The rate of growth of population P of turtles is proportional to the square root of P.
At time t = 0 (months), the population numbers 900, and is increasing at the rate of 60 turtles
per month, then find the population of turtles after 5 months.

Answer:12

Step-by-step explanation:

Answer:

this is a principal application not I m buying

Answer:

2.4

Step-by-step explanation:

We would first calculate the mean, because we would need it to calculate our varance.

Mean= sum of the number of given data set/ total number

Mean = (9 +8 +9 +5 +9 )/5

= 40/5= 8

variance (σ2):= [(9-8)^2 + (8-8)^2 + (9-8)^2 +(5-8)^2 +(9-8)^2]/5

=( 1+ 0 + 1 +9 +1)/5

= 12/5

variance (σ2)= 12/5

=2.4

Answer:

2.4

Step-by-step explanation:

Step 1: Find the mean.

The mean (or average) of the data set is found by adding all the numbers in the data set and subtracting by the number of numbers, as shown below.

\(\frac{9+8+9+5+9}{5}=\frac{40}{5}=8\)

Step 2: Find the standard deviation.

Find the standard deviation by subtracting the mean from each of the numbers in the data set and squaring the result:

\((9-8)^{2}+(8-8)^{2}+(9-8)^{2}+(5-8)^{2}+(9-8)^{2}\)

\(1+0+1+9+1 = 12\)

Step 3: Find the variance.

Divide the standard deviaton by the number of numbers to get the variance.

Variance =  \(\frac{12}{5}\) OR 2.4

Hope this helps!

Answer:

EF = 10;   AD = 3 ;     BC = 17        

Step-by-step explanation:

The median (EF) of a trapezoid equal half the sum of the length of the two bases of the trapezoid (AD and BC)

EF = 1/2 (AD + BC)

x = 1/2( x - 7 + 2x - 3)

x = 1/2 (3x - 10)      

2x = 3x - 10                  Multiply all terms by 2     or   x = 3/2x - 5

-x = -10                                                                         x - 3/2x  = -5

x = 10                                                                             -1/2x = -5

                                                                                      x = 10

So EF = 10

     AD = x - 7               BC = 2x - 3

     AD = 10 - 7             BC = 2(10) - 3

     AD = 3                   BC = 20 - 3    

                                    BC = 17                                                    

Answer:

D

Step-by-step explanation:

the domain is all x values. so:

0, 4, 5, 10

I think that's answer d

Answer:

Step-by-step explanation:

The domain is the x so 0,4,5,10 or D

The x and y intercepts are:

x=(1,0)

y=(0,3)

Answer:

y=4x+11

Step-by-step explanation:

The formula for slope intercept is y=mx+b

m= slope

b= y intercept

hence, y=4x+11

Answer:

\(\fbox {D. 3,200.4 mm}\)

Step-by-step explanation:

Given :

[ 1 inch = 2.54 centimeters ]

Unit conversions to keep in mind :

Solving

The length of the ramp is 6.91 feet

Given data:

To determine the length of the ramp, we can use trigonometry. So, use the sine function, which relates the angle of the ramp to the ratio of the opposite side (length of the ramp) to the hypotenuse (the distance the ramp covers).

Given that the angle of the ramp is 24°, set up the equation:

sin(24°) = opposite/hypotenuse

The opposite side is the length of the ramp and the hypotenuse is the distance it covers, which is 17 feet.

sin(24°) = length of the ramp / 17

To find the length of the ramp, rearrange the equation:

The length of the ramp = sin(24°) * 17

L ≈ 6.91 feet

Hence, the length of the ramp is approximately 6.91 feet.

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Answer:

It'll take 25 more minutes

Step-by-step explanation:

Answer:

5, -5

Step-by-step explanation:

We have the problem x^2+5=30

Same to both sides

x^2=25

And 25 is a perfect square, x = 5

BUUUUUUUT..........

x could also equal to -5 because no numbers that are squared can be negative

Confused?

Squaring a number means doing the number multiplied by itself

A negative multiplied by a negative equals a positive

A positive multiplied by a positive equals a positive

Under no circumstances can something squared be a negative number

-5*-5 also equals 25.

So those are your two numbers

Let me know if you have any questions

Considering the zeros, the graph for the sinusoidal function is:

\(F(x) = \sin{\frac{\pi}{7}(x-3)}\)

The sine function is given by:

\(F(x) = A\sin{Bx}\)

In which:

In this problem:

\(\frac{2\pi}{B} = 14\)

\(B = \frac{2\pi}{14}\)

\(B = \frac{\pi}{7}\)

Thus:

\(F(x) = \sin{\frac{\pi}{7}x}\)

Like this, the zeros are at \(x = -14\) and \(x = 0\). We want it at \(x = -11, x = 3\), thus, we shift the function 3 units to the right, that is, the function is:

\(F(x) = \sin{\frac{\pi}{7}(x-3)}\)

The graph is sketched at the end of this answer, and has the desired behavior, which are points (-11,0) and (3,0).

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1. The amount borrowed is $3,000.

2. The ordinary interest is $80.

1. To find the amount borrowed, we can use the formula I = (P x i x t), where I is the interest, P is the principal (amount borrowed), i is the interest rate, and t is the time in years. Rearranging the formula, we have P = I / (i x t). Plugging in the given values, P = 270 / (0.09 x (2/12)) = $3,600.

2. To find the ordinary interest, we can again use the formula I = (P x i x t), where I is the interest, P is the principal, i is the interest rate, and t is the time in years. Since the time given is in days, we need to convert it to years. So, t = 60 / 365 = 0.1644 years. Plugging in the values, I = 4000 x 0.12 x 0.1644 = $79.07.

1. The amount borrowed, we can rearrange the formula TA = P + I to solve for P (the principal amount). Given that the interest (I) is $270, the interest rate (i) is 9%, and the time (t) is two months, we can substitute these values into the formula.

P = I / (i x t)

P = $270 / (0.09 x 2)

Calculating this expression gives us:

P = $1,500

Therefore, the amount borrowed is $1,500.

Using the formula TA = P + I, we can rearrange it to solve for P:

P = TA - I

In this case, the total amount (TA) is the amount borrowed plus the interest. We are given that the interest is $270, and we need to find the principal amount (P) when the interest rate (i) is 9% and the time (t) is two months.

Substituting the given values into the formula, we have:

P = $270 / (0.09 x 2)

Simplifying the expression, we get:

P = $270 / 0.18

Calculating this expression gives us:

P = $1,500

Therefore, the amount borrowed is $1,500.

2. To find the ordinary interest for a loan of $4,000, at 12%, for 60 days, we can use the formula I = (P x i x t). Given that the principal amount (P) is $4,000, the interest rate (i) is 12%, and the time (t) is 60 days, we can substitute these values into the formula.

I = (P x i x t)

I = ($4,000 x 0.12 x 60) / 365

Calculating this expression gives us:

I ≈ $78.08 (rounded to two decimal places)

Therefore, the ordinary interest for the loan is approximately $78.08.

Explanation and Calculation:

Using the formula I = (P x i x t), we can calculate the ordinary interest for the loan.

In this case, the principal amount (P) is $4,000, the interest rate (i) is 12%, and the time (t) is 60 days.

Substituting the given values into the formula, we have:

I = ($4,000 x 0.12 x 60) / 365

Simplifying the expression, we get:

I ≈ $78.08

Therefore, the ordinary interest for the loan is approximately $78.08.

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Answer:

15

Step-by-step explanation:

The total sum of the squares is the sum of residual sum of squares and the explained sum of squares.

Simple regression analysis means that there is 1 dependent variable and 1 independent variable.

In this, there is 3 types of sum of squares:

They are related to each other as:

TSS = RSS + ESS

That is the total sum of the squares will be equal to the residual sum of squares plus the explained sum of squares.

Therefore, we get that, the total sum of the squares is the sum of residual sum of squares and the explained sum of squares.

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The cost of one pair of earing will be £8.59.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that four friends, each bought matching necklaces and two pairs of earrings the necklace was priced at 15.00 if the total bill for all 4 friends was 128.00.

The cost of one pair of earing will be,

£128-£15-£15-£15-£15= £68

Number of pairs of earing,

2x4=8 pairs of earrings

The cost of one pair of earrings is,

£68 / 8 = £8.50

Therefore, the cost of one pair of earing will be £8.59.

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Answer:

SAS, ASA, and AAS

Step-by-step explanation:

SSA, AAA are NOT Theorems. SSS requires three sides and HL requires the triangles to be a right triangle (90 degrees).

Also, the two triangles forms Vertical angles.

Step-by-step explanation:

The correct statement in the following is b. The variance of a random walk process increases as a linear function of time. This is because of the fact that it keeps adding the variance of the next increments to the variability we have in getting to where we are now.

