Please show me how to solve this problem?

All the answers to the given parts are mentioned below -

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.

We can write the proportional relationship as -

y = kx

Now, from the given information, we can write -

2 scoops need 0.5 gallon of water

6 scoops need 1.5 gallon of water

So -

k = 2/0.5

k = 2/(1/2)

k = 2 x 2 = 4

Equations that represents the relationship can be written as -

y = 4x + c

Now, 2 scoops need 0.5 gallon of water.

2 = 4 x 1/2 + c

2 = 2 + c

c = 0

So, the equation will be y = 4x.

Graph of y = 4x is attached at the end.

For 10 scoops of water -

10 = 4x

x = 2.5 gallons of water is needed.

Therefore, all the answers to the given parts are mentioned above.

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D. I and IV are the quadrants the cosine function is positive

To determine in which quadrants the cosine function is positive, we need to consider the signs of cosine in different quadrants of the Cartesian coordinate system.

The unit circle is a useful tool to understand the behavior of trigonometric functions. In the unit circle, the x-coordinate represents the cosine value, while the y-coordinate represents the sine value. The cosine function is positive in the quadrants where the x-coordinate is positive.

Quadrant I is the top-right quadrant, where both the x and y coordinates are positive. In this quadrant, cosine is positive because the x-coordinate is positive.

Quadrant II is the top-left quadrant, where the x-coordinate is negative, but the y-coordinate is positive. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant III is the bottom-left quadrant, where both the x and y coordinates are negative. In this quadrant, cosine is negative because the x-coordinate is negative.

Quadrant IV is the bottom-right quadrant, where the x-coordinate is positive, but the y-coordinate is negative. In this quadrant, cosine is positive because the x-coordinate is positive.

Based on this analysis, we can conclude that cosine is positive in Quadrant I and Quadrant IV. Therefore, the correct answer is D. I and IV.

It's important to note that this applies to the standard unit circle and the principal values of cosine. When considering periodicity and multiple revolutions around the unit circle, the positive regions of cosine will repeat every 360 degrees or 2π radians.

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\(\Large\maltese\underline{\textsf{Our problem:}}\)

The lines shown below are perpendicular. Is this statement true or false?

\(\Large\maltese\underline{\textsf{This problem has been solved!}}\)

In order for a pair of lines to be perpendicular, they must intersect at a \(\bf{90^\circ}\) angle. (a right angle)

\(\bf{Since\;the\;green\;line\;and\;the\;red\;one\;intersect\;at\;a\;right\;angle,}\\they\;are\;perpendicular.\\\\Hope\;you\;will\;have\;a\;fantabulous\;day!}\)

\(\rule{300}{1.7}\)

\(\boxed{\bf{aesthetic \not101}}\)

Answer:

0 times because 8 is greater than 0

Step-by-step explanation:

Answer:

the answer would be 0 because if you try to put 8 into 0, it wont so your answer would be 0

Round this however your teacher instructs.

=================================================

Work Shown:

mu = 830 = mean

sigma = 96.7 = standard deviation

x = 915 = given raw score we want to convert

z = (x - mu)/sigma

z = (915 - 830)/(96.7)

z = (85)/(96.7)

z = 0.8790072 approximately

Answer:16x16

Step-by-step explanation:

Answer:

3(x + 6) = 30

Hope that helps! :)

Step-by-step explanation:

The length of the segment is 2.4 centimeters.

The scale is 2.4 cm :24 mm.

How to change mm to cm?

One millimeter, or one-thousandth of a meter, is equal to one mm. One centimeter, also known as one hundredth of a meter, is equal to one centimeter.

Accordingly, 1 cm 10 mm. Divide the number of mm by 10 to get the number of cm when converting mm to cm.

Given that length of the segment is 24mm. now we know that,1 mm is equal to 0.1 cm,

So,

\(10 \: mm=1 \: cm \\ or, \: 1 \: mm = \frac{1}{10} \: cm \\ or, 24 \: mm × ( \frac{1}{10} ) = 2.4 \: cm.\)

The scale is 2.4 cm :24 mm.

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Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

The true statement about the axis of rotation is the option;

It is parallel to a side of the equilateral triangle, but is separate from the equilateral triangle.

The axis of rotation is a straight line around which all points on a rotating body rotates.

The diagram shows a figure with a hollow cylindrical cross section and triangular cross section on the left and right, which indicates that the figure is created by the rotation of the equilateral triangle about height of the cylinder, such that the axis of rotation is a vertical line through the center of the hollow cylinder. Therefore, the axis of rotation is parallel to the height of the cylinder, and therefore, it is parallel to the base of the equilateral triangle, but it it seperate from walls of the cylinder, and therefore, separate from the equilateral triangle

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The entries for Row 3 in step 3 are : 0, -1, -2, 1

R_{1} = Row1

R_{2} = Row  2

R_{3} = Row  3

For the third step, STEP 3 :

THE VALUE OF Row 3 is obtained thus :

\(R_{3} = R_{3} - 3R_{1}\)

\(From \: step \: 1 : R_{1} = [1 1 1 0]\)

\(R_{1} = [1 1 1 0] \\  \\

\(R_{3} = [3 2 1 1]  \\  

\\ 3R_{1} = 3(1 1 1 0) = [3 3 3 0]\)

