jackson wants to test an assumption on the number of red candies in a bag of fruity tooty's candy. the company claims that five flavors are given an equal distribution in each bag, meaning that the proportion of each color should be 20%. jackson decides to focus his efforts on examining whether there is a difference in the proportion of red candies than what the company claims. what should jackson state for the null hypothesis and alternative hypothesis?

Answer:

The height of flag pole=8.3m

Step-by-step explanation:

We are given that

Height of boy=1.4 m

\(\theta=36^{\circ}\)

Distance of boy from the flag pole=9.5 m

We have to find  the height of the flag pole​.

BCDE is a rectangle

BC=ED=1.4 m

CD=BE=9.5 m

In triangle ABE

\(\frac{AB}{BE}=tan36^{\circ}\)

Using the formula

\(tan\theta=\frac{Perpendicular\;side}{base}\)

\(\frac{AB}{9.5}=tan 36^{\circ}\)

\(AB=9.5tan36^{\circ}\)

AB=6.90 m

Height of flag pole=AB+BC=6.90+1.4

Height of flag pole=8.3m

The solution of the pairs of lines are as follows,
(1) Line 1 and line 2 are perpendicular to each other.
(2) Line 1 and line 3 are parallel to each other.
(3) Line 2 and line 3 are perpendicular to each other.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Calculate the slope of each line,

LIne 1
3y = 2x + 5
y = 2/3x + 5/3
Compared with the standard equation of line y = mx + c,

Slope m = 2/3
Similarly.
The slope of line 2 = -3/2
The slope of line 3 = 2/3

Now. properties of pair of lines state that the slope of parallel lines is equal and the slope of perpendicular lines are negative reciprocal of each other,
So
Slope of line 1 = slope of line 3
But,
The slope of line 2 is the negative reciprocal of the slope of lines 1 and 3.

Thus, the solution of the pair of lines has been shown above.

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Answer:

i think its 1.

Step-by-step explanation:

f(x)=‐3x+3

-3. -3

-3=-3x

divide by -3

1=x

ANSWER

True

EXPLANATION

When the order matters, the number of ways to arrange items is determined with a permutation. This way, sets of items with the same items but in different order are counted as different sets. For example, (blue, red, green) is not the same as (green, red, blue).

On the other hand, when order does not matter, the number of ways to arrange items is determined with a combination. This way, sets with the same items are counted as the same set. In the previous example, both sets have the same combination of colors, so they are counted as the same set.

Hence, it is true that when the order does matter, the number of ways to arrange items is determined with a permutation.

Answer:

x^4 - mx^2 + n^2 = 0

Step-by-step explanation:

We can use algebraic manipulation to solve for m and n. First, we can square the equation xy = n to get:

(x^2)(y^2) = n^2

Since we also have x^2 + y^2 = m, we can substitute y^2 with m - x^2 to get:

x^2(m - x^2) = n^2

Expanding the left side of the equation, we get:

mx^2 - x^4 = n^2

Multiplying both sides by 16, we get:

16mx^2 - 16x^4 = 16n^2

Adding 32xy to both sides, we get:

16mx^2 + 32xy - 16x^4 = 16n^2 + 32xy

Substituting n for xy, we get:

16mx^2 + 32n - 16x^4 = 16n^2 + 32n

Rearranging the equation, we get:

16mx^2 - 16x^4 - 16n^2 = 0

Dividing both sides by -16, we get:

x^4 - mx^2 + n^2 = 0

Answer:

(4x+4y)²

Step-by-step explanation:

Given x²+y² = m ,xy=n.

Now 16m+32n = 16(m+2n)

= 16(x²+y²+2xy) = 4²(x+y)²[ x²+y²+2xy= (x+y)²]

(4x+4y)².

The derivative of f(x) at x = c does not exist.

To find the derivative of f(x) at x = c using the alternative form of the derivative, we first need to calculate the derivative of f(x) with respect to x.

Given that f(x) = x^3 - 2x^2 + 9, we can find the derivative of f(x) using the power rule and the constant multiple rule. The power rule states that the derivative of x^n, where n is a constant, is n*x^(n-1). The constant multiple rule states that the derivative of a constant multiplied by a function is equal to the constant multiplied by the derivative of the function.

