carlton emailed a link to the survey for his senior honors project and hoped to receive replies from everyone he contacted. instead, he only received 31 completed surveys from the 100 people on his list. his response rate is approximately

Based on the given information that the demand curve for hummus has a constant slope of -2, we can say that the price elasticity of demand for hummus is relatively elastic. This means that a small change in price will result in a relatively larger change in the quantity demanded of hummus.

In other words, consumers are sensitive to changes in the price of hummus and are likely to reduce their consumption if the price increases, and vice versa.

To know more about slope visit:

https://brainly.com/question/3605446

#SPJ11

The price elasticity of demand for hummus cannot be determined solely from the information provided, as it depends on both the slope and the price-quantity relationship.

The price elasticity of demand (Ed) is a measure of how responsive the quantity demanded of a good is to a change in its price. It is calculated using the formula:

Ed = (% change in quantity demanded) / (% change in price)

Since the demand curve for hummus has a constant slope of -2, this tells us that for every unit increase in price, the quantity demanded decreases by 2 units. However, to calculate the price elasticity of demand, we also need information about the price and quantity levels.

The slope of the demand curve alone does not provide enough information to determine the price elasticity of demand. The elasticity varies along the curve, being more elastic at high prices and low quantities, and less elastic at low prices and high quantities.

While the slope of the demand curve for hummus is -2, this information alone is not sufficient to determine the price elasticity of demand. Additional information about the price and quantity levels is needed to calculate the elasticity accurately.

To know more about hummus visit:

https://brainly.com/question/15269710

#SPJ11

Answer:

15625x^6y^6

Step-by-step explanation:

5^6= 5×5×5×5×5×5=15625

(xy)^6=x^6y^6

The unit rate of change of ddd with respect to ttt is 4/3.

To graph the proportional relationship between ddd and ttt, we first need to find the unit rate of change. Since an increase of 333 units in ttt corresponds to an increase of 444 units in ddd, we can calculate the unit rate as follows:

Unit Rate = (Change in ddd) / (Change in ttt) = 444 / 333 = 4/3

So, a change of 1 unit in ttt corresponds to a change of 4/3 units in ddd.

Now, let's graph the relationship. The equation representing this proportional relationship is:

ddd = (4/3)ttt

This is a linear relationship with a slope of 4/3 and passes through the origin (0,0). To plot the graph, start at the origin and use the slope to plot additional points, such as:
- For ttt = 3, ddd = 4 (since 4/3 * 3 = 4)
- For ttt = 6, ddd = 8 (since 4/3 * 6 = 8)

Plot these points and draw a straight line through them, representing the proportional relationship between ddd and ttt. The unit rate of change of ddd with respect to ttt is 4/3.

To learn more about equation, refer below:

https://brainly.com/question/29657983

#SPJ11

Answer:

where is the options? or is any given.

Step-by-step explanation:

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

Learn more about graph from

https://brainly.com/question/19040584

#SPJ11

Answer:

92

Step-by-step explanation:

83*4 = 332

And 80*3 = 240

332-240 = 92

So you would need 92

Answer:

i need help

Step-by-step explanation:

The relative frequency distribution of the three categories includes

We must get percentage of students in Yes (Y), No (N) and No Response (NR) categories to allow us to create the relative frequency distribution for the athletic department.

Data:

The total number of students surveyed is 1000.

The percentage of students who answered Yes will be:

= (Y / Total) * 100

= (733 / 1000) * 100

= 73.3%

The percentage of students who answered No will be:

= (N / Total) * 100

= (162 / 1000) * 100

= 16.2%

The percentage of students who did not respond will be:

= (NR / Total) * 100

= (105 / 1000) * 100

= 10.5%.

Read more about frequency distribution

brainly.com/question/27820465

#SPJ1

Answer:

Is already in standard form.

Leading Coefficient: -1

Step-by-step explanation:

Standard form denotes that the degrees must order form highest to lowest left to right. We see that our degrees are 3, 2, 1 and 0, so it is already in standard form.

Leading coefficient is the number in front of the highest degree term. We see that our highest degree term is y³. The number multiplied to it/in front of it is a -, or a -1, so our leading coefficient is -1.

The percentage of utility companies that earned revenue less than 3939 million or more than 6161 million dollars is 0.1484 or 14.84% (rounded to the nearest hundredth).

We can use the standard normal distribution to find the percentage of utility companies that earned revenue less than 3939 million or more than 6161 million dollars.

