Lucy wrote a pattern using the rule "Subtract 3." The first two numbers in her pattern
were 36 and 33. Which answer choice is a number that is part of Lucy's pattern?

98879Answer:898987

ytf56r5ytr76trt

Step-by-step explanation:

The dimensions of the scale model of your room would be 3/4 inch represents 1 foot. To determine the dimensions of the scale model, we need to apply the scale ratio of 3/4 inch represents 1 foot.

Let's assume the length and width of your actual room are L feet and W feet, respectively. To find the dimensions of the scale model, we can multiply the actual dimensions by the scale ratio.

The length of the scale model would be L * (3/4) inch, and the width would be W * (3/4) inch.

For example, if your actual room is 12 feet long and 10 feet wide, the dimensions of the scale model would be:

Length of the scale model = 12 feet * (3/4) inch = 9 inches

Width of the scale model = 10 feet * (3/4) inch = 7.5 inches

Therefore, the scale model would have a length of 9 inches and a width of 7.5 inches, based on the given scale ratio.

It's important to note that when creating a scale model, maintaining the proportionality between the actual dimensions and the model dimensions is crucial to accurately represent the physical space in a smaller scale.

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The slope field shown in the question is that of a differential equation of the form y'= f(x,y).

The solutions of this equation are the curves in the slope field that emanate from each point and that have the same slope as the line at that point. Thus, for each point (x,y) in the slope field, it is possible to calculate the particular solution that passes through that point.

The first statement is false because it involves the second derivative of the particular solution, which cannot be determined from the slope field. The second statement is false because a concave up graph requires that the derivative of the solution be increasing at x=0, but the slope field does not indicate the sign of the derivative of the particular solution. The third statement is false because a concave up graph requires that the derivative of the solution be decreasing at x=-1, which cannot be determined from the slope field. The fourth statement is false because a concave down graph requires that the derivative of the solution be increasing at x=0, which cannot be determined from the slope field.

In summary, none of the statements can be determined to be true or false from the slope field shown.

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so (0,-3) and  (2,0) is a solution.   (2,2) and (-3,0) is not a solution. as  the equation of the line passing through the points (0,-3) and (2,0) is y = (3/2)x - 3 we need to substitute points to check valid or not

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. In other words, an equation says that one expression on the left side of the equals sign is the same as the expression on the right side of the equals sign. An equation typically includes variables

In the given question,

To determine the equation of the line passing through the points (0,-3) and (2,0), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

The slope of the line can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (0,-3) and (x₂, y₂) = (2,0)

m = (0 - (-3)) / (2 - 0) = 3/2

So the equation of the line is:

y = (3/2)x - 3

Now we can check which ordered pair is a solution to this equation by plugging in the x and y values into the equation and seeing if it holds true.

A. (0,-3)

y = (3/2)x - 3

-3 = (3/2)(0) - 3

-3 = -3

This is true, so (0,-3) is a solution.

B. (2,0)

y = (3/2)x - 3

0 = (3/2)(2) - 3

0 = 0

This is true, so (2,0) is a solution.

C. (2,2)

y = (3/2)x - 3

2 = (3/2)(2) - 3

2 = 0

This is false, so (2,2) is not a solution.

D. (-3,0)

y = (3/2)x - 3

0 = (3/2)(-3) - 3

0 = -9/2

This is false, so (-3,0) is not a solution.

Therefore, the solutions to the equation represented by the graph are A. (0,-3) and B. (2,0).

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one solution of the equation is approximately 1.8925469 radians.

The equation is:

tan(x) + 3 = 0

Subtracting 3 from both sides, we get:

tan(x) = -3

Taking the inverse tangent of both sides, we get:

x = arctan(-3)

However, the tangent function is periodic with period π, which means that there are infinitely many solutions to this equation. In general, the solutions are given by:

x = arctan(-3) + nπ, where n is an arbitrary integer.

