Mel slides down waterslide A,
and Victor slides down waterslide B. After 2 seconds, Mel was 50 feet in
the air, and after 5 seconds, she was 35 feet in the air. After 1 second, Victor was 60 feet in the air, and
after 4 seconds, he was 50 feet in the air. Who was descending at a
faster rate?
Mel: (2, 50) and (5, 35)
Victor: (1, 60) and (4, 50)
Mel's rate of change is
second.
That means that her height in the air decreases
feet every
Victor's rate of change is
second.
That means that his height in the air decreases _
feet every
DONE
Intro
0 000

Answer:

20- gon

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

given the sum of the interior angles is  3240° , then

180° (n - 2) = 3240 ( divide both sides by 180° )

n - 2 = 18 ( add 2 to both sides )

n = 20

then the polygon is a 20- gon

The answers are :- 1) Δ ABC ~ Δ DEF, by AA rule and 2) Δ RTS and Δ MQP are not similar.

Similar triangles are the triangles that look similar to each other, but their sizes might not be exactly the same.

Given are two pairs of triangles, we need to determine if they are similar or not,

1) Δ ABC and Δ DEF :-

We know that, the sum of the interior angles of a triangle is 180°,

Therefore,

∠ A + ∠ B + ∠ C = 180°

60° + ∠ B + 79° = 180°

∠ B = 180°-139°

∠ B = 41°

In Δ DEF,

∠ F = 79° and ∠ E = 60°

That means,

∠ B ≅ ∠ F and ∠ E ≅ ∠ C

Since, we get two corresponding angles congruent,

Therefore, by the definition of similar triangles,

Δ ABC ~ Δ DEF, By AA rule.

2) Δ RTS and Δ MQP :-

∠ R ≅ ∠ M

RT / MQ = TS / QP = 4 / 5

RS / MP = 20 /26 = 10 / 13

That means,

RT / MQ = TS / QP ≠ RS / MP

Since, we have a condition in similarity, that if, in two triangles two corresponding sides are in equal ratio, and an angle between these sides are congruent then the triangle are similar by SAS rule,

But the angle R and angle M is not in between the sides having equal ratio,

Therefore, Δ RTS and Δ MQP are not similar.

Hence, the answers are :- 1) Δ ABC ~ Δ DEF, by AA rule and 2) Δ RTS and Δ MQP are not similar.

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Given the data on the length of the metacarpal bone (X) and the height (Y) of 22 sets of skeletal remains, we are asked to find the random variables, the equation of the best-fitting line (least squares regression equation), interpret the slope and Y-intercept, predict the height for a given length of metacarpal, and compute the residual for a specific data point (47, 172).

(a) The random variables are X (length of metacarpal) and Y (height).

(c) To find the equation of the best-fitting line, we need to perform linear regression. Using the given data, we calculate the slope (β₁) and the Y-intercept (β₀) of the regression line. The equation will be in the form ^Y = β₀ + β₁X.

(d) The slope (β₁) represents the expected change in Y (height) for every 1-unit increase in X (length of metacarpal). Its interpretation will include the units of Y divided by the units of X.

(e) The Y-intercept (β₀) represents the expected height when X (length of metacarpal) is 0. The interpretation will include the units of Y.

(g) To compute the residual for the ordered pair (47, 172), we substitute X = 47 into the regression equation ^Y = β₀ + β₁X and subtract the actual Y-value (172). The residual is the difference between the predicted and observed Y-values.

To provide specific numerical values for the equations and predictions, the original data and calculations are needed.

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Use the direct comparison test to determine the convergence or divergence of the series, [infinity]∑n=0 7^n/8^n+ 5 ≤ [infinity]∑n=0 7^n/8^n. The series converges.

To use the direct comparison test, we need to find a series whose terms are smaller than the given series and which we know to converge or diverge.

Note that for n ≥ 0, we have:

7^n / 8^n+5 ≤ 7^n / 8^n

This is because 8^n+5 is greater than 8^n, so dividing by the larger denominator gives a smaller result.

Now, we know that the series:

[infinity]∑n=0 7^n/8^n

converges, since it is a geometric series with ratio 7/8 which is less than 1.

Therefore, by the direct comparison test, the given series:

[infinity]∑n=0 7^n/8^n+5

must also converge, since each term is smaller than the corresponding term in the convergent series.

Hence, we can conclude that:

[infinity]∑n=0 7^n/8^n+ 5 ≤ [infinity]∑n=0 7^n/8^n

and therefore, the given series converges.