First, we need to standardize the values using the formula:

z = (x - μ) / σ

where x is the revenue value, μ is the mean revenue, and σ is the standard deviation.

For x = 3939 million:

z = (3939 - 5050) / 77 = -1.45

For x = 6161 million:

z = (6161 - 5050) / 77 = 1.44

Using a standard normal distribution table or calculator, we can find the probability of a value being less than -1.45 or greater than 1.44.

P(z < -1.45) = 0.0735

P(z > 1.44) = 0.0749

The percentage of utility companies that earned revenue less than 3939 million or more than 6161 million dollars is:

0.0735 + 0.0749 = 0.1484 or 14.84% (rounded to the nearest hundredth).

for such more question on percentage

https://brainly.com/question/27855621

#SPJ11

While there is agreement on the use of focus groups for evaluating brand names, there are differences in the methods proposed for identifying symbolism associated with posting selfies and searching for ideas for new applications.

In comparing my initial post with my classmate's initial post, there are both areas of agreement and disagreement regarding the research methods suggested for different scenarios.

Agreement:

Both my initial post and my classmate's post agree on the use of focus groups for evaluating potential brand names for a new app. Focus groups allow for gathering opinions and insights from individuals in a controlled environment, as my classmate mentioned. I also referenced Babin (2019) to support this method.

Disagreement:

In terms of identifying the symbolism associated with posting selfies online, I suggested using detailed interviews, while my classmate proposed depth interviews.

While both methods aim to uncover deeper motivations and intentions, my classmate specifically highlighted the need for probing and asking a series of questions. Both approaches can provide valuable insights, but the emphasis on depth interviews suggests a more targeted and focused approach.

For searching for ideas for new smartphone or tablet applications, I suggested conducting detailed interviews with target customer groups, while my classmate proposed creating an attribute list.

While my suggestion focuses on gathering specific customer preferences and needs through direct interaction, my classmate's suggestion of attribute listing involves breaking down existing products and recombining their attributes to generate new ideas. These are two different approaches to idea generation, and the choice depends on the specific context and objectives of the research.

For more such questions on agreement visit:

https://brainly.com/question/28521601

#SPJ8

Answer:

f(g(x)) = -4

Step-by-step explanation:

take 2 points in g(x)

(-6,0) (-4,-4)

g(x) = -2x - 12

g(-6) = -2(-6) - 12

g(-6) = 12 - 12 = 0

put 0 in x in f(x)

take 2 points in f(x)

(-4,0) (-2,-2)

f(x) = -x -4

f(0) = 0 - 4

f(0) = - 4

f(g(x)) = -4

showing the work below

Equation of a Line

(-6,0) (-4,-4)

To work with the two given points (-6,0) and (-4,-4), you can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope, you can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

So, substituting the given values, we get:

m = (-4 - 0) / (-4 - (-6))

m = -4 / 2

m = -2

To find the y-intercept, we can use one of the points and the slope in the slope-intercept form:

y = mx + b

0 = -2(-6) + b

0 = 12 + b

b = -12

Therefore, the equation of the line passing through the points (-6,0) and (-4,-4) is:

y = -2x - 12

(-4,0) (-2,-2)

To find the equation of the line passing through the two given points (-4,0) and (-2,-2), we can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the given values, we get:

m = (-2 - 0) / (-2 - (-4))

m = -2 / 2

m = -1

To find the y-intercept, we can use one of the points and the slope in the slope-intercept form:

y = mx + b

0 = -1(-4) + b

0 = 4 + b

b = -4

Therefore, the equation of the line passing through the points (-4,0) and (-2,-2) is:

y = -x - 4

ChatGPT

To ensure that the remainder of the series Σk=0 [infinity] 5(-1)^k/k! is less than 10^-1 in magnitude, we need to sum at least 4 terms.

The series Σk=0 [infinity] 5(-1)^k/k! is a convergent series, which means that the sum of the series approaches a finite value as the number of terms in the series approaches infinity. However, when we sum a finite number of terms, the sum of the series is an approximation to the true value of the sum. The difference between the true value of the sum and the sum of the finite number of terms is called the remainder.

To find the remainder of the series Σk=0 [infinity] 5(-1)^k/k!, we need to determine how many terms we need to sum to ensure that the remainder is less than 10^-1 in magnitude. One way to do this is to use the formula for the remainder of a convergent series:

|Rn| ≤ an+1/(1-r)

where Rn is the remainder after summing the first n terms of the series, an+1 is the (n+1)th term of the series, and r is the common ratio of the series.