Using a calculator to approximate arctan(-3), we get:

arctan(-3) ≈ -1.2490458

Therefore, the general solution to the equation is:

x ≈ -1.2490458 + nπ, where n is an arbitrary integer.

If we substitute n = 1, we get:

x ≈ -1.2490458 + π

Using a calculator to approximate this value, we get:

x ≈ 1.8925469

So one solution of the equation is approximately 1.8925469 radians.

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Answer:

I'm not good at this I'm good at math

Answer:

28.79 cm.

Step-by-step explanation:

The perimeter of a semicircle is equal to the sum of the diameter (which is twice the radius) and half of the circumference of the circle.

The diameter of the semicircle is 2 × 5.6cm = 11.2cm.

The circumference of a full circle with radius 5.6cm is 2π × 5.6cm = 11.2π cm.

Therefore, the circumference of the semicircle is 1/2 of the circumference of the full circle, which is 1/2 × 11.2π cm = 5.6π cm.

The perimeter of the semicircle is the sum of the diameter and the circumference, which is:

11.2cm + 5.6π cm ≈ 28.79cm (rounded to two decimal places)

Therefore, the perimeter of the semicircle is approximately 28.79 cm.

Answer:

pi ( 5.6 ) + 11.2 or approximately 28.79291 cm

Step-by-step explanation:

The outside of the semicircle or the perimeter is 1/2 of the circumference and the length that closes the circle is the diameter.

Perimeter = 1/2 C + d

                 = 1/2 *pi*d + d

The diameter is 2 times the radius.

                 = 1/2 ( pi) * (2r) + 2r

                  = pi r + 2 r

                   = pi ( 5.6 ) + 11.2

Approximating pi, we get approximately 28.79291

In a coordinate plane, a vertical line is a straight, upward- and downward-pointing line that is perpendicular to the y-axis. The point C is V: x = 3.

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Answer:

a^2 b^3 (b^2 - a b + a^2)

Step-by-step explanation:

Factor the following:

a^2 b^5 - a^3 b^4 + a^4 b^3

Hint: | Factor common terms out of a^2 b^5 - a^3 b^4 + a^4 b^3.

Factor a^2 b^3 out of a^2 b^5 - a^3 b^4 + a^4 b^3:

Answer: a^2 b^3 (b^2 - a b + a^2)

Answer:

x = 91

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

x + 89 = 180

x = 91

Answer:

B. The function shown on the graph has a smaller rate of change but a higher starting point

Step-by-step explanation:

Question options obtained from a similar question are;

A. The function shown on the graph has a greater rate of change and a higher starting point

B. The function shown on the graph has a smaller rate of change but a higher starting point

C. The function shown on the graph has a greater rate of change but a lower starting point

The function shown on the graph has a smaller rate of change but a higher starting point

Explanation;

The given function with which the graph is compared is y = 4·x + 2

From the given function, we have;

The rate of change of the function is the coefficient of 'x', therefore, the rate of change of the function = 4

When y = 0, 4·x + 2 = 0,

∴ x = -2/4 = -0.5

The y-intercept is given when x = 0

∴ The y-intercept, y = 4 × 0 + 2 = 2

The starting point of the function, is (0, 2)

From the graph, we have;

The y-intercept = (0, 4)

Therefore, the starting point of the line, the y-intercept, (0, 4), is higher than the starting point of the given function, (0, 2)

The coordinates of two (clear) points on the line in the graph are (0, 4) and (-2, -2)

The rate of change of the line, m = (4 - (-2))/(0 - (-2)) = 3

Therefore, the graph has a lesser rate of change, 3, than the rate of change of the given function, 4

When compared with the given function, 'the function shown on the graph has a smaller rate of change and a higher starting point'.

An angle of 55° is equivalent to approximately 0.96 radians. An arc length of 30 units is traced out by an angle of 6 radians on a circle of radius 5.

To convert an angle of 55° into radians, we use the formula: radians = (π/180) x degrees. Substituting the given value, we get:

radians = (π/180) x 55°

radians = 0.96 radians (rounded to the nearest hundredth)

Therefore, an angle of 55° is equivalent to approximately 0.96 radians.

To find the arc length traced out by an angle of 6 radians on a circle of radius 5, we use the formula: arc length = radius x angle in radians. Substituting the given values, we get

arc length = 5 x 6 radians

arc length = 30 units

Therefore, the arc length traced out by an angle of is 30 units (rounded to the nearest hundredth).

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Answer:

1.6667 meters per minute

Step-by-step explanation:

To convert meters per second into meters per minute, let's first think about the difference between seconds and minutes.

There are 60 seconds in one minute, so to find our meters per minute speed, we will divide the distance by 60.

100 / 60 = 1.6667 meters per minute

Hope this helped!

Answer:

it is d my guy :)

Step-by-step explanation:

Using the normal distribution, it is found that:

a) The 65th percentile is of 37.31.

b) The 90th percentile is of 42.68.

c) There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.

d) There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

Question a:

The 65th percentile is X when Z has a p-value of 0.65, so X when Z = 0.385.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.385 = \frac{X - 35}{6}\)

\(X - 35 = 0.385(6)\)

\(X = 37.31\)

The 65th percentile is of 37.31.

Question b:

The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.28 = \frac{X - 35}{6}\)

\(X - 35 = 1.28(6)\)

\(X = 42.68\)

The 90th percentile is of 42.68.

Question c:

The probability is the p-value of Z when X = 38 subtracted by the p-value of Z when X = 28, hence:

X = 38:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{38 - 35}{6}\)

\(Z = 0.5\)

\(Z = 0.5\) has a p-value of 0.6915.

X = 28:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{28 - 35}{6}\)

\(Z = -1.17\)

\(Z = -1.17\) has a p-value of 0.121.

0.6915 - 0.121 = 0.5705.

There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.

Question d:

The probability is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 41, hence:

X = 44:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{44 - 35}{6}\)

\(Z = 1.5\)

\(Z = 1.5\) has a p-value of 0.9332.

X = 41:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{41 - 35}{6}\)

\(Z = 1\)

\(Z = 1\) has a p-value of 0.8413.

0.9332 - 0.8413 = 0.0919

There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.

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Using it's concept, the percentile rank for a score of 85 on this test is the 50th percentile.

When a measure is in the xth percentile of a data-set, it is greater or equal than x% of the measures and lesser than (100 - x)%.

In this problem, there are 20 scores, and 85 corresponds to the 10th highest score, hence the percentile is given by:

p = 10/20 = 0.5 x 100% = 50th percentile.

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Answer: 3n+2

Step-by-step explanation:

ANSWER

My answer is in the photo above.l hope it helps

Answer: 22.5 gallons of gas

Step-by-step explanation:

1 1/2 = 3/2 or 1.5

Take 1.5 divided by 10 = 0.15 gallon per mile

Then take 0.15 times 150 miles = 22.5 gallons of gas

Answer:

23.2

12

..........................................

Answer:

9/4y+10

Step-by-step explanation:

1/4y+10+2y

9/4y+10

unless u meant y^2 then the answer would be

0.25(y+40+4y^2)

Answer:

\(\%Off-Campus = 45.5\%\)

Step-by-step explanation:

Given

----------------------Dorms ---- Off-Campus ---- Total

Freshman -------- 88  ------  ---------12   ------- 100

Sophomore  ------62  ---------------38  --------- 100

Junior --------------43 -----------------  57  ---------- 100

Senior -------------25  -----------------75  ------------ 100

Total ---------------218 -------------182  --------------400

Required

Determine the percentage of off-campus students

From the above table, we have that:

\(Off-Campus = 182\)

\(Total\ Surveyed = 400\)

The percentage is then calculated as follows;

\(\%Off-Campus = \frac{Off-Campus}{Total-Surveyed} * 100\%\)

\(\%Off-Campus = \frac{182}{400} * 100\%\)

\(\%Off-Campus = 0.455 * 100\%\)

\(\%Off-Campus = 45.5\%\)

Hence, option C answers the question

Answer:

oh 45%

Step-by-step explanation:

Since sn = 1/2 - 1/(n + 2), as n → ∞, sn → 1/2. Therefore, the given series converges to 1/2.

