Hogie lizards have tail lengths that are normally distributed with a mean of 22.5 cm and a standard deviation of 3.6 cm. What tail length is at the 40th percentile for these lizards?

Given:

The given values are:

[tex]a=0.2094539899[/tex]

[tex]b=2.507467975[/tex]

[tex]r^2=0.9435996398[/tex]

[tex]r=0.9713905701[/tex]

To find:

The exponential regression equation for the given values (Rounded to three decimal places).

Solution:

The general form of exponential regression equation is:

[tex]y=a\cdot b^x[/tex]          ...(i)

Where, a is the initial value and b is the growth/decay factor.

We have,

[tex]a=0.2094539899[/tex]

[tex]b=2.507467975[/tex]

Round these numbers to three decimal places.

[tex]a\approx 0.209[/tex]

[tex]b\approx 2.507[/tex]

Substitute [tex]a=0.209, b=2.507[/tex] in (i) to find the exponential regression equation.

[tex]\hat{y}=0.209\cdot 2.507^x[/tex]

Therefore, the correct option is C.

Answer:

53 by 83.5.

just divided the two numbers by 1/4

Answer:

848 and 1336

Step-by-step explanation:

You would actually multiply 212 and 334 by 4.

You need to multiply 1/4 by 4 to get 1.

212 x 4 = 848

334 x 4 =1336

[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]

Slope: 0

y - intercept: (0, -3)

Kindly click the attached photo ^^

[tex]\color{pink}{==========================}[/tex]

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[tex]\sf\color{pink}{༄⁂✰Bae \: Yoonah}[/tex]

Let number if boys be x

ATQ

[tex]\\ \sf\longmapsto \dfrac{x+5}{x}=\dfrac{4}{3}[/tex]

[tex]\\ \sf\longmapsto 3(x+5)=4x[/tex]

[tex]\\ \sf\longmapsto 3x+15=4x[/tex]

[tex]\\ \sf\longmapsto 4x-3x=15[/tex]

[tex]\\ \sf\longmapsto x=15[/tex]

[tex]\\ \sf\longmapsto x+5=15+5=20[/tex]

9514 1404 393

Answer:

  0.75

Step-by-step explanation:

You know that ...

  P(S or T) = P(S) +P(T) -P(S and T)

When events are mutually exclusive, P(S and T) = 0. Then ...

  P(S or T) = 5/8 + 1/8 = 6/8 = 3/4

  P(S or T) = 0.75

Answer:

The relation is linear

Step-by-step explanation:

Answer:

Yes, the relationship shown is linear. The equation of the line is y=-1.25x-13.25.

Step-by-step explanation:

This data is linear as y decreases at a constant rate. The equation of a line is y=mx+b, where m=slope and b=y intercept

To find m:

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

m=[tex]\frac{(-2)-(-7)}{(-9)-(-5)}[/tex]

m=[tex]\frac{5}{-4}[/tex]

m=[tex]-\frac{5}{4}[/tex]=-1.25

To find b, you can use any of the given points:

(-9,-2)

(-2)=-1.25(-9)+b

-2=11.25+b

-2-11.25=b

b=-13.25

Therefore, using the calculated values for m and b:

y=mx+b

y=-1.25x-13.25

Answer:

Smaller Figure 3

Larger Figure 5

Scale factor = 15/25 = 3/5

Answer:

1.3809%

Step-by-step explanation:

Given ;

Sample size, n = 4500

Phat = 64% = 0.64

The margin of error :

Zcritical * √[Phat(1 - Phat) / n]

At 95% confidence level:

Zcritical at 95% = 1.96

Margin of Error :

1.96 * √[0.64(0.36) / 4500]

1.96 * 0.0071554

= 0.0138099

= 0.0138099 * 100%

= 1.3809%

9514 1404 393

Answer:

  (x, y) ⇒ (x +(-1), y +(-1))

Step-by-step explanation:

Reflection over the y-axis is the transformation ...

  (x, y) ⇒ (-x, y)

After that reflection, the figure is translated left 1 and down 1. That transformation is ...

  (x, y) ⇒ (x -1, y -1)

_____

Additional comment

The composition of the two transformations is ...

  (x, y) ⇒( -x -1, y -1)

Answer: x-1, y-1

Step-by-step explanation:

Answer:

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

p1 -> 1993

20 out of 100, so:

[tex]p_1 = \frac{20}{100} = 0.2[/tex]

[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]

p2 -> 1997

10 out of 100, so:

[tex]p_2 = \frac{10}{100} = 0.1[/tex]

[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]

Distribution of p1 – p2:

[tex]p = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower bound of the interval is:

[tex]p - zs = 0.1 - 1.645*0.05 = 0.01775 [/tex]

The upper bound of the interval is:

[tex]p + zs = 0.1 + 1.645*0.05 = 0.18225 [/tex]

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Answer:

p=-7

Step-by-step explanation:

5p=-35

Divide both sides by 5

5p/5 =-35/5

therefore p=-7

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{5p= -35}\\\\\underline{\huge\text{DIVIDE 5 BOTH SIDES}}\\\\\mathsf{\dfrac{5p}{5p}= \dfrac{-35}{5}}\\\\\large\text{CANCEL out: }\dfrac{5}{5}\large\text{ because that gives you 1}\\\large\text{KEEP: }\dfrac{-35}{5}\large\text{ because that gives you the value of p.}\\\\\large\textsf{p = }\mathsf{\dfrac{-35}{5}}\\\\\mathsf{-35\div5= p}\\\\\large\text{Simplify above and you have your result to the p-value.}\\\\\boxed{\boxed{\huge\text{Therefore your answer is: \textsf{p = -7}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

[tex]43.13 = 5.25h + 9[/tex]

Step-by-step explanation:

Let's solve this by making an equation.

$9 for the helmet, and $5.25 per hour.

h will stand for hours, C will stand for Amanda's cost.

[tex]C = 5.25h + 9[/tex]

Now, substitute in what we learned from the problem.

[tex]43.13 = 5.25h + 9[/tex]

This is an equation you can use to solve for the hours.

9514 1404 393

Answer:

  24

Step-by-step explanation:

Corresponding lengths are proportional. The ratio of the full length to the given part is ...

  (30 +x)/30 = 45/25

  1 +x/30 = 1 +4/5 . . . perform the division

  x/30 = 4/5 . . . . . . . . subtract 1

  x = 30(4/5) = 24

The missing side length is 24.

=ac-b(cosc-ccosa)

=sinc/sina

Answer: False

Step-by-step explanation:

This is because sin 0 is equal to 0 but cot 0 is equal to undefined

Given:

Minni is arranging 3 different music CDs in a row on a shelf.

To find:

The sample space for the arrangement of a jazz CD (J), a pop CD (P), and a rock CD (R).

Solution:

We know that the total number of ways to arrange n items is n!.

Minni is arranging 3 different music CDs in a row on a shelf. So, the total number of ways is:

[tex]3!=3\times 2\times 1[/tex]

[tex]3!=6[/tex]

The sample space for the arrangement of a jazz CD (J), a pop CD (P), and a rock CD (R) is:

{JPR, JRP, PJR, PRJ, RJP, RPJ}

Therefore, the required sample space is {JPR, JRP, PJR, PRJ, RJP, RPJ}.

Answer:

RPJ, JPR, PRJ, JRP, RJP, JPR.

Step-by-step explanation:

Answer:

17 instructors

Step-by-step explanation:

If each instructor will get 10 children, we have to divided the total number of children taking swimming lessons by the number of children assigned to each instructor (10):

165/10 = 16.5

Unfortunately, we can't have 16 and a half instructors. Since 5 children are remaining, we can round up 16.5 to 17 and get 17 instructors. This implies that 16 instructors will teach 10 children (160 in total) and 1 instructor will teach 5 children (5 in total). 160+5 = 165 total children.

Answer: -1

Step-by-step explanation:

sum of 2 and 3   subtracted   from the product of 2    difference of 7 and 4

            (2+3)            -                         2                                 (  7    -    4   )   =  -1  

       (2+3)-2(7-4) =

        5 - 2(3) =

         5-6 = -1

The sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4 is equivalent to 1.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4

From the question, we can model the equation as -

x = 2 × (7 - 4) - (2 + 3)

x = 2(3) - 5

x = 6 - 5

x = 1

Therefore, the sum of 2 and 3 subtracted from the product of 2 and the difference of 7 and 4 is equivalent to 1.

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Step-by-step explanation:

you cannot just put the actual numbers in and calculate ?

and you can't provide the correct problem statement, as it seems.

I assume you mean

an = 3n² - 1

a sequence starts with a1, so, n>=1

a1 = 3×1² - 1 = 3-1 = 2

a2 = 3×2² -1 = 3×4 - 1 = 12 - 1 = 11

a3 = 3×3² - 1 = 3×9 - 1 = 27 - 1 = 26

a4 = 3×4² - 1 = 3×16 - 1 = 48 - 1 = 47

a5 = 3×5² - 1 = 3×25 - 1 = 75 - 1 = 74

there, that is all there is to it. you really needed help with that ?

