Deg × π/180 = 2.618 \: Radians[/tex]

2)π/2 's degree measure

[tex] \rm \: \implies \: π/2 × 180/π= 180/2 = 90 \: degrees[/tex]

Basically,we need to use formulas to solve these type of sums.

Answer:

[tex]\sqrt{65}[/tex]

Step-by-step explanation:

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

[tex]4^{2} +7^{2} =c^{2}[/tex]

[tex]16+49=c^{2}[/tex]

[tex]65=c^{2}\\\sqrt{65}=c[/tex]

Answer:

65

Step-by-step explanation:

Answer:

402.9092

Step-by-step explanation:

surface area of cylinder - top base = 301.5946

surface area of cone - base = 101.3146

add together 402.9092

Answer:

Output: 3

Step-by-step explanation:

(x, y)

(Input, Output)

(2, 3)

Answer: 6

Step-by-step explanation: 10-4=6

Answer:

126 cm^2 (please mark me brainliest)

Step-by-step explanation:

(14x16)/2+(2*14)/2=

112+14=126

Answer:

See below

Step-by-step explanation:

Use protractor to measure the UNmarked angle (approx 135 degrees)

    then subtract this value from 360 degrees to find the angle in question

Answer:

4 cm

Step-by-step explanation:

Scale

Scale factor=10

Distance of Greenwood=40km

Now apart in map

Answer:

$70.76 or 70.7595

Step-by-step explanation:

Here’s the function:

67.39(1+0.05)^1

Hope this helps! ;-)

The set of equation that models the point of intersection of the arrow

and the target is: y = -0.002x² +0.25x + 6 and y = 0.15x.

Given parameters:

Point of intersection of the line and the parabola=(85.21,12.78)

Hence:

First set

y = -0.002 × 48.67² + 0.25 × 85.21 + 6= 12.78

Linear function y ≠ x

Third set

y = -0.002 × 85.21² + 0.25 × 85.21+ 6= 12.78

y = C·x

12.78 = 85.21·x

C=12.78/85.21

C=0.149

C=0.15 (Approximately)

Hence:

y=0.15x

Therefore the set of equation that models the point of intersection of the arrow and the target is: y = -0.002x² +0.25x + 6 and y = 0.15x.

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6x4=24

24x1/2=12

12+3=15

15+2=17

17 is the answer

Answer:

36

Step-by-step explanation:

A^2+B^2=C^2

10^2+B^2=38^2

We are solving for B squared

So 100+B^2=1444

                      -100

1344 and now take the square root of that number and you have your answer of 36

I hope this helps and have a good night!

The sequence is recursively defined by

[tex]\begin{cases}a_1 = 1 \\ a_2 = 2 \\ a_n = a_{n-1} a_{n-2} & \text{for } n \ge 3\end{cases}[/tex]

By this definition,

[tex]a_{n-1} = a_{n-2} a_{n-3} \implies a_n = a_{n-2}^2 a_{n-3}[/tex]

[tex]a_{n-2} = a_{n-3} a_{n-4} \implies a_n = (a_{n-3} a_{n-4})^2 a_{n-3} = a_{n-3}^3 a_{n-4}^2[/tex]

[tex]a_{n-3} = a_{n-4} a_{n-5} \implies a_n = (a_{n-4} a_{n-5})^3 a_{n-4}^2 = a_{n-4}^5 a_{n-5}^3[/tex]

[tex]a_{n-4} = a_{n-5} a_{n-6} \implies a_n = (a_{n-5} a_{n-6})^5 a_{n-5}^3 = a_{n-5}^8 a_{n-6}^5[/tex]

and so on.

Recall the Fibonacci sequence, {1, 1, 2, 3, 5, 8, 13, 21, …}, where the next term in the sequence is the sum of the previous two terms. If [tex]F_n[/tex] is the n-th Fibonacci number, then continuing the pattern above we would arrive at

[tex]a_n = {a_2}^{F_{n-1}} {a_1}^{F_{n-2}} = 2^{F_{n-1}}[/tex]

Notice that the sequence of positive powers of 2 leaves a periodic sequence of residues mod 10 :

[tex]2 \equiv 2 \pmod{10}[/tex]

[tex]2^2 \equiv 4 \equiv 4 \pmod{10}[/tex]

[tex]2^3 \equiv 8 \equiv 8 \pmod{10}[/tex]

[tex]2^4 \equiv 16 \equiv 6 \pmod{10}[/tex]

[tex]2^5 \equiv 2 \times 2^4 \equiv 2 \times 6 \equiv 2 \pmod{10}[/tex]

[tex]2^6 \equiv 2^2 \times 2^4 \equiv 4 \times 6 \equiv 4 \pmod{10}[/tex]

and so on; the period of this sequence of residues is 4.

The period of [tex]F_n[/tex] taken mod 4 is 6 :

[tex]\{1, 1, 2, 3, 5, 8, \ldots\} \equiv \{1, 1, 2, 3, 1, 0, \ldots\} \pmod 4[/tex]

(This follows from the "properties" section in the link in comment. In this case, π(4) = 3/2 × 4 = 6.)

It follows that

[tex]34 \equiv 4 \pmod 6 \implies F_{34} \equiv 3 \pmod 4 \implies 2^{F_{34}} \equiv 2^3 \equiv 8 \pmod{10}[/tex]

which means the last digit of [tex]a_{35}[/tex] is 8.

If the significance level is about 5% then the result is not statistically significant; which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.

The term significance level has to do with the probability of rejecting the null hypothesis even though it is true.

The significance level tells us if a result is statistically significant. Thus, if the significance level is about 5% then the result is not statistically significant; which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.'

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A)The result is statistically significant, which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.

Did the project

Pull out a factor of 1/n from the summand and the result follows.

[tex]\displaystyle \lim_{n\to\infty} \sum_{i=1}^n \frac{i^4}{n^5} = \lim_{n\to\infty} \frac1n \sum_{i=1}^n \left(\frac in\right)^4 = \boxed{\int_0^1 x^4 \, dx}[/tex]

[tex]\cfrac{7x^{-\frac{3}{2}} ~~ y^{\frac{5}{2}} ~~ z^{-\frac{2}{3}}}{56 x^{-\frac{1}{2}} ~~ y^{\frac{1}{4}}}\implies \cfrac{7}{56}\cdot \cfrac{y^{\frac{5}{2}} ~~ y^{-\frac{1}{4}}}{x^{-\frac{1}{2}} ~~ x^{\frac{3}{2}} ~~ z^{\frac{2}{3}}}\implies \cfrac{1}{8}\cfrac{y^{\frac{5}{2}-\frac{1}{4}}}{x^{-\frac{1}{2}+\frac{3}{2}}~~ z^{\frac{2}{3}}}[/tex]

[tex]\cfrac{y^{\frac{9}{4}}}{8x z^{\frac{2}{3}}}\implies \cfrac{\sqrt[4]{y^9}}{8x\sqrt[3]{z^2}}\implies \cfrac{\sqrt[4]{y (y^2)^4}}{8x\sqrt[3]{z^2}}\implies \cfrac{y^2 \sqrt[4]{y}}{8x\sqrt[3]{z^2}}[/tex]

Answer:

prob of being a red=1/2

prob of being an ace=1/13

Check the picture below.