A dolphin dives down into the ocean and resurfaces along a path that is modeled by x2 – 16x – 8y = 0, where the distances are in feet. How many feet is the dolphin from its starting point along the water's surface? (5 points)

The construction that the figure represents is perpendicular bisector

A perpendicular bisector is a line that cuts through the intersection of two other line segments at a right angle.

So, a perpendicular bisector always splits a line segment through its middle, as we can see. By definition, the word "bisect" denotes an even or uniform division.

Perpendicular Bisector Properties for AB in the figure

It cuts AB in half, or into two equal halves.

It is perpendicular to AB or at right angles to it.

The distance between each point along the perpendicular bisector from points A and B is equal.

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answer: Mean:5

median:4

range: 9

mode: 2

Step-by-step explanation:

Answer:

That looks correct to me!

The region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative

Without calculation we need to state if the each of the integrals below are positive, negative, or zero. let d be the region inside the unit circle centered at the origin

xeˣ is positive for positive , and negative for negative , but the exponential factor makes the positive part dominating, so that the integral over D is positive overall.

The integrals over B and T are identical by symmetry, and both are equal to half the value of the integral over D, so they are both positive as well.

The integral over L is negative because it takes strictly non-positive values of x .

Similarly, the integral over R is positive because it considers non-negative values of x.

Therefore, the region inside the unit circle centered at the origin is 1. positive 2. positive 3. positive 4. positive 5. negative

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We can prove the formula given in the question as a theorem using the truth table method.

A Truth Table is referred to as a logic table that can be used to perform logic functions with some formulas. The logic functions that can be performed include Boolean algebra.

Let A, B, and C represent propositions. We construct a truth table as follows:

A B C (A → (B − C)) (B → (A → C))

T T T T T

T T F T F

T F T T T

T F F T T

F T T T T

F T F T T

F F T T T

F F F T T

From the truth table, we can see that the formula holds for all possible truth values of A, B, and C. Therefore, the formula is a theorem.

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CSC 23° can be written as sec 67° in as its cofunction.  

A branch of mathematics called trigonometry in geometry focuses on the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to angles and sides.

The six trigonometric ratios are sin, cos, tan, cot, cosec, and sec.

From Trigonometrical Ratios of (90° - θ)

=> sin (90° - θ) = cos θ

=> cos (90° - θ) = sin θ

=> tan (90° - θ) = cot θ

=> csc (90° - θ) = sec θ

=> sec (90° - θ) = csc θ

=> cot (90° - θ) = tan θ

Here we have CSC 23°

Here we need to write csc 23° into its cofunction

From Trigonometrical Ratios of (90° - θ)

csc (90° - θ) = sec θ

23° can be taken as (90 - 67)°  

=>  csc 23° = csc (90 - 67)° = sec 67°    

Therefore,

CSC 23° can be written as sec 67° in as its cofunction.

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The differential equation that can represent all circles in the xy plane is given as follows:

[tex]\frac{dy}{dx} = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]

The equation of a circle of center (h,k) and radius r is given as follows:

(x - h)² + (y - k)² = r².

The equation can be arranged to isolate the variable y as follows:

(y - k)² = r² - (x - h)²

y - k = square root (r² - (x - h)²)

y = square root (r² - (x - h)²) + k

To obtain the differential equation, then this equation must be differentiated towards variable x as follows:

[tex]\frac{dy}{dx} = \frac{d}{dx}(\sqrt{r^2 - (x - h)^2} + k)[/tex]

Applying the chain rule, along with the derivative for the square root, we have that:

[tex]\frac{d}{dx}(\sqrt{r^2 - (x - h)^2} + k) = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]

Meaning that the differential equation is given as follows:

[tex]\frac{dy}{dx} = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]

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The linear equation obtained is y = 0.3X + 18.3

A linear equation is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x represents an unknown variable. The solutions of linear equations are often graphed on a coordinate plane, forming a straight line. Linear equations can be used to model many real-world situations, such as population growth, the rate of change of a physical quantity, or the total cost of an item. Linear equations can also be used to solve systems of equations, where several equations must be solved simultaneously.