In this case, the common ratio of the series is -1/5, and the (n+1)th term of the series is 5*(-1)^(n+1)/(n+1)! . We want to find the smallest value of n such that |Rn| ≤ 10^-1. Substituting these values into the formula for the remainder, we get:

|5*(-1)^(n+1)/(n+1)!| ≤ 10^-1/(1-(-1/5))

Simplifying this inequality, we get:

|(n+1)!| ≥ 120*(5/4)^(n+1)

Taking the logarithm of both sides of this inequality, we get:

log|(n+1)!| ≥ log[120*(5/4)^(n+1)]

Using Stirling's approximation for n!, we can simplify the left-hand side of this inequality:

(n+1)*log(n+1) - (n+1) ≥ log[120*(5/4)^(n+1)]

Simplifying the right-hand side, we get:

(n+1)*log(n+1) - (n+1) ≥ log(120) + (n+1)*log(5/4)

Dividing both sides by log(n+1), we get:

n+1 - 1/log(n+1) ≥ (log(120) + (n+1)*log(5/4))/log(n+1)

This inequality can be solved numerically to find that the smallest value of n that satisfies the inequality is n = 3.87 (rounded to two decimal places). Since n must be an integer, we need to round up to n = 4. Therefore, we need to sum at least 4 terms of the series Σk=0 [infinity] 5(-1)^k/k! to ensure that the remainder is less than 10^-1 in magnitude.

To learn more about magnitude click here: brainly.com/question/31022175

#SPJ11

Answer:

Imao 5

Step-by-step explanation:

just divide

Answer:

5 cups.

Step-by-step explanation:

The egg to flour ratio is 7:35

If you narrow it down, it is 1:5

You have to divide it.

Answer:

-78.85

Step-by-step explanation:

Using Order of Operations (PEDMAS):

23.15 – [ 115 + ( 12 - 25)]

= 23.15 – [ 115 + (-13)]

= 23.15 – [ 115 - 13]

= 23.15 -  102

= -78.85

Other factors like temperature, air density, and humidity can affect the ball's flight. For instance, denser air, often associated with colder temperatures, can impede the ball's movement and reduce its travel distance.

In addition to the angle of elevation, several other determining factors come into play when determining whether a hit ball will clear the center field fence. Two significant factors to consider are the initial velocity of the ball and the atmospheric conditions.

The initial velocity of the ball strongly influences its trajectory and distance. A higher initial velocity will result in a longer travel distance, increasing the chances of clearing the fence. However, if the ball is not hit with enough velocity, it may not have the necessary power to surpass the fence height.

Atmospheric conditions, including wind speed and direction, can greatly impact the ball's flight path. A strong tailwind can provide additional lift and carry to the ball, aiding its trajectory and helping it clear the fence. Conversely, a headwind can have the opposite effect, causing the ball to lose speed and distance, potentially falling short of the fence.

Furthermore, other factors like temperature, air density, and humidity can affect the ball's flight. For instance, denser air, often associated with colder temperatures, can impede the ball's movement and reduce its travel distance.

Considering these factors along with the angle of elevation provides a more comprehensive understanding of whether a hit ball will clear the center field fence. Each factor interacts and contributes to the ball's final destination, making baseball a game where multiple variables must be accounted for to achieve success.

For more questions on factors

https://brainly.com/question/5660582

#SPJ8

145 is the answer bruh i cant type

a)The value of the constant C for which the integral converges is C = 4. and

b) The value of the integral for the value of C found in part (a) is  :  \(\[I=\left(x^2+1\right)\ln(x+4)-2\left(x-4\ln(x+4)\right)+2\ln(4).\]\)

(a)If \($I=\int_0^x\frac{x^2+1}{5x-4x+C}dx$\) is convergent then the denominator should not be equal to zero.

\(\[\Rightarrow 5x-4x+C=x(5-4)+C=x+C\neq0\]\[\Rightarrow x\neq -C\]\)

Thus, the integral is convergent for \($x\neq -C$\).

Therefore,\(\[\int_0^x\frac{x^2+1}{5x-4x+C}dx\]\)

For the integral to converge, we need to find the value of C for which the denominator is zero.i.e.  

\($5x-4x+C =0$ at \\$x = -C$\)

Thus the integral is convergent if \($x \neq -C$\).

