The coordinates given here are three more attractions and their locations
• Aquarium: (-4,1)
Music Hall of Fame: (2,3)
• Lighthouse (-4,-6)
Wesley will bike on the streets. Select all of the route plans that would require Wesley to bike at least 9 miles
Ferris Wheel to Lighthouse to Bridge
O Music Hall of Fame to Art Museum to Ferris Wheel
Aquarium to Bridge to Lighthouse
Aquarium to Art Museum to Music Hall of Fame
O Bridge to Aquarium to Art Museum

The cosine function that could model the block's height in inches above the ground at time t seconds is:

h(t) = 9cos(1.67π(x - 2.1)) + 39.

The cosine function is defined as follows:

g(x) = acos(bx+c)+d.

The coefficients have these following roles:

In this problem, we have that the maximum value is of 48 and the minimum value is of 30(difference of 18), hence the amplitude is given as follows:

2a = 18

a = 9.

A standard cosine function with amplitude 9 would vary the between -9 and 9, while this one varies between 30 and 48, hence the vertical shift is of d = 39.

The minimum and maximum values form half the period, hence:

π/B = 2.7 - 2.1

B = π/0.6

B = 1.67π.

The maximum value in the standard function is at x = 0, while at this function is at x = 2.1, hence the phase shift is of 2.1 units to the right, that is, c = -2.1.

Hence the cosine function is:

h(t) = 9cos(1.67π(x - 2.1)) + 39.

This function is graphed at the end of the answer, showing that the minimum and the maximum values are as desired.

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Answer:

34 degrees

Step-by-step explanation:

Before solving for g, we must remember that the inside of a triangle will always equal 180 degrees. Also, keep in mind that the little square at the top left corner of the triangle represents 90 degrees, so we can add both the existing degrees we know of:

90 + 56 = 146

And to find g, we simply subtract 180 by 146:

180 - 146 = 34

So, g is 34 degrees

Hope this helps :)

The maximum temperature during summer in that year was 34°C.

It's not possible for the maximum temperature in Gulmarg, Kashmir to rise by 44°C during the summer.

A temperature rise of that magnitude would be extremely unusual and potentially dangerous.

However, assuming that the question meant to ask about the difference between the minimum temperature in January and the maximum temperature in summer, we can proceed with the calculation.

The minimum temperature in January was -10°C, and if we add 44°C to it, we get:

-10°C + 44°C = 34°C

Therefore, the maximum temperature during summer in that year was 34°C.

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Answer:

4/6 or 2/3. Depends if your teacher wants it reduced.

Step-by-step explanation:

Each number has a 1 out of 6 chance to be rolled. so it's 1/6 for rolling a 3, 1/6 for rolling a 4, 1/6 for rolling a 5, and 1/6 for rolling a 6. 4 x 1/6 = 4/6

Answer:

4x+3

Step-by-step explanation:

8 and 6 are multiple of 2 so divide 8 /2 = 4 and divide 6/2=3

Answer: 95

Step-by-step explanation:

The easiest way to solve this problem is to solve for each of the triangles:

(formula: B*H/2) 10*3/2 + 10*16/2

15+80

95

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Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

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

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that \(\mu = 14, \sigma = 2\)

Sample of 100:

This means that \(n = 100, s = \frac{2}{\sqrt{100}} = 0.2\)

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

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

By the Central Limit Theorem

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

\(Z = \frac{14.2 - 14}{0.2}\)

\(Z = 1\)

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

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

The sum (A+B)(x) and difference (A-B)(x) of two quadratic functions A(x) and B(x) were found, along with their values for x=5, vertices, intercepts, and where they are increasing/decreasing.

To find (A+B)(x), we simply add the two functions:

(A+B)(x) = A(x) + B(x) = (\(-0.25x^2+20x\)) + (\(-0.19x^2+15.2x\)) = \(-0.44x^2\) + 35.2x

To find (A-B)(x), we simply subtract B(x) from A(x):

(A-B)(x) = A(x) - B(x) = (\(-0.25x^2+20x\)) - (\(-0.19x^2+15.2x\)) = \(-0.06x^2\) + 4.8x

When x=5, we can evaluate each expression:

(A+B)(5) = \(-0.44(5)^2\) + 35.2(5) = 60

(A-B)(5) = \(-0.06(5)^2\) + 4.8(5) = 12

To find the vertices and intercepts of the functions A(x) and B(x), we can use the vertex and intercept formulas for quadratic functions:

For A(x):