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Answer:

\(\mathrm{Factoring}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}\)

Step-by-step explanation:

This is a particularly tough question. It involves polynomial division(a real laborious process) and solving using quadratic formula.

I presume your school has provided you the resources for both.

Anyways, here goes a brief explanation

To find the roots(zeros) of a polynomial, \(f(x)\) , set \(f(x) = 0\)  and solve for values of \(x\)

In general, if \(a\) is a zero of \(f(x)\), then \(f(x) \div(x-a)\)  will leave no remainder. In other words, it is a factor of the polynomial. It also means \(x - a = 0\)

The given polynomial is  \(4 x^{3} - 15 x^{2} - 31 x + 30\)

We are given that \(- 2\)  is a zero of \(f(x)\). This simply means that \(f(-2) = 0\)

Plugging \(-2\) into the function gives

\(f(-2) = 4(-2)^3 -15(-2)^2 - 31x + 30\\\\ = 0 =4\left(-8\right)-15\cdot \:4-31\left(-2\right)+30\)

Which indeed is 0

Here \(a = -2\) , so \(x - (-2)\) which is \(x + 2\) is a factor of\(f(x)\). It also means that
\(x-(-2) = 0 \;or\; x + 2 = 0\)

Steps to factor the polynomial \(4 x^{3} - 15 x^{2} - 31 x + 30\) :

Multiplying both sides of the above by \(4\) gives \(4x -3 = 0.\) So \(4x-3\) is the third factor, replacing \(x - \dfrac{3}{4}\)

The factors of \(4 x^{3} - 15 x^{2} - 31 x + 30\)
are:

\(x+2, x-5 \;and \;4x-3\)

Answer:
\(\mathrm{Factor}\:4x^3-15x^2-31x+30:\quad \boxed{\left(x+2\right)\left(4x-3\right)\left(x-5\right)}\)

Use a polynomial division calculator which you can find on the web and a quadratic formula calculator (on the we or on your own calculator)

Answer:

Ok i will try if i can do it

With one package (less actually) she can fill the 48ft^2 of the rectangular area.

We know that Sandy needs 7.8 square feet of space per hyacinth bulb, and the hyacinth bulbs are sold in packages of 8.

The rectangular region has a surface area of:

A = 8ft*6ft = 48 ft^2

The number of hyacinth bulbs that she can put in that surface is:

N = (48 ft^2/7.8 ft^2) = 6.15

So with 6 hyacinth bulbs, she can almost complete the rectangular area, and on each package there come 8 of them, so with one package she should be fine.

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Answer:

The answer is 7 PACKAGES

Step-by-step explanation:

I took the test!

Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Option a. calculate a correlation coefficient is the right response because a correlation coefficient measures the strength and direction of the relationship between two interval level variables.

This is because a correlation coefficient measures the strength and direction of the relationship between two interval level variables. It provides a numerical value that ranges from -1 to 1, where -1 indicates a strong negative correlation, 0 indicates no correlation, and 1 indicates a strong positive correlation.

A scatter plot is also useful in visualizing the relationship between two variables, but it does not provide a numerical value like the correlation coefficient. A test of significance and variance calculation are not typically used as first steps in assessing the relationship between two variables.

Hence, option a. calculate a correlation coefficient is the correct answer.

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Answer:

a

Step-by-step explanation:

The rules that defines the graphed function include the following: B. y = x + 2; y = 5

By critically observing the graph, we can logically deduce that the function represents a piecewise-defined function and there are two lines on this graph.

The first line has the following points;

(0, 2) and (3, 5)

Therefore, we would express 2 and 5 as a sum of 2 as follows;

(0, 0 + 2) and (3, 3 + 2)

This ultimately implies that, the y-value is the sum of 2 and the x-value:

y = x + 2

The other line has a constant y-value of 5 for any or all x-values:

y = 5

In conclusion, the rules that defines the graphed function are y = x + 2 and y = 5

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Answer:

a=25 , b=14

Step-by-step explanation:

Step-by-step explanation:

Let,

Ankit's age = x

So, ankit's father's age = 3x + 5

Given,

Age of Ankit's father's age = 50

Therefore,

By the problem,

=> 3x + 5 = 50

=> 3x = 50 - 5

=> 3x = 45

\( = > x = \frac{45}{3} \)

=> x = 15

Hence,

Present age of Ankit is 15 years (Ans)

Answer: 1. Dilation.

Step-by-step explanation: All of these transformations do not change the shape's form except for a dilation. It is nessacary to change the shape, so it is a dilation.