For the given integral to be convergent, the value of C can be obtained by solving the following equation:

\(\[5x-4x+C = 0 \implies \\x = \frac{-C}{1}\\ = -C\]\)

Thus the integral will converge only if \($x \neq -C$\).

Hence the value of C is \[C=4.\]

Now, we can evaluate the integral as follows:

\(\[I=\int_0^x\frac{x^2+1}{5x-4x+4}dx\]\[I=\int_0^x\frac{x^2+1}{x+4}dx\]\)

We can solve the integral using integration by parts.

Let u = \($x^2+1$\) and

dv = \($\frac{1}{x+4}$\), then

du = 2xdx and

v = ln(x+4).

\(\[I=\int_0^x\frac{x^2+1}{x+4}dx = \left(x^2+1\right)\ln(x+4)-2\int_0^x\frac{x}{x+4}dx\]\[I = \left(x^2+1\right)\ln(x+4)-2\int_0^x\frac{x+4-4}{x+4}dx\]\[I = \left(x^2+1\right)\ln(x+4)-2\int_0^x\left(1-\frac{4}{x+4}\right)dx\]\[I = \left(x^2+1\right)\ln(x+4)-2\left(x-4\ln(x+4)\right)+2\ln(4)\]\)

Hence, the value of the integral for \($C=4$\) is:

\(\[I=\left(x^2+1\right)\ln(x+4)-2\left(x-4\ln(x+4)\right)+2\ln(4).\]\)

Therefore,

a) the value of the constant C for which the integral converges is C = 4. and

b) the value of the integral for the value of C found in part (a) is  :

\(\[I=\left(x^2+1\right)\ln(x+4)-2\left(x-4\ln(x+4)\right)+2\ln(4).\]\)

To know more about integral, visit:

https://brainly.com/question/22747210

#SPJ11

The evaluated integral for C = 1 is (1/2)x^2 - x + 2ln|x + 1|.

Answer to part (b): l = (1/2)x^2 - x + 2ln|x + 1|.

To find the value of the constant C for which the integral converges, we need to examine the behavior of the integrand as x approaches 0.

The integrand is given as (x^2 + 1)/(5x - 4x + 1/C).

As x approaches 0, the denominator approaches 1/C. For the integral to converge, the integrand should not have a singularity at x = 0. Therefore, the denominator should not be equal to zero.

Setting the denominator equal to zero, we have:

5x - 4x + 1/C = 0

x = -1/(C - 1)

For the integral to converge, x cannot take the value -1/(C - 1). In other words, -1/(C - 1) should not be within the interval of integration [0, x].

Since x cannot be equal to -1/(C - 1) and the interval starts at x = 0, we require that -1/(C - 1) > 0, or C - 1 < 0. This implies C < 1.

Therefore, for the integral to converge, the constant C must be less than 1.

Answer to part (a): C < 1.

To evaluate the integral for the value of C found in part (a), let's assume C = 1 for simplicity.

The integral becomes:

I = ∫[0, x] (x^2 + 1)/(5x - 4x + 1) dx

= ∫[0, x] (x^2 + 1)/(x + 1) dx

To compute this integral, we can use algebraic manipulation and integration techniques. First, let's divide the numerator by the denominator:

I = ∫[0, x] (x - 1 + 2/(x + 1)) dx

Expanding and splitting the integral, we have:

I = ∫[0, x] (x - 1) dx + ∫[0, x] 2/(x + 1) dx

Integrating term by term, we get:

I = (1/2)x^2 - x + 2ln|x + 1| | [0, x]

Evaluating the integral at the upper and lower limits, we have:

I = (1/2)x^2 - x + 2ln|x + 1| | [0, x]

= [(1/2)x^2 - x + 2ln|x + 1|] | [0, x]

= (1/2)x^2 - x + 2ln|x + 1| - [(1/2)(0)^2 - 0 + 2ln|0 + 1|]

= (1/2)x^2 - x + 2ln|x + 1|

Therefore, the evaluated integral for C = 1 is (1/2)x^2 - x + 2ln|x + 1|.

Answer to part (b): l = (1/2)x^2 - x + 2ln|x + 1|.

To know more about integral visit

https://brainly.com/question/18125359

#SPJ11

Answer:

1.C 2.D

Step-by-step explanation:

Answer:

1 is C and 2 is D

Step-by-step explanation:

Answer:

The absolute value of 7 is 7

Step-by-step explanation:

Brainliest?