Applying the power rule and constant multiple rule to f(x), we get:

f'(x) = 3x^2 - 4x

Now, we can evaluate f'(x) at x = c, which in this case is x = -2:

f'(-2) = 3(-2)^2 - 4(-2)

= 3(4) + 8

= 12 + 8

= 20

So, the derivative of f(x) at x = -2 is 20. However, we are asked to find the derivative at x = c = -2 using the alternative form of the derivative.

The alternative form of the derivative states that the derivative of a function at a specific point is equal to the limit of the difference quotient as x approaches the given point. In other words, the derivative at x = c is equal to the limit of (f(x) - f(c))/(x - c) as x approaches c.

Substituting c = -2 into the alternative form of the derivative, we get:

f'(-2) = lim(x->-2) (f(x) - f(-2))/(x - (-2))

However, if we try to evaluate this limit, we get an indeterminate form of 0/0. This means that the derivative of f(x) at x = -2 does not exist, as the limit of the difference quotient is undefined. Therefore, the main answer is that the derivative of f(x) at x = c does not exist.

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Answer:

Point D

Step-by-step explanation:

\( \huge \qquad \sf Answer\)

How to locate a point on a graph (x - y plane) :

The x - coordinate of a point on the graph shows its distance from y - axis and sign refers to its direction that is +ve sign means right side of y - axis and -ve sign means left side of y - axis.

We have been given its x - coordinate as 9, so the required point should be At a distance of 9 units from y - axis and in right side of y - axis.

And similarly, y - coordinate shows distance of point from x - axis, +ve for upward direction and -ve for downward direction.

and we have given the y - coordinate as 0, ao its distance from x - axis is 0. that means the point lies of x - axis.

And by Observing the points clearly we can figure out that the required point is D. that satisfy the condition.

Answer:

A = 974

Step-by-step explanation:

The formula for surface area of a rectangular prism is A=2(wl+hl+hw)

so yeah enjoy freedom for the rest of the day

Answer:

974 inches2

Step-by-step explanation:

Surface Area = 2×(11×8 + 11×21 + 8×21) = 974 inches2

The shortest distance from the origin to the curve x2 + xy + y2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

We have to find the shortest and longest distances from the origin to the curve x^2 + xy + y^2 = 3. This can be done using the Lagrange multiplier technique.

Given, x^2 + xy + y^2 = 3.

We have to minimize and maximize the distance of the origin from the given curve. The distance of the origin from the point (x, y) is given by √(x²+y²).

Therefore, we have to minimize and maximize the function f(x, y) = √(x²+y²) subject to the constraint x^2 + xy + y^2 = 3.

Now, we have to form the Lagrange function.

L(x, y, λ) = f(x, y) + λ(g(x, y))

where, g(x, y) = x2 + xy + y2 - 3L(x, y, λ) = √(x²+y²) + λ(x2 + xy + y2 - 3)

Now, we have to find the partial derivatives of L with respect to x, y, and λ.

∂L/∂x = x/√(x²+y²) + 2λx+y = 0 ............. (1)

∂L/∂y = y/√(x²+y²) + λx+2λy = 0 ............. (2)

∂L/∂λ = x² + xy + y² - 3 = 0 ............. (3)

Solving equations (1) and (2), we get x/√(x²+y²) = 2y/x.

Since x and y cannot be equal to 0 simultaneously, we can say that x/y = ±2.

Substituting x = ±2y in equation (3), we get y²(5±2√7) = 9.

Now, we can solve for x and y to get the values of (x, y) at which the minimum and maximum value of the distance of the origin occurs.

Using x = 2y, we get y²(5+2√7) = 9 ⇒ y = ±3/√(5+2√7)

Using x = -2y, we get y²(5-2√7) = 9 ⇒ y = ±3/√(5-2√7)

Therefore, the four points at which the distance is minimum and maximum are {(2/√(5+2√7), 1/√(5+2√7)), (-2/√(5+2√7), -1/√(5+2√7)), (2/√(5-2√7), -1/√(5-2√7)), (-2/√(5-2√7), 1/√(5-2√7))}.

To find the minimum and maximum distances, we can substitute these points in f(x, y) = √(x²+y²).

After substituting, we get the minimum distance as √(6-2√7) and the maximum distance as √(6+2√7).

Therefore, the shortest distance from the origin to the curve x^2 + xy + y^2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

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Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

No

Step-by-step explanation:

Answer:

proportional

Step-by-step explanation:

B’B is 3.5

Step-by-step explanation:

Segment A'B' is parallel to segment AB.

So, The length of segment AB is 7.5 units

The length of segment B'B is 3.5 units

Given :

Segment A'B' is parallel to segment AB. Few sides of the triangle is given.

Apply basic proportionality theorem

When  A'B' is parallel to segment AB then sides are proportional

\(\frac{CB'}{B'B} =\frac{CA'}{A'A}\)

Substitute the values

\(\frac{7}{B'B} =\frac{6}{3} \\cross \; multiply\\7(3)=B'B(6)\\21=B'B(6)\\Divide \; by \; 6\\B'B= \frac{21}{6} \\B'B=3.5\)

Now we find AB by making a proportion

\(\frac{CA'}{CA} =\frac{BA'}{BA} \\\frac{6}{9} =\frac{5}{AB} \\Cross \; multiply\\6(AB)=5 \cdot 9\\6AB=45\\Divide \; by \; 6\\AB=7.5\)

The length of segment AB is 7.5 units

The length of segment B'B is 3.5 units

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The Babylonian approximation 3;41 is equal to 3.683, which is very close to the correct value of 3.637. we need to calculate the correct value for the ratio of the area of a regular heptagon to the square of a side.

First, we need to convert the Babylonian approximation 3;41 into a decimal. To do this, we divide 41 by 60, which is equal to 0.683. Then, we add this decimal to the whole number 3, resulting in 3.683.

Next, we need to calculate the correct value for the ratio of the area of a regular heptagon to the square of a side. To do this, we use the equation A = (7/4)s^2, where A is the area of the heptagon and s is the length of the side. We can rearrange this equation to become (A/s^2) = (7/4). This results in a value of 3.637 for the ratio.

Finally, we compare the two values. 3.683 is very close to 3.637, so the Babylonian approximation is accurate.

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Answer:

a = 97° , b = c = 146°

Step-by-step explanation:

a and 83° are same- side interior angles and sum to 180°

a + 83° = 180° ( subtract 83° from both sides )

a = 97°

34° and b are same- side interior angles and sum to 180°

b + 34° = 180° ( subtract 34° from both sides )

b = 146°

b and c are corresponding angles and are congruent , so

c = b = 146°

Answer:

< a = 97 degrees.

< b = 146 degrees.

< c = 146 degrees.

Step-by-step explanation:

We have 2 lines crossing 2 parallel lines.

Internal angles between the 2 parallel lines add up to 180 degrees, so

34 + <b = 180

<b = 180 - 34 = 146 degrees

Also

<a + 83 = 180 degrees (also internal angles)

---> <a = 97 degrees

< c and < b are corresponding angles so are congruent, therefore

<c = < b = 146 degrees.

No, the presence of an effect does not necessarily imply that error variance will go away.

The presence of an effect does not necessarily imply that error variance will go away. In fact, error variance is an inherent part of any statistical model and represents the amount of variation in the response variable that is not explained by the predictor variables.

Even if a predictor variable has a significant effect on the response variable, there may still be some unexplained variation in the response that is attributable to error variance.

It is important to take into account and control for error variance in any statistical analysis, as it can affect the precision and accuracy of the estimates of the model parameters and can also influence the interpretation of the results.

One way to control for error variance is to use appropriate statistical methods, such as analysis of variance (ANOVA), regression analysis, or other modeling techniques that take into account the variability in the data.

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Answer:7√(10x)×√6/(√6×√6)=7/6×√60x

Step-by-step explanation:

Answer:

x=19

Step-by-step explanation:

y=7 - 2=(y) 5 then x=21 - 2=(x)19

Answer:

x = 18

Step-by-step explanation:

4x-6= 3.5x+3

4x - 9 = 3.5

Answer:h=a/3b

Step-by-step explanation:

Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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Answer: 2.5, 5.4

Step-by-step explanation:

\(-16t^2 +126t=213\\ \\ 16t^2 -126t+213=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4\)

To bring the 2,000 kg wagon to rest, the buffer stop needs enough springs to absorb its kinetic energy. The number of springs and their stiffness can be calculated using given parameters and formulas.