\(R_{3} - 3R_{1} \:  =

(3 - 3), (2 - 3), (1 - 3), (1 - 0) = (0, -1, -2, 1)\)

Hence, the entry for Row 3 in step 3 will be :

(0, - 1, - 2, 1)

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Answer:

a

 \(\frac{\alpha }{2} = 2.5 \%\)

b

  \(N = 25\)

Step-by-step explanation:

From the question we are told that

   The number of bootstrap samples is  n =  1000

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally the percentage of values that must be chopped off from each tail  for a 95% confidence interval is mathematically evaluated as

      \(\frac{\alpha }{2} = \frac{0.05}{2} = 0.025 = 2.5 \%\)

=>    \(\frac{\alpha }{2} = 2.5 \%\)

Generally the number of the bootstrap sample that must be chopped off to produce a 95% confidence interval is

      \(N = 1000 * \frac{\alpha }{2}\)

=>   \(N = 1000 * 0.025\)

=>   \(N = 25\)

Answer:

Step-by-step explanation:

Hey

Answer:

10-5g >80

Step-by-step explanation:

10-5g >80

This is the    statment if u want it.

Answer: L=45, W=9

Step-by-step explanation:

Perimeter P=108  so if  L=5W,

P=2(L+W)=2(5W+W)=2(6W)=12W

108=12W

W=108/12=9

L=5*9=45

Differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from \(x_{0}\) to \(x_{0}\) + dx is \($$d S=\left(12 x_0\right) d x$$\)

As per the given data:

The surface area is given by

\($$S = 6 x^2$$\)

Differentiate both sides with respect to  f(x)

\($$S^{\prime}(x)=\frac{d}{d x}\left(6 x^2\right)\\\\=6(2) x^{2-1}$$\)

= 12 x

The estimated change in surface area is given by

\($$d S=S^{\prime}(x) d x= > d S\\\\$$\)

= (12 x) dx

The change in surface area at \($x=x_{0} $\) is

\($$d S=\left(12 x_0\right) d x$$\)

Therefore the answer is \($$d S=\left(12 x_0\right) d x$$\)

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Write a differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from \(x_{0}\) to \(x_{0}\) + dx

Answer:

so on the bottom you will see an x and on the left side you will see an y, for 1,4 the 1 will be on the x and the 4, just go up to the four for 2,8 on the x you will go on two on the bottom, for y you will go up to the 8, for 4,16 the x is four and you will go up to 16, for 5,20 the x will be 5 and then go up to 20. I really hope that this helped

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 2/5 cookies in 4 mins

To find the unit rate in minutes, divide 6 2/5 and 4 by 4.

In one minute is 1.6 cookies.

To find the unit rate in cookies, we divide by 6 2/5.

For one cookie, there are 5/8 minutes.

[ rate 5stars~ and give thanks for more po! welcome! ]

Step-by-step explanation:

We have the triple integral:

∫∫∫E x^2 + y^2 + z^2 dV

where E is the ball x^2 + y^2 + z^2 ≤ 81.

In spherical coordinates, the volume element is given by:

dV = ρ^2 sin φ dρ dθ dφ

where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis).

Substituting into the integral, we get:

∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^2 sin φ (ρ^2) dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^4 sin φ dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π (1/5)(9^5) sin φ dθ dφ

= (2π/5)(9^5)(-cos φ)|φ=0 to φ=π

= (2π/5)(9^5)(-(-1 - 1))

= (4π/5)(9^5)

≈ 114413.73

Therefore, the value of the triple integral is approximately 114413.73.

Answer:

The equation of this line is y = -4.

Answer:

y=-4

Step-by-step explanation:

zero slope m=0

y-y1=m(x-x1)

y-(-4)=0(x-(-9))

y+4=0

y=-4

Answer:

A

Step-by-step explanation:

the answer is A

(f+g)(x)= f(x)+g(x)

Answer:

16 cm shorter, 149 cm

Step-by-step explanation:

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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The number of pounds of cookie dough needed is 1,440. Therefore, option B is the correct answer.

Given that,

Last year, they sold 1,080 pounds of cookie dough to 360 people.

This means that they sold an average of 3 pounds of cookie dough per person.

Number of pounds of cookie dough = 3 pounds/person × Number of people

Here, 3×460=1,380

3×500=1500

To get a more accurate estimate, we can take the average of these two numbers, which is 1,440 pounds of cookie dough.

Therefore, option B is the correct answer.

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Answer:

Its 2/8

Step-by-step explanation:

2/8 simplified is 1/4

Answer:

The answer will be 2/8 because if you think about it 4/8 is 1/2 and 1/2 of 4/8 is 2/8 and since 1/2 4/8 is 2/4 which is actually 1/2 of 1/2 so that makes it 1/4 hope this helps!!

(to make it clear the answer is 2/8)

Answer:

Step-by-step explanation:

If you added all angles of triangle, add up to 180

to find 3rd angle subtract other 2 from 180.

ex.

1. 180-49-82 =49

2.  all angles are same so divide 180/3 =60

3. 45

4.  90

5. 79

6.   29

7.  70

8.   76

9.   30

10.  55