Answer:

The absolute value function takes any number and converts it to its non-negative equivalent.

7=7

Step-by-step explanation:

The reqiured two digit number is 54

Let, a two-digit number be n

the digit at tens place as x and the digit at unit place be y

The tens digit of a two-digit number exceeds the units digit by 1.

x = y + 1                      .............(1)

if the number is divided by the sum of its digits, the quotient is 6.

(10x + y)/(x + y) = 6

Substitute above value of x in this equation.

(10(y + 1) + y) = 6(y + 1 + y)

10y + 10 + y = 6(2y + 1)

11y + 10 = 12y + 6

y = 4

Substitute above value of y in equation (1),

x = 4 + 1  

x = 5

So, the number would be, 10x + y = 50 + 4

                                                      = 54

Therefore, the number is 54

Learn more about the equation here:

https://brainly.com/question/649785

#SPJ4

Answer:

yes

Step-by-step explanation:

(x,y) -> (1,-9)   y=-9

The sample size increases, the probability of obtaining a sample mean less than 3500 decreases. The mean of the sample mean distribution is equal to the population mean, which is 7500.

a) The probability that, on a single test, x is less than 3500 can be calculated using the standard normal distribution. We need to standardize the value using the z-score formula: z = (x - μ) / σ. Substituting the given values, we get z = (3500 - 7500) / 1750 ≈ -2.286.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -2.286. The probability is approximately 0.0116, or 1.16%. Therefore, there is a 1.16% chance that a single test result will be less than 3500, indicating leukopenia.

(b) When the doctor uses the average x (sample mean) for two tests taken about a week apart, the probability distribution of x (sample mean) follows a normal distribution. The mean of the sample mean distribution is equal to the population mean, which is 7500. The standard deviation of the sample mean distribution is equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 2.

The probability distribution of x (sample mean) < 3500 can be calculated by standardizing the value using the z-score formula and then finding the corresponding probability from the standard normal distribution table or a calculator. With two tests, the probability distribution will be narrower compared to a single test. The exact probability depends on the specific value of the sample mean and the standard deviation of the sample mean distribution.

(c) When considering three tests taken a week apart, the process is similar to part (b). The mean of the sample mean distribution remains the same at 7500, but the standard deviation of the sample mean distribution is now divided by the square root of 3, since the sample size is 3. As the sample size increases, the standard deviation of the sample mean distribution decreases, resulting in a narrower distribution.

The probability distribution of x (sample mean) < 3500 can be calculated using the z-score formula and finding the corresponding probability from the standard normal distribution table or a calculator. With three tests, the probability distribution will be even narrower compared to two tests.

In summary, as the sample size increases, the probability of obtaining a sample mean less than 3500 decreases. With more tests, we can have greater confidence in the accuracy of the sample mean and draw stronger conclusions about the individual's condition. If a person had a sample mean less than 3500 based on three tests, it would indicate a higher level of certainty about the presence of leukopenia, potentially leading to further investigation or treatment options.

Learn more about mean here:

https://brainly.com/question/30112112

#SPJ11

Answer:

See below for proof.

Step-by-step explanation:

Given equations for x and y:

  \(x=v_0 \cdot t \cdot \cos \theta\)

  \(y=-16 \cdot t^2 + v_0 \cdot t \cdot \sin \theta\)

Rearrange the equation for x to isolate t by dividing both sides of the equation by v₀ · cos θ:

\(\implies t=\dfrac{x}{v_0 \cdot \cos \theta}\)

Square the equation for x:

\(\implies x^2=(v_0 \cdot t \cdot \cos \theta)^2\)

\(\implies x^2={v_0}^2 \cdot t^2 \cdot \cos^2 \theta\)

Rearrange to isolate t² by dividing both sides of the equation by v₀² · cos²θ:

\(\implies t^2= \dfrac{x^2}{{v_0}^2 \cdot \cos^2 \theta}\)

Now we have created expressions for t and t² in terms of x.