The given series is Σn=3∞ 2/(n² - 1)n. We need to express sn as a telescoping sum. Let's start by finding a general formula for the nth term of the series, tn.

tn = 2/(n² - 1)n = 2/[(n - 1)(n + 1)]n.

The given expression can be written as:

Σn=3∞ 2/(n² - 1)n

= Σn=3∞ [1/ (n - 1) - 1/(n + 1)]

Multiplying numerator and denominator of the first term by (n + 1) and the second term by (n - 1), we get

Σn=3∞ [1/ (n - 1) - 1/(n + 1)]

= [1/2 - 1/4] + [1/3 - 1/5] + [1/4 - 1/6] + .......+ [1/n - 1/(n + 2)] + .......

Now, let's find a formula for the nth partial sum, sn.

s1 = [1/2 - 1/4]

s2 = [1/2 - 1/4] + [1/3 - 1/5]

s3 = [1/2 - 1/4] + [1/3 - 1/5] + [1/4 - 1/6]......

s2 = [1/2 - 1/4] + [1/3 - 1/5]

s3 = [1/2 - 1/4] + [1/3 - 1/5] + [1/4 - 1/6]....+ [1/n - 1/(n + 2)]

s3 - s2 = [1/4 - 1/6] + [1/5 - 1/7] + [1/6 - 1/8].....- [1/3 - 1/5]

s4 - s3 = [1/5 - 1/7] + [1/6 - 1/8] + [1/7 - 1/9].....- [1/4 - 1/6]

s4 - s1 = [1/3 - 1/5] + [1/4 - 1/6] + [1/5 - 1/7].....- [1/n - 1/(n + 2)]

It can be observed that, on simplifying sn, the terms get cancelled, leaving only the first and last terms. Hence, sn can be written as:sn = [1/2 - 1/(n + 2)]

Therefore, the given series is a telescoping series, which means that each term after a certain point cancels out with a previous term, leaving only the first and last terms.

Since sn = 1/2 - 1/(n + 2), as n → ∞, sn → 1/2. Therefore, the given series converges to 1/2.

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Answer:

θ = π/3 and 5π/3

Step-by-step explanation:

x = r cos θ and y = r sin θ.  Therefore:

dy/dx = (dy/dθ) / (dx/dθ)

dy/dx = (r cos θ + r' sin θ) / (-r sin θ + r' cos θ)

In this case, r = 1 + cos θ and r' = -sin θ.

dy/dx = ((1 + cos θ) cos θ + (-sin θ) sin θ) / (-(1 + cos θ) sin θ + (-sin θ) cos θ)

dy/dx = (cos θ + cos²θ − sin²θ) / (-sin θ − sin θ cos θ − sin θ cos θ)

dy/dx = (cos θ + cos²θ − (1 − cos²θ)) / (-sin θ (1 + 2 cos θ))

dy/dx = (cos θ + 2 cos²θ − 1) / (-sin θ (1 + 2 cos θ))

The tangent line is horizontal when the numerator of dy/dx is 0 and the denominator of dy/dx is not 0.

0 = 2 cos²θ + cos θ − 1

0 = (cos θ + 1) (2 cos θ − 1)

cos θ = -1 or 1/2

θ = π/3, π, 5π/3

0 = -sin θ (1 + 2 cos θ)

sin θ = 0 or cos θ = -1/2

θ = 0, 2π/3, π, 4π/3

Therefore, the answer is θ = π/3 and 5π/3.

The probability of being a goalkeeper today is 0.42, or 42%.

To determine the probability of being a goalkeeper today, we need to consider the probabilities associated with each coach and their likelihood of coaching.