Given that data :
x = year ;
y = trunk diameter, in inches
Year ________trunk diameter
1 __ 18.6
3 __ 19.2

5 __ 19.8
7 __ 20.4
9 ___21.0
11 __ 21.6
13 __ 22.2
Using the linear regression calculator :
The linear equation obtained is :
y = 0.3X + 18.3
Where ;
Slope = 0.3 ; intercept, c = 18.3

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From the the graph f(x) = -x-3

Part a

The value of f(-4) = 1

Part b

The value of f(5) = -8

Part c

The value of f(0) = -3

The function is given that

f(x) = -x-3

The function is the mathematical statement that shows the relationship between the independent variable and dependent variable. The function consist of the different variables, numbers and mathematical operator.

The function is

f(x) = -x - 3

Part a

The value of f(-4)

Substitute the value of x in the function

f(-4) = - (-4) - 3

= 4 - 3

= 1

Part b

The value of f(5)

f(5) = -5 - 3

= -8

Part c

The value of f(0)

f(0) = -0 - 3

= -3

Therefore, the value of f(-4), f(5) and f(0) are 1, -8 and -3 respectively

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Answer: x = 1, y = -1

Step-by-step explanation:

      To solve this system by elimination, we will set it up so both of the y, or x, variables have opposite coefficients.

3x - 5y = 8

2x+ 3y = -1

3(3x - 5y = 8)

5(2x+ 3y = -1)

9x - 15y = 24

10x + 15y = -5

      The 15y and -15y cancel each other out, so we're left with 9x + 10x on the left side and 24 - 5 on the right side of the equation.

19x = 19

x = 19/19

x = 1

      Now, we will plug this back into one of the equations to solve for y.

3x - 5y = 8

3(1) - 5y = 8

3 - 5y = 8

-5y = 5

y = -1

Answer:1/4 (I think)

Answer:

g = 18(1/3)

Step-by-step explanation:

The sub is made of 18 sections of 1/3, so it is 18(1/3) feet long (or 6ft when simplified)

f 57 and 63 are the 90% confidence limits for the population mean, then [60, 60] might be the 97% confidence limit.

A population is a discrete collection of things having observable traits, such humans or animals, for the purpose of analysis and data collection. It is made up of a comparable collection of species that live in a specific area and have the ability to interbreed.

The average calculated from the whole population, distribution, or group is known as the population mean. It is calculated by dividing the total number of population variables by the sum of all population variables. The population mean can be found here as. Observations in the population are added together to form X.

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Answer:

(−3, 2); 2 < y < ∞

Step-by-step explanation:

It's either (−3, 2); 2 < y < ∞ or (−3, 2); −∞ ≤ y < ∞ but I'm pretty sure its (−3, 2); 2 < y < ∞

The expression 2 3/5 ÷ 5 3/8 given is written in simplest form as  104/215

The problem is a division problem in mixed numbers

converting to improper fractions we have

= 2 3/5 ÷ 5 3/8

= 13/5 ÷ 43/8

inverting the divisor to change to multiplication

= 13/5 ÷ 43/8

= 13/5 * 8/43

= 104/215

The division problem is simplest form give 104/215

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Opposite sides of a parallelogram are equal.

Opposite sides of a parallelogram are equal in the second case

RT is congruent to RT is obvious.

ΔRST and ΔRUT are congruent because a diagonal of a parallelogram divides it into two congruent triangles.

We know pair of interior alternate angles are equal.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, Line segment TU is congruent to line segment RS because in a parallelogram opposite are equal same reason for line segment RU and ST.

We also know that the diagonal of a parallelogram divides the parallelogram into two equal triangles hence ΔRST and ΔRUT are congruent.

We also know that the pair of alternating angles are equal hence,

∠RST and ∠TRU are congruent.

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a) The distribution of X is a discrete geometric distribution with pmf p(x) = (5/36)(1/6)^(x-1).b) The theoretical mean (mu) of X is 6.c) The theoretical variance of X is 35.d) The expected value of Y is 6 and the variance of Y is 3.875.

The distribution of X is a discrete geometric distribution, which means that the probability of X taking on any particular value is given by the formula p(x) = (5/36)(1/6)^(x-1). The theoretical mean (mu) of X is 6, which means that on average it should take 6 trials to obtain a sum of 7. The theoretical variance of X is 35, which means that there is a considerable amount of variability in the number of trials needed to obtain a sum of 7. If we consider the random variable Y, the average number of trials needed to roll a sum of 7 based on 25 trials, then the expected value of Y is 6 and the variance of Y is 3.875. This indicates that the average number of trials needed to obtain a sum of 7 is 6 and that the variability decreases as more trials are taken.

a) p(x) = (5/36)(1/6)^(x-1)

b) theoretical mean (mu) of X mu = 6

c) Var(X) = (5/36)*∑x=1∞(1/6)^(x-1)^2 - mu^2

       = (5/36)*(1-1/36^2) - 6^2

       = 35

d) The expected value of Y , E(Y) = 6

Var(Y) = Var(X/6)

       = Var(X)/6^2

       = 35/6^2

       = 3.875

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The randomized variable's sample distribution would be as follows: H+/- 1.96 * √3)/√n

A random variable in mathematics would be a variable for whom the value is the numerical result of an unpredictable event and a random number generator X on a sample space. S denotes the rule that gives each of the outcomes S in a collection a numerical value.

In this case, we have assumed that x is a constant random variable with values ranging from 0 to 3, but we are unsure of its distribution, mean, or variance.

The mean of x, which we designate by the letter h, is what we're now interested in estimating. To provide a conservative estimate (upper bound), we'll choose 1.5 for the standard deviation of x.

In this case, we must estimate h. To do this, we select the sample size n, the samples x1, x2,.., xn, all of which share the same dissemination as x, and accurately measure the sample mean.

Therefore, we have used a normal distribution to determine the variation of x as (0,6),

And it equals to 3, then apply CLT resulting in

=> H+/- 1.96 * √3)/√n

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Answer:

[tex]\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]

Step-by-step explanation:

Given:

[tex]\tan \left(\sin^{-1}\left(\dfrac{x}{2}\right)\right)[/tex]

[tex]\boxed{\begin{minipage}{5cm}\underline{Trigonometric Identity}\\\\$\tan(\arcsin(x))=\dfrac{x}{\sqrt{1-x^2}}$\\ \end{minipage}}[/tex]

Use the tan(arcsin(x)) trigonometric identity and replace x for (x/2):

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\left(\dfrac{x}{2}\right)^2}}[/tex]

Simplify the denominator:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{1-\dfrac{x^2}{4}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\sqrt{\dfrac{4-x^2}{4}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{\sqrt{4}}}}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{\left(\dfrac{x}{2}\right)}{\dfrac{\sqrt{4-x^2}}{2}}}[/tex]

[tex]\textsf{Apply the fraction rule}: \quad \dfrac{\frac{a}{c}}{\frac{b}{c}}=\dfrac{a}{b}[/tex]

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}}[/tex]

Multiply the numerator and denominator by the denominator to eliminate the radical from the denominator:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x}{\sqrt{4-x^2}} \cdot \dfrac{\sqrt{4-x^2}}{\sqrt{4-x^2}}[/tex]

Simplify:

[tex]\implies \tan\left(\arcsin \left(\dfrac{x}{2}\right)\right)=\dfrac{x\sqrt{4-x^2}}{4-x^2}[/tex]

The true statements are as follows

This is a chi-square test for association

The null and alternative hypothesis is

The null hypothesis is that here is no association between state and sporting preference.

The alternative hypothesis is that there is an association between state and sporting preference.

as given in the question

a survey was conducted with large group of teenagers from

6 different states.

let the portion of teenagers who selected the sports most preferred as (p)

(p1) as the the teenagers that for state 1

(p2) as for the teenagers that for state 2

(p3) as for the teenagers that for state 3

(p4) as for the teenagers that for state 4

(p5) as for the teenagers that for state 5

(p6) as for the teenagers that for stage 6

the formula of chi-square test is

[tex]\chi^2=\sum\frac{(O_i-E_i)^2}{E_i}[/tex]

where

[tex]O_i[/tex] is the observed value

[tex]E_i[/tex] is the expected value

[tex]\chi^2[/tex] is chi squared value

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Note:

The full question is

A survey was conducted with a large group of teenagers from 6 different states and it asked them for their favorite sport out of a large list of sports. The study aims to look at whether a teenager's state of residence is associated with their sporting preferences.

Assume that p is the proportion of teenagers who selected the sport most preferred in their state of residence, such that p1 is that for State 1 , p2 is that for State 2 and so on.

Select from the following all statements that are true as well as the hypothesis that corresponds to this study:

[tex]This\ is\ a\ chi-square test for association.& \mathrm{H}_0: \mathrm{p}_1 \neq \mathrm{p}_2 \neq \ldots \neq \mathrm{p}_6 \\& \mathrm{H}_{\mathrm{a}}: \mathrm{p}_1 \neq \mathrm{p}_2 \neq \ldots \neq \mathrm{p}_6 \\& \mathrm{H}_0: \mathrm{p}_1=\mathrm{p}_2=\ldots=\mathrm{p}_6$\mathrm{H}_0$ : There is no association between state and sporting preference. $\mathrm{H}_{\mathrm{a}}$ : There is an association between state and sporting preference. This is a one-way ANOVA test for equality of means.[/tex]

[tex]$\mathrm{H}_0$ : There is an association between state and sporting preference.$\mathrm{H}_{\mathrm{a}}: \mathrm{p}_1=\mathrm{p}_2=\ldots=\mathrm{p}_6$$\mathrm{H}_{\mathrm{a}}$ : There is no association between state and sporting preference.[/tex]

Answer:

[tex]x=-6[/tex]

Step-by-step explanation:

Solve for x.

Combine [tex]x[/tex] and [tex]\frac{1}{6}[/tex].

Combine [tex]x[/tex] and [tex]\frac{2}{3}[/tex].

[tex]-\frac{x}{6} -5=\frac{2x}{3}[/tex]

Move all terms containing x to the left side of the equation.

Subtract [tex]\frac{2x}{3}[/tex] from both sides of the equation.

[tex]-\frac{x}{6} -5-\frac{2x}{3}=0[/tex]

To write [tex]-\frac{2x}{3}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex].

[tex]-\frac{x}{6}-\frac{2x}{3}*\frac{2}{2}-5 =0[/tex]

Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.

[tex]-\frac{x}{6}-\frac{2x*2}{6}-5 =0[/tex]

Combine the numerators over the common denominator.

[tex]\frac{-x-2x*2}{6}-5 =0[/tex]

Simplify the numerator.

Factor [tex]x[/tex] out of [tex]-x-2x*2[/tex].

[tex]\frac{x(-1-2*2)}{6}-5 =0[/tex]

[tex]\frac{x(-1-4)}{6}-5 =0[/tex]

[tex]\frac{x*-5}{6}-5 =0[/tex]

Move the negative in front of the fraction.

[tex]-\frac{5x}{6} -5=0[/tex]

Add 5 to both sides of the equation.

[tex]-\frac{5x}{6}=5[/tex]

Multiply both sides of the equation by [tex]-\frac{6}{5}[/tex].

[tex]-\frac{6}{5}(-\frac{5x}{6})=-\frac{6}{5}*5[/tex]

Simplify the left side by cancelling the common factors of 5 and 6.

[tex]x=-\frac{6}{5} *5[/tex]

Move the leading negative in [tex]-\frac{6}{5}[/tex] into the numerator.

[tex]x=\frac{-6}{5} *5[/tex]

Cancel the common factor of 5.

[tex]x=-6[/tex]

A rating/review would be much appreciated. Wish you a happy holiday season!

Answer:

---------------------------------

Given equation:

Fist, multiply both sides by 6 to clear the fraction:

Collect the terms with the variable and solve for x:

The value of the missing angle of the triangle is; x = 31°

Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

Now, from the diagram, we can tell that ∠GAB is congruent to ∠CBA by alternate angles theorem.

Thus, ∠GAB = 28°

Similarly, sum of angles on a straight line = 180°. Thus;

∠EDA = 180 - (4x + x)

∠EDA = 180 - 5x

Also, sum of angles in a triangle is 180 degrees. Thus;

∠CAB = 180 - (90 + 28)

∠CAB = 62°

Thus;

62 + 3x + 180 - 5x = 180

62 - 2x = 0

2x = 62

x = 62/2

x = 31°

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On solving the provided question we can say that - mean of x mean of y

27.37136 30.73706

In statistical inference studies, an alternative hypothesis is a statement. This is represented by Ha or H1, which conflicts with the null hypothesis. It only serves as a zero replacement. The claims that researchers are investigating in hypothesis testing are alternative theories.

[tex]t = -11.067, \\df = 2301.5, \\p-value < 2.2e-16[/tex]

alternative hypothesis: true difference in means is less than 0

95 percent confidence interval:

[tex]-Inf -2.865266[/tex]

sample estimates:

mean of x mean of y

27.37136 30.73706

Conclusion:-

Here   p-value = 2.2e-16 < 0.05(Level of significance)

Therefore we reject  at 5% Loss

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Answer:

y - 8 = 2 (x - 6)

Step-by-step explanation:

The point-slope equation is ...

y - y1  = m ( x - x1 )

In the coordinate (6,8)

x = 6 and y = 8

m = 2

Plug in values to find the point-slope form

y - 8 = 2 (x - 6)

We are done!

The Greatest Common Divisor (GCD) of 85 and 51 is 17.

The greatest common factor that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Explanation

Step 1: Divide 85 by 51. The quotient is 1 and the remainder is 34.

Step 2: Divide 51 by 34. The quotient is 1 and the remainder is 17.

Step 3: Divide 34 by 17. The quotient is 2 and the remainder is 0.

Step 4: Since the remainder is 0, the Greatest Common Divisor (GCD) of 85 and 51 is 17.

The GCD of 85 and 51 is 17.

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∠4=∠6 because each pair of alternate interior angles is equal ( The two column proof is attached ).

Every two-column proof has exactly two columns. One column represents our statements or conclusions and the other lists our reasons. In other words, the left-hand side represents our “if-then” statements, and the right-hand side explains why we know what we know.

We can clearly observe here that ∠1=∠5 , ∠2=6, ∠3=∠7, ∠4=∠8 as Corresponding angles are equal.

∠4 + ∠3 = 180°……..(1) PQ is the straight line

∠6 + ∠7 = 180°……..(2) t is the straight line

therefore from the two equations we get

∠4 =∠6

Hence, ∠4  ≅∠6 ( The two column proof is attached )

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Amount of money needed to carry to the sari sari store is 59.

a) According to question

Amount of eggs to buy = 3

Rate of eggs = 8

Total amount for eggs = 3x8=24

Amount of  hotdogs to buy = 2

Rate of hotdogs = 10

Total amount to pay for hotdogs = 2x10=20

Amount of  bread to buy = 3

Rate of bread = 5

Total amount to pay for bread=3x5=15

So money needed to take to the sari sari store=24+20+15=59

b) Polynomial is 4x²+2x-3

1) x=1

  4(1)²+2(1)-3

  4+2-3

  3

2) x=2

 4(2)²+2(2)-3

 4(4)+4-3

 16+4-3

 17

3) x=3

 4(3)²+2(3)-3

 4(9)+6-3

 36+6-3

 39

4) x=5

 4(5)²+2(5)-3

 4(25)+10-3

 100+10-3

 107

5) x=6

 4(6)²+2(6)-3

 4(36)+12-3

 144+12-3

 153

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Preferred shares = 0.40/25.00 = 1.60%    

Common shares = 0.07/17.50 = 0.40%

What is stock  market?

The phrase "stock market" describes a number of marketplaces where shares of publicly traded firms can be purchased and sold. Such financial transactions take place on official exchanges and in over-the-counter (OTC) markets that adhere to a predetermined set of rules.

Year Total         Preference   Common   Dividend per

             dividend     dividend      dividend    common share

1       80000 80000 0 0.32 0.00

2       90000 90000 0 0.36 0.00

3       150000 130000 20000 0.52 0.04

4       150000 100000 50000 0.40 0.10

5       160000 100000 60000 0.40 0.12

6       180000 100000 80000 0.40 0.16

Note:       2.40 0.42

Preference dividend per year = 250000*$20*2%=  100000  

Preference dividend for the 3rd year includes arrear dividend of $20000 for the 1st year

and $10000 for the second year, in addition to the $100000 dividend of that year.

Average annual dividend per share:      

Preferred shares = 2.40/6 = $0.40      

Common shares = 0.42/6 = $0.07      

Average annual percentage return:      

Preferred shares = 0.40/25.00 = 1.60%    

Common shares = 0.07/17.50 = 0.40%

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