Substitute these into the equation for y:

\(\implies y=-16 \cdot t^2 + v_0 \cdot t \cdot \sin \theta\)

\(\implies y =-16 \cdot \left(\dfrac{x^2}{{v_0}^2 \cdot \cos^2 \theta}\right)+ v_0 \cdot \left(\dfrac{x}{v_0 \cdot \cos \theta}\right) \cdot \sin \theta\)

Simplify:

\(\implies y =-\dfrac{16}{{v_0}^2} \cdot \left(\dfrac{x^2}{\cos^2 \theta}\right)+\left(\dfrac{x}{\cos \theta}\right) \cdot \sin \theta\)

\(\implies y =-\dfrac{16}{{v_0}^2} \cdot \left(\dfrac{1}{\cos^2 \theta}\right) \cdot x^2+x \cdot \left(\dfrac{\sin \theta}{\cos \theta}\right)\)

\(\textsf{Use\;the\;identities\;\;$\sec^2\theta=\dfrac{1}{\cos^2\theta}$\;\;and\;\;$\tan\theta=\dfrac{\sin\theta}{\cos\theta}$}:\)

\(\implies y=-\dfrac{16}{{v_0}^2} \cdot \sec^2 \theta \cdot x^2+x \cdot \tan \theta\)

\(\textsf{Hence\;proving\;that\;\;$y=-\dfrac{16}{{v_0}^2} \cdot \sec^2 \theta \cdot x^2+x \cdot \tan \theta$}.\)

The equation can be written as,

\(y = \dfrac{-15x^2} { (v_o^2) + (\dfrac{1} { v_o^2})tan^{-1}(\dfrac{y} { x})}\).

An object or particle that is projected in a gravitational field, such as from the surface of the Earth, and moves along a curved path while only being affected by gravity is said to be in projectile motion.

To begin with, we know that the horizontal displacement of the projectile is given by \(x = v_ot cos(\theta)\), where vo is the initial velocity of the projectile and θ is the angle it makes with the positive x-axis. Therefore, we can rearrange this equation to solve for time t:

\(t = \dfrac{x} { (v_o cos(\theta))}\)

Next, we can use the equation for vertical displacement under constant acceleration due to gravity: \(y = -16t^2+ v_ot sin(\theta)\). Substituting the expression for t derived above, we obtain:

\(y = -16[\dfrac{x} { (vo cos(\theta)}]^2 + v_o([\dfrac{x} { (v_o cos(\theta)}] sin(\theta)\)

Simplifying this expression, we get:

\(y = \dfrac{-16x^2} { (v_o^2 cos^2(\theta)) + x tan(\theta)}\)

Now, we need to eliminate the angle θ in terms of x and y. We can do this by using the fact that tan(θ) = y / x, which gives:

\(\theta= tan^{-1}(\dfrac{y} { x})\)

Substituting this expression for θ into our previous equation, we obtain:

\(y =\dfrac{ -16x^2 }{(v_o^2 cos^2(tan^{-1}(\dfrac{y} { x}))} + x\ tan(tan^{-1}(\dfrac{y} { x})\)

Since tan(tan⁻¹(z)) = z, we can simplify this expression further:

\(y = \dfrac{-16x^2} { (v_o^2 (1 + (\dfrac{y} { x})^2))} + y\)

Finally, by rearranging terms, we get the desired equation:

\(y = \dfrac{-15x^2} { (v_o^2) + (\dfrac{1} { v_o^2})tan^{-1}(\dfrac{y} { x})}\)

To know more about projectile motion follow

https://brainly.com/question/24216590

#SPJ1

The sample space as Feechi makes three attempts at a basket in a basketball game is BBB, BMB, MBM, MMM).Option A

The sample space represents all possible outcomes of Feechi's three attempts, where each attempt can either result in a basket (B) or a miss (M).

Option A lists the following four outcomes: BBB, BMB, MBM, and MMM. Each outcome is a sequence of three letters, where B represents a basket and M represents a miss.

Therefore, the correct answer IS (BBB, BMB, MBM, MMM).

Learn more about sample space at https://brainly.com/question/10558496

#SPJ1

The sample space for Feechi's result would be = (BBB, BBM, BMB, BMM, MBB, MBM, MMB, MMM). That is option D.

The various moves to make a successful attempt at the basket was done 3 times.

When she gets a B = Basket

When she gets an M = Miss

The possible outcome of the sample space would be = (BBB, BBM, BMB, BMM, MBB, MBM, MMB, MMM).

This is because only 8 unique arrangements can be gotten from the list of possible outcomes.

Learn more about probability here:

https://brainly.com/question/30901667

#SPJ1

Answer: A

Step-by-step explanation:

first, find the amount of coffee shops in year 2000, the "starting point"

1,500 - 100 - 100 (going back 2 years) = 1,300

as the amount of shops is increasing, the slope must be positive, so the answer is A