[tex] - | 4 | < x < - |1| [/tex]

dunno if that's the desired form tough, but it states the same definition

The given inequality rewritten using absolute value sign​ as |-4|<x<|-1|.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -4<x<-1.

An absolute value inequality is an expression with absolute functions as well as inequality signs.

Here, using absolute value sign​ we get

|-4|<x<|-1|

Therefore, the given inequality rewritten using absolute value sign​ as |-4|<x<|-1|.

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Answer:

5 %

Step-by-step explanation:

1000 g = 1 kg

50 kg = 0.05 kg

0.05 = 5%

Therefore, 50 g as a percentage of 1kg is 5%.

Answer:

Option C. √5/3

Step-by-step explanation:

We'll begin by simplifying √15 / 3√3. This can be obtained as follow:

√15 / 3√3

Rationalise

√15 / 3√3 × (√3 /√3)

(√15 × √3) / (3√3 × √3)

√45 / (3 × 3)

√45 / 9

Recall:

√45 = √(9 × 5) = √9 × √5 = 3√5

Thus,

√45 / 9 = 3√5 / 9

√45 / 9 = √5 / 3

Therefore,

√15 / 3√3 = √5 / 3

Thus, option C gives the right answer to the question.

Answer:  [tex]\$162[/tex]

Step-by-step explanation:

Given

There are 210 units of hotel

Each room charge $90 when fully occupied

occupied room charges is $24 per day

Suppose x rooms are vacant, so, there 210-x occupied

Daily expense on maintenance[tex]=(210-x)\times 24[/tex]

Earning from 210-x rooms[tex]=(210-x)(90+x)[/tex]

Profit(P)=Earning - Expense

[tex]\Rightarrow P=(210-x)(90+x)-(210-x)24\\\Rightarrow P=21,600+210x-90x-x^2-5040+24x\\\Rightarrow P=-x^2+144x+16,560\\[/tex]

To get the maximum profit, determine the derivative of P w.r.t. x and equate it to zero

[tex]\Rightarrow \dfrac{dP}{dx}=-2x+144\\\\\Rightarrow -2x+144=0\\\\\Rightarrow x=72[/tex]

Charges for maximum profit is [tex]90+72=\$162[/tex]

Number of occupied rooms are [tex]210-72=138[/tex]

The hotel charge per day will be $162  in order to maximize daily profit.

Given that,  Hotel has 210 units

Let us consider that x rooms are vacant.

Total occupied rooms = [tex](210-x)[/tex]

Since, Each occupied room costs $24 per day to service and maintain

So, Total expense = [tex]24*(210-x)=5040-24x[/tex]

Since, For  all rooms are occupied when the hotel charges $90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant.

So, Total earing = [tex](210-x)*(90+x)=-x^{2} +120x+21600[/tex]

Profit = Total earning - Total expense

[tex]P=-x^{2} +120x+21600-5040+24x\\\\P=-x^{2} +144x+16560[/tex]

In order to maximize profit, Differentiate profit expression with respect to x.

    [tex]\frac{dP}{dx}=\frac{d}{dx}(-x^{2} +144x+16560) \\\\\frac{dP}{dx}=-2x+144=0\\\\\\x=\frac{144}{2}=72[/tex]

Thus, Hotel charges per day for maximum profit = [tex]90+x=90+72=162[/tex]

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Answer: hello your question is poorly written attached below is the complete question

answer:

1 ) =  I (

2) = F

3) = Z

4) = D

Step-by-step explanation:

attached below is the required solution.

1 ) =  I ( The sequence diverges to infinity )

2) = F ( The sequence has a finite non-zero limit )

3) = Z ( The sequence converges to zero )

4) = D ( The sequence diverges )

Answer:

it should be letter c 5/3 I could be wrong but I hope this help

Step-by-step explanation:

A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.

h=-16t^2+16t+32

Answer:

216 * 80^4 * y^8 *z

Step-by-step explanation:

Just use the foil method to solve and add like terms.

Answer:

B. 7i

Step-by-step explanation:

first we need to find the root of the expression

[tex]\sqrt{-49} = \sqrt{49} *\sqrt{-1} \\ \\ \sqrt{49} = 7\\\\and\\\\ \sqrt{-1} = i[/tex]

so the answer is B. 7i