Given:

- Probability of being goalkeeper with Coach Sam: 0.5

- Probability of being goalkeeper with Coach Alex: 0.3

- Probability of Coach Sam being the coach today: 0.6

To calculate the probability, we can use the concept of conditional probability.

Probability of being a goalkeeper today = (Probability of Coach Sam being the coach today) * (Probability of being a goalkeeper with Coach Sam) + (Probability of Coach Alex being the coach today) * (Probability of being a goalkeeper with Coach Alex)

Substituting the given values:

Probability of being a goalkeeper today = (0.6 * 0.5) + (0.4 * 0.3)

Probability of being a goalkeeper today = 0.3 + 0.12

Probability of being a goalkeeper today = 0.42

Therefore, the probability of being a goalkeeper today is 0.42, or 42%.

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Charlotte traveled in 414.44 feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.

The first step is to convert miles per hour to feet per second.

(69.6 mi/hr)* (5280 feet/mi)*(1 hr/3600 sec) = 102.08 feet/sec

We know that,

Speed = \(\frac{Distance}{Time}\)

Here, we have given,

Time = 4.06 s

Speed (feet/sec) = 102.08 feet/sec

We need to find, the distance charlotte traveled in feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.

Putting the values in the formula, we get

Distance = Speed x Time

= 102.08 x 4.06

= 414.44 Feet

Hence, charlotte traveled in 414.44 feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.

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The mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

The mean of a geometric distribution is given by:

Mean = 1/p

Here, p is the probability of success on a single trial.

In this case, p = 0.80

So, the mean of the geometric distribution = 1/0.80 = 1.25

The variance of a geometric distribution is given by:

Variance =\((1-p) / p^2\)

By substituting the value of p = 0.80, we get:

Variance = \((1-0.80) / 0.80^2 = 0.20 / 0.64 = 0.3125\)

So the variance of the geometric distribution = 0.3125

Therefore, the mean and variance of a geometric distribution in which the probability of success is 0.80 are 1.25 and 0.3125 respectively.

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The lower bound for the function f(n) = 4n^3 + 2n^2 + n is Ω(n^3).


To find the lower bound, we need to determine the term with the highest growth rate in the function f(n). In this case, the highest growth rate is determined by the cubic term 4n^3. The other terms, 2n^2 and n, have a lower growth rate, and therefore, their impact on the overall growth of the function becomes less significant as n increases.

As a result, we can say that the lower bound for the function f(n) is dominated by the cubic term 4n^3, which means that the function f(n) grows at least as fast as Ω(n^3).


The lower bound for the function f(n) = 4n^3 + 2n^2 + n is Ω(n^3). This means that the function grows at least as fast as a cubic function, and the other terms have a lesser impact on the overall growth rate as n increases.

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Arthur should leave a $28.26 tip

Answer:

$y=\frac{-2}{9}x+\frac{61}$

Step-by-step explanation:

For two lines to be parallel to each other, it means they have to have the same slope. So, the question is really asking for the line through $(8, 5)$ that has the same slope as the line shown.

We can start by finding the slope of the line shown. Recall that given two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$, the slope of the line between them is $\frac{y_{2}-y_{1}}{x_{2}-x{1}}$, or more commonly remembered as rise over run. Plugging in the points $(-3, 1)$ and $(6, -1)$ into the equation for the slope, we see that the slope of the line shown is $\frac{-1-1}{6-(-3)}=\frac{-2}{9}$.

We recall that the point-slope form of a line is such that given a point $(x_{1}, y_{1})$ and the slope $m$, the equation for a line with that slope through the given point is $y-y_{1}=m(x-x_{1})$(Note: divide by $x-x_{1}$. What does that remind you of?). Plugging in our point and slope, we have that the equation for the line we want is $y-5=\frac{-2}{9}(x-8)$. Expanding the right-hand side gives $y-5=\frac{-2}{9}x+\frac{16}{9}$.

Adding $5$ to both sides gives the desired $\boxed{y=\frac{-2}{9}x+\frac{61}}$

I don't understand it at all