To calculate the number of springs required in the buffer stop, we need to find the energy of motion that needs to be absorbed. The kinetic energy (KE) of the wagon is given by KE = (1/2)mv^2, where m is the mass (2,000 kg) and v is the velocity (0.69 m/s). The KE is 477.9 J.Next, we calculate the potential energy stored in the compressed springs. The compression distance is 15 cm, which is 0.15 m. The potential energy (PE) stored in each spring is given by PE = (1/2)kx^2, where k is the stiffness of the spring and x is the compression distance.

The total energy absorbed by all the springs is equal to the kinetic energy of the wagon. Therefore, the number of springs required is given by N = KE / PE, where N is the number of springs.To determine the stiffness of the spring, we use the formula k = (Gd^4) / (8nD^3), where G is the shear modulus (0.8 x 10^5 N/mm^2), d is the wire diameter (2 cm), n is the number of coils (15), and D is the mean diameter of the coils (20 cm).

By substituting the values into the equations, we can find the number of springs and the stiffness of each spring.

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Answer:

Below

Step-by-step explanation:

4/ 9 z - 5/9 z + 2 - 3/9 z  - 9

(4-5-3)/9 z +2 - 9

-4/9 z +2-9

-4/9 z  - 7

The corresponding confidence interval is the narrowest for the 99% level of confidence, as higher confidence levels require wider intervals to provide increased certainty.

A confidence interval represents the range within which the true population parameter is likely to fall based on the sample data. The level of confidence indicates the probability that the true parameter lies within the interval.

When the level of confidence increases, the width of the confidence interval also increases. This is because a higher level of confidence requires a wider interval to capture a larger range of possible values.

In the given options, the 99% level of confidence will provide the narrowest confidence interval. This is because it allows for a higher margin of error and wider range, resulting in a narrower interval. On the other hand, lower confidence levels such as 90%, 95%, and 98% will have wider intervals to provide a higher level of certainty.

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The option that shows that the derivative of a function as well as its intervals is decreasing is option C (Image attached).

A derivative is known to be a tool that help us to know the altering relationship that between two variables. The derivative formula is known to be ddx. xn=n.

Note that:

F¹(x) =  e^sinx - cosx - 1

Set:

F¹(x) > 0

e^sinx  > cosx - 1

0.633 < x < 4.155  and 6,916 < x < 9

So, if you look at the equation, the option that fits into the equation is option c:

Therefore, The option that shows that the derivative of a function as well as its intervals is decreasing is option C (Image attached).

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Answer:

75-82,            in Exercises 75-82, find the average rate of change of the function from x1 to x2. function f(x) = 3x +8 x-values x1=0, x2=3

Answer:x > 1/5

Step-by-step explanation:

Answer:5 steps

Step-by-step explanation:

Respond quickly. You have 60 days from the time the billing statement is sent to request a correction, so act quickly. ...

Your request needs to be in writing. ...

Then you wait. ...

Don't withhold payment! ...

Cover yourself.

To find the point on the plane x - 2y + 3z = 6 that is closest to the point (0, 1, 1), we can use the concept of orthogonal projection. The closest point will be the projection of the given point onto the plane.

The equation x - 2y + 3z = 6 represents a plane in three-dimensional space. We are required to find the point on this plane that is closest to the point (0, 1, 1).

To find the closest point, we can use the concept of orthogonal projection. The projection of a point onto a plane is the point on the plane that is closest to the given point. This can be achieved by finding a vector that is orthogonal (perpendicular) to the plane.

The normal vector of the plane is (1, -2, 3) since it represents the coefficients of x, y, and z in the plane equation. We can use this normal vector to calculate the projection of the given point onto the plane.

The projection of the point (0, 1, 1) onto the plane is given by the formula:

Projection = (0, 1, 1) - [(0, 1, 1) dot (1, -2, 3)] / ||(1, -2, 3)||² * (1, -2, 3)

Simplifying the equation and performing the calculations will yield the coordinates of the point on the plane that is closest to (0, 1, 1).

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The value of x is 94.8

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Sin(tetha) = opp/hyp

cos (tetha) =adj/hyp

tan (tetha) =opp/adj

67 is the opposite and x is the hypotenuse in the triangle

sin45 = 67/x

1/√2 = 67/x

x = 67√2

x= 94.8( nearest tenth)

therefore the value of x is 94.8

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