Vertex = (-b/2a, f(-b/2a)) = (-20/-0.5, A(20/-0.5)) = (40, 400)

x-intercepts: 0 = \(-0.25x^2\) + 20x, so x = 0 or x = 80

y-intercept: A(0) = 0

For B(x):

Vertex = (-b/2a, f(-b/2a)) = (-15.2/-0.38, B(15.2/-0.38)) = (40, 304)

x-intercepts: 0 = \(-0.19x^2\) + 15.2x, so x = 0 or x = 80

y-intercept: B(0) = 0

Both functions are decreasing for x < 40, and increasing for x > 40. The vertex (40, 400) is the maximum point for A(x), and the vertex (40, 304) is the maximum point for B(x).

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Answer:

113 (d)

Step-by-step explanation:

Since the room is square-shaped, you square root the area (12,769) to find the length of each wall. You will get the answer 113. To check this answer multiply 113 by 113 and make sure you get the correct area; it works, so you know the answer  is D.

Answer:  3528.25

Step-by-step explanation:Make a sideview sketch

you should have 2 triangles, one right-angled containing the height and a scalene triangle with angles 24° , 153° (the supplement of 27°) and 3°

the side opposite the 3° angle is 1000

by let the side opposite the 24° be x, (also the hypotenuse of the right-angled triangle)

x/sin24 = 1000/sin3

x = 1000sin24/sin3

let the height of the mountain be h

sin 27 = h/x

h = x sin27 = (1000sin24/sin3)(sin27)

= 3528.25

Answer:

16 units

Step-by-step explanation:

The distance of the point P ( -2 , 6 ) to the line y = x - 8 is given by the equation D = 8√2 units = 11.3 units

The shortest distance between any two points on an infinite straight line is called the distance from a point to a line. The length of the line segment connecting the point to the closest point on the line is the perpendicular distance between the point and the line.

Let the equation of line be = Ax + By + C = 0

Let the point be P ( x₀ , y₀ )

Distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )

Given data ,

Let the distance be represented as D

Now , let the point be P = P ( -2 , 6 )

Let the equation of line be A

The value of A is

y = x - 8  

Subtracting y on both sides of the equation , we get

x - y - 8 = 0   be equation (1)

Now , Distance from a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )

Substituting the values in the equation , we get

Distance from a point to line D = | 1 ( -2 ) + ( -1 ) ( 6 ) - 8 | / √ ( 1² + 1² )

On simplifying the equation , we get

Distance from a point to line D = | -2 - 6 - 8 | / √2

Distance from a point to line D = | -16 | / √2

Distance from a point to line D = 16/√2

Multiply the numerator and denominator of the fraction by √2 , we get

Distance from a point to line D = 16√2 / 2

Distance from a point to line D = 8√2 units

Hence , the distance is 8√2 units = 11.3 units

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If the null hypothesis is correct, the probability that the test will result in a type 1 mistake is what is known as the alpha level for a hypothesis test. In other words, even in the absence of a treatment effect, the alpha level impacts the likelihood of collecting sample data in the critical zone.

The alpha level establishes the boundaries for identifying the key area that results in "extremely unlikely" or significant results that deviate from the null hypothesis. The likelihood of making a Type I error is one in twenty, according to researchers who use an alpha value or level of significance of.05.

The chance of rejecting the null hypothesis when it is true is known as the significance level, which is alternatively written as alpha or. For instance, a significance level of 0.05 represents a 5% probability of assuming the existence of a difference when none actually exists.

Hence we get the required answer.

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Answer:

y = 10

Step-by-step explanation:

calculate the slope m of the 2 points using the slope formula and equate to the given slope.

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (5, 6 ) and (x₂, y₂ ) = (10, y )

m = \(\frac{y-6}{10-5}\) = \(\frac{y-6}{5}\)

equate this expression for m to the given m of \(\frac{4}{5}\)

\(\frac{y-6}{5}\) = \(\frac{4}{5}\) ( cross- multiply )

5(y - 6) = 20 ( divide both sides by 5 )

y - 6 = 4 ( add 6 to both sides )

y = 10

Solution

Explanation:

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

Use the following property

Therefore the value of cosine in the second quadrant is negative

Then, cos (-3π/4) =

Domain: all reals, (-∝, ∝)

All inputs for x result in a solution.

1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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Answer:

2583 i think

Step-by-step explanation:

The correct answer is option B

That is

Answer:

Step-by-step explanation:

Use the similarity of two triangles.