1. 4 and 8 ==》 corresponding angles

_____________________________

2. 5 and 6 ==》 linear pair angles

_____________________________

3. 2 and 8 ==》 alternate exterior angles

_____________________________

4. 3 and 6 ==》 same side interior angles

_____________________________

5. 2 and 4 ==》 vertical angles

Answer:

If I am understanding the question correctly, every 6 feet in real life will be equivalent to 1 inch "on paper", or in the blueprint. Using dimensional analysis, which is a methodology for converting from one unit to another, we have:

18 feet * 1 inch / 6 feet = 3 inches

On the other axis,

24 feet * 1 inch / 6 feet = 4 inches

Therefore, the blueprint for this 18x24 foot room, with a scale of 6 feet:1inch, should be 3x4 inches.

Solid transformation is a method that requires a change in the length of sides of a given shape or a change in its orientation. Thus the required answers are:

i. Yes, line segment AB is the same as line segment CD.

ii. This implies that translation does not affect the length of a given line, but there is a change in its location.

Solid transformation is a method that requires a change in the length of sides of a given shape or a change in its orientation. Some types of transformation are reflection, translation, dilation, and rotation.

Thus in the given question, translation would not affect the length of line segment AB, thus line segment AB and CD are the same. Also, A translated line segment would have the same length as its object, but at another location.

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Answer:

1. 90 degrees because of supplementary angles

2. 180 degrees

3. 90 degrees

4. 37 degrees, since the sum of the interior angles add to 180, 180-90-53 = 37.

5. 127 degrees, supplementary angles 180-53

6 . 23 degrees, use the triangle sum theorem 180-30-127

(a) Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

(b) Where both players are indifferent between their available strategies.

(c)  The normal form representation of the game is above.

(d) No player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

(a) To derive the best response functions, we need to find the strategies that maximize the payoffs for each player given the mixed strategy of the other player.

Player Row's best response function:

If Player Column chooses L with probability q, Player Row's expected payoff for choosing U is 0q + 2(1-q) = 2 - 2q.

If Player Column chooses R with probability 1-q, Player Row's expected payoff for choosing U is 0*(1-q) + 1*q = q.

Therefore, Player Row's best response is given by:

BR_Row(q) = { U if q < 1/3, D if q > 1/3 (indifferent if q = 1/3)

Player Column's best response function:

If Player Row chooses U with probability p, Player Column's expected payoff for choosing L is 0p + 2(1-p) = 2 - 2p.

If Player Row chooses D with probability 1-p, Player Column's expected payoff for choosing L is 0*(1-p) + (-1)*p = -p.

Therefore, Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

Plotting the best response functions on a graph with p on the horizontal axis and q on the vertical axis will result in two line segments: BR_Row(q) is horizontal at U for q < 1/3 and horizontal at D for q > 1/3, while BR_Column(p) is vertical at L for p < 1/2 and vertical at R for p > 1/2.

The two segments intersect at the point (p, q) = (1/2, 1/3).

(b) To find the Nash equilibria, we look for the points where the best response functions intersect. In this case, the only Nash equilibrium is at (p, q) = (1/2, 1/3), where both players are indifferent between their available strategies.

Now let's move on to the rock-paper-scissors-lizard game:

(c) The normal form representation of the game can be written as follows:

    R    P    S    L

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

R | 0,0 -1,1 1,-1 1,-1

P | 1,-1 0,0 -1,1 1,-1

S | -1,1 1,-1 0,0 -1,1

L | -1,1 -1,1 1,-1 0,0

(d) To find the Nash equilibria, we look for any strategy profiles where no player can unilaterally deviate to improve their payoff.

In this game, there are no pure strategy Nash equilibria since each strategy can be countered by another strategy with a higher payoff.

However, there is a mixed strategy Nash equilibrium where each player chooses their actions with equal probabilities: r = p = s = l = 1/4.

In this case, no player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

In summary, the rock-paper-scissors-lizard game has a unique mixed strategy Nash equilibrium where each player randomly chooses their actions with equal probabilities.

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There are 1,120 different ways to order an egg, a pancake with a choice of syrup, and a beverage.

Given data: 4 different ways to have an egg cooked, 7 different choices of pancakes, 5 different types of syrups and 8 different beverages.The total number of different ways are there to order an egg, a pancake with a choice of syrup, and a beverage can be calculated as follows: Multiplying the number of choices for each item together.

That is 4 ways to have an egg cooked x 7 choices of pancakes x 5 choices of syrup x 8 beverages= 4 x 7 x 5 x 8= 1120 Thus, there are 1,120 different ways to order an egg, a pancake with a choice of syrup, and a beverage.

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Since the variable of interest is the proportion of employees who participate in volunteer activities, the data is categorical (either "participates" or "does not participate").  Option A is Correct.

To find the appropriate inferential statistic for this scenario, we need to consider two factors: the type of data and the sample size.

Additionally, since the sample size is relatively large (n = 60), we can assume that the sampling distribution of the proportion is approximately normal, even if the population distribution is not.

Based on these factors, the appropriate inferential statistic for this scenario would be a confidence interval for the population proportion. This would allow us to estimate the range of plausible values for the true proportion of employees who participate in volunteer activities, based on the sample data.

We could also calculate a hypothesis test to determine if the sample proportion is significantly different from a hypothesized population proportion, but this would require us to specify a null hypothesis and alternative hypothesis, and to choose a significance level. Without more information about the research question and goals of the survey, it is difficult to determine if a hypothesis test would be appropriate or necessary. Option A is Correct.

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Correct Question:

A bank surveyed all of its 60 employees to determine the proportion who participate in volunteer activities. Which of the following statements is true?

A. The bank should not use the data from this survey because this is an observational study.

B. The bank can use the result of this survey to prove that working for the bank causes employees to participate in volunteer activities.

C. The bank did not select a random sample of employees, so the survey will not provide the bank with useful information.

D. The bank would have to use the survey data to construct a confidence interval in order to estimate the proportion of employees who participate in volunteer activities.

E. The bank does not need to use an inference procedure to determine the proportion of employees who participate in volunteer activities because the survey was a census of all employees.

Answer: \(\frac{1}{3}\)

Step-by-step explanation:

The formula to find slope is \(m=\frac{y_2-y_1}{x_2-x_1}\). We have to plug our 2 points into the values.

\(m=\frac{7-8}{4-7} =\frac{-1}{-3} =\frac{1}{3}\)

So our slope is \(\frac{1}{3}\)

Answer:

1 | noun | a message that is stated or declared; a communication (oral or written) setting forth particulars or facts etc

2 | noun | a fact or assertion offered as evidence that something is true

3 | noun | (music) the presentation of a musical theme

4 | noun | a nonverbal message

5 | noun | the act of affirming or asserting or stating something

6 | noun | (computer science) a line of code written as part of a computer program

7 | noun | a document showing credits and debits

(7 meanings)

Answer:

D

Step-by-step explanation:

the three main trig functions are

sin = opposite / hypotenuse

cos = adjacent / hypotenuse

tan = opposite / adjacent

( opposite = side opposite of angle , hypotenuse = longest side and adjacent = other side )

Sin(55) = a/c as side a is opposite of the angle and c is the hypotenuse so D might be the answer

cos(55) would be b/c as the adjacent of that angle is b and the hypotenuse is c. B and C show the wrong ratios so B and C can't be the answer

tan(55) would be a/b as side a is opposite of the angle and b is the adjacent, A says c/a which is wrong

so we can conclude the answer is D

The circumference of a gazebo is 47.1 ft

To calculate the circumference, you can use the formula C=2πr. This formula states that the circumference of a circle is equal to two times the constant π (approximated as 6.28) multiplied by the radius of the circle. The radius of a circle is equal to half of the diameter, so in this case the radius would be 7.5 ft (half of 15 ft).

Therefore, to calculate the circumference of a gazebo with a diameter of 15 ft, you can use the formula C=2πr. Plugging in the radius of 7.5 ft, the equation would become C=2π(7.5) which results in a circumference of 47.12 ft. To round this answer to one decimal place, the final answer is 47.1 ft

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The expression represents a polynomial with three terms.

A polynomial is an expression consisting of variables (often denoted by x, y, z, etc.) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can be used to express a wide range of algebraic equations, from simple linear equations to more complex equations. Polynomials can also be used to construct functions with properties that are useful for solving real-world problems.

The expression represents a polynomial with three terms.

The constant term is -1, and the leading coefficient is 8. The leading term is 8x³.

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Answer:

hope that will help you

Given:

The above expression can be expressed as,

Answer:

y = 58.4 when x = 9

Step-by-step explanation:

Here y = 98 - 4.4x, and x = 9.  We are to find the value of y.

Substituting 9 for x, we get:

          y = 98 - 4.4(9), or

          y = 98 - 39.6, or

           y = 58.4

y = 58.4 when x = 9