The value of 'x' that satisfies the equation 6.4x2.5 + 4.41 ÷ 2.1 ÷ x = 26 is 0.9.

To solve this equation, we need to use the order of operations (PEMDAS) and follow the steps below:

First, we perform the division: 4.41 ÷ 2.1 = 2.1

Then, we perform the division by 'x': 2.1 ÷ x = 2.1/x

Next, we multiply 6.4 and 2.5: 6.4 x 2.5 = 16

Now we substitute the results from steps 2 and 3 into the equation: 16 + 2.1/x = 26

We then subtract 16 from both sides: 2.1/x = 10

We multiply both sides by x: 2.1 = 10x

Finally, we divide both sides by 10: x = 0.9

Therefore, the value of 'x' that satisfies the equation is 0.9.

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The area of the parallelogram in the diagram given is: 1,330 in.²

Area of a parallelogram = (base × height)

Given the following dimensions of the parallelogram:

Base = 38 in.

Height = 35 in.

Area of the parallelogram = 38 × 35

Area of the parallelogram = 1,330 in.²

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Answer

x^2      -    y^2     x4    

0.25           9

The number of problems which are finished by Liam from his homework sheet when his homework contains 40 problems is 32.

Percentage of a number is the part of the whole number which is expressed in the fraction of hundredth. It is represented with "%" symbol.

Jenny has finished 20 of the 25 math problems on her homework sheet. Thus, the total percentage of problems he finished is,

\(n=\dfrac{20}{25}\times100\\n=80\%\)

Liam has finished the same percent of problems from his homework sheet which is 80%. His homework contains 40 problems. Thus, the number of problems has Liam finished,

\(x=\dfrac{80}{100}\times40\\x=32\)

Hence, the number of problems which is finished by Liam from his homework sheet when his homework contains 40 problems is 32.

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The equation of the normal line to the curve at the point (1, 3) is y = 2x + 1.

To find the equation of the normal line to the curve at the point (1, 3), we need to first find the slope of the tangent line at this point. We can do this by taking the derivative of the equation of the curve with respect to x and evaluating it at (1, 3):

2x + 4y(dy/dx) - 4 - 6x(dy/dx) - 6y = 0

Simplifying and solving for dy/dx, we get:

dy/dx = (x - 2y)/(2x - 6)

At the point (1, 3), we have:

dy/dx = (1 - 2(3))/(2(1) - 6) = -1/2

This is the slope of the tangent line at (1, 3). The normal line to the curve at (1, 3) will be perpendicular to the tangent line and will therefore have a slope of 2 (the negative reciprocal of -1/2).

So, the equation of the normal line can be written in point-slope form as:

y - 3 = 2(x - 1)

Simplifying, we get:

y = 2x + 1

Therefore, the equation of the normal line to the curve at the point (1, 3) is y = 2x + 1.

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Answer:

• The amount invested at 6% is $1,150.

• The amount invested at 12% is $1,750.

Explanation:

Let the amount invested at 6% = x

Kelvin has $600 more in the 12% account, therefore:

The amount invested at 12% = $(x+600).

The total interest is $279.

We solve the equation for x.

The amount invested at 6% is $1,150.

The amount invested at 12% is:

The amount invested at 12% is $1,750.

Answer:

1,300 children

Step-by-step explanation:

40%=0.4

so

520÷0.4=1300

Answer:

\(8(156 \times 1.1) + 12(156 \times 1.2) \)

Answer:23.4$

Step-by-step explanation:

Answer:

x is less than or equal to 7

Step-by-step explanation:

The correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A correlation coefficient measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient of 0.90 indicates a strong positive linear correlation between happiness and GPA of high school students.

A positive correlation means that as one variable (in this case, happiness) increases, the other variable (GPA) also tends to increase. The magnitude of the correlation coefficient, which ranges from -1 to 1, represents the strength of the relationship. A value of 0.90 indicates a very strong positive linear correlation, suggesting that there is a consistent and significant relationship between happiness and GPA.

This means that as the level of happiness increases among high school students, their GPA tends to be higher as well. The correlation coefficient of 0.90 suggests a high degree of predictability in the relationship between these two variables.

It is important to note that correlation does not imply causation. While a strong positive correlation indicates a relationship between happiness and GPA, it does not necessarily mean that one variable causes the other. Other factors or variables may also influence the relationship between happiness and GPA.

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Answer:

use a z* value accurate to TWO places for this problem. (Not z = 2)

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

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