The ratio of corresponding sides is equal.

Let the height of the tree is x, then we have:

Answer:

12.68 m  (nearest hundredth)

Step-by-step explanation:

Similar Triangle Theorem

If two triangles are similar, the ratio of their corresponding sides is equal.

Smaller triangle

Larger triangle

Ratio of height to base:

\(\implies \sf height_{small}:base_{small}=height_{large}:base_{large}\)

\(\implies \sf 1.85:4.15=h:28.45\)

\(\implies \sf \dfrac{1.85}{4.15}=\dfrac{h}{28.45}\)

\(\implies \sf h= \dfrac{1.85}{4.15} \cdot 28.45\)

\(\implies \sf h=12.68\:m \:\:(nearest\:hundredth)\)

Therefore, the height of the tree to the nearest hundredth of a meter is 12.68 m.

Answer:

1. Substitute the value of f(x) into the problem. 8=3x-1.

2. Isolate the variable. Add 1 to both sides to isolate the variable term by using the opposite operation to move the constant term across the equal sign. ...

3. Continue to isolate the variable. ...

4. Simplify.

Step-by-step explanation:

Answer: Yes

Step-by-step explanation: Here, we want to decide

if 2 is a solution for the equation 4n - 3 = -2n + 9.

We can do this by simply plugging in 2 for n.

If the statement holds true, then 2 is a solution.

Plugging in 2 for n, we have 4(2) - 3 = -2(2) + 9.

Remember that a negative times a positive is a negative.

So we have 8 - 3 = -4 + 9.

Simplifying further, we have 5 = 5.

Notice that 5 = 5 is a true statement.

So yes, 2 is a solution for the equation 4n - 3 = -2n + 9.

Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

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In the given similar triangles below, we have to find the measure of Dwrite. Triangle 1, ABC, is similar to Triangle 2, DEF. The two triangles are similar because their corresponding angles are congruent and their sides are proportional.

In order to find the measure of Dwrite, we can use the concept of proportionality. The sides of similar triangles are proportional to each other.

This means that if we know the ratio of the sides of one triangle, we can use that ratio to find the corresponding sides of the other triangle. We can use this property to find the value of Dwrite.

To start, let's write down the ratio of the sides of Triangle 1 and Triangle 2. We can choose any two corresponding sides to do this, but we'll choose AB and DE because they are easiest to measure: AB/DE = 6/8.5We know that the measure of AB is 6, so we can solve for the measure of DE: DE = AB x (DE/AB)DE = 6 x (8.5/6)DE = 8.5Now we know that the measure of DE is 8.5.

We can use this to find the measure of Dwrite. We know that DE and Dwrite are corresponding sides of Triangle 2 and Triangle 1, respectively.

So we can write a proportion using the ratio of DE to Dwrite: DE/Dwrite = 8.5/xWe know that DE is 8.5, so we can substitute that in:8.5/Dwrite = 8.5/Now we can solve for x by cross-multiplying:8.5x = 8.5Dwrite = 1Therefore, the measure of Dwrite is 1.

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Answer:

Step-by-step explanation:

Given Formula:

Solution:

Hence, the width of the chocolate box is 8 units.

Answer:

W = 8

Step-by-step explanation:

Volume  = length * width * height

100 = 5 * W * 2.5

W = 100/ ( 5 * 2.5)

W = 8

Answer:17.416

Step-by-step explanation:

I think you misspelled teen as ten so if so, this is the answer.

Answer:

150 people

Step-by-step explanation:

Lets call the total amount of people at the talent show x. Since 3/6=1/2, we know that half the people are girls, 1/3 are boys. If we added 1/2 and 1/3 we get 5/6, 1-5/6=1/6, so now we know that 1/6 of the people are adults. Because it says "If there were 50 more girls than adults" so from that we can see that 1/2x =1/6x+50. If we were to simplify the equation, we 1/3x=50, so x=150

Answer:

Hi, your answer here would be based on reading this graph.  For question a, there are a total of 12 people who like vanilla with sprinkles, which means that it is 12 out of 24 or 1/2 or 0.5 or 50 percent.

For b) there is a total of 9 for chocolate, so the probability is 9 out of 24 or 37.5 percent or 3/8 or 0.375

For c) there are a total of 6 with no sprinkles out of 24 so it is 1/4 or 0.25 or 25 percent.

Step-by-step explanation:

Please mark me as brainliest :)

The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.

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Answer:

can u please put the whole question here.

Step-by-step explanation: