Which equation represents a line parallel to the line shown on the graph?
A.y = 4 x minus 1
B.y = negative 4 x + three
C.y = one-fourth x + 5
D.y = negative one-fourth x minus 1

The measure of angle A'B'C' is 21.

We know that ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.

We are given that;

Angle ABC = 21°

Scale factor= 3

Now, dilation is a transformation that preserves the shape and angles of a figure, but changes its size by a scale factor.

Thus, the measure of angle A’B’C’ is equal to the measure of angle ABC, regardless of the scale factor or the center of dilation.

Therefore, by the given angle the answer will be 21.

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There are 52 cards in the deck and so the probability of guessing the card right is 1/52.

Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.

Here,

We can find this probability by seeing that

=1/4×1/13

=1/52

Because there are 52 cards in the deck, the probability of correctly predicting the card is 1/52.

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An eating disorder characterized by bingeing and purging is called bulimia nervosa.

The minimum amount of body fat needed for good health is variable and can depend on factors such as age, gender, and individual circumstances. However, essential body fat is typically estimated to be around 3-5% for men and 8-12% for women.

The term used to describe a person who is very overfat is obese. Obesity refers to having excessive body fat, which can have negative effects on health.

People with anorexia nervosa, an eating disorder characterized by restrictive eating and an intense fear of gaining weight, often see themselves as too fat even when they are extremely thin. This distorted body image is a characteristic feature of anorexia nervosa.

A technique for assessing body fat levels that involves being weighed under water is called hydrostatic weighing or underwater weighing. It is considered one of the more accurate methods for determining body composition.

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Answer: \(x=6\)

Step-by-step explanation: Since the triangles are similar, line them up so that the equivalent angle is in the same spot on both triangles. In triangle JKL the 12 represents the same side on QRS being 20. This means that triangle QRS's sides are 5/3 greater than the other triangle. To solve for x, set up the equation based on the similar sides and it is,

\(7x-2 = 5/3(24)\)

which means that

\(7x-2 = 40\)

then

\(7x=42\)

lastly,

\(x=6\)

The slope-intercept form of the line is \(y=\dfrac{1}{4}x\).

Given:

A line passes through the two points \((4,1)\) and \((8,2)\).

To find:

The slope-intercept form of the line.

Explanation:

The slope-intercept form of a line is:

\(y=mx+b\)

Where, \(m\) is slope and \(b\) is the y-intercept.

The line passes through the two points \((4,1)\) and \((8,2)\). So, the equation of the line is:

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(y-1=\dfrac{2-1}{8-4}(x-4)\)

\(y-1=\dfrac{1}{4}(x-4)\)

Using the distributive property, we get

\(y-1=\dfrac{1}{4}(x)+\dfrac{1}{4}(-4)\)

\(y=\dfrac{1}{4}x-1+1\)

\(y=\dfrac{1}{4}x\)

Therefore, the slope-intercept form of the line is \(y=\dfrac{1}{4}x\).

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Answer:

X +50= 180

X=130

y=130(VOA)

Answer:

x and y are 130°

Step-by-step explanation:

180-50=130

x and y = 130

if the angles are equal when a line goes through the lines they are parallel

a) If the confidence level had been 90% instead of 98%, the new confidence interval would be (0.325, 0.475).

b) If the sample size had been 255 instead of 170, the new confidence interval would be (0.292, 0.508).

c) If the confidence level had been 99% instead of 98%, the new confidence interval would be (0.304, 0.496).

a) First, we find the mean of the original confidence interval:

Mean = (Lower Limit + Upper Limit) / 2 = (0.313 + 0.487) / 2 = 0.4

Margin of Error = (Upper Limit - Mean) = (0.487 - 0.4) / 2 = 0.0435

New Margin of Error = Margin of Error * \((Z_{90} / Z_{98})\)

where \(Z_{90}\) is the critical value for a 90% confidence level, and \(Z_{98}\) is the critical value for a 98% confidence level.

From the standard normal distribution table, we find:

\(Z_{90}\) ≈ 1.645

\(Z_{98}\) ≈ 2.326

New Margin of Error = 0.0435 * (1.645 / 2.326) ≈ 0.0306

Finally, we construct the new confidence interval using the adjusted margin of error:

New Confidence Interval = (Mean - New Margin of Error, Mean + New Margin of Error)

                     = (0.4 - 0.0306, 0.4 + 0.0306)

                     ≈ (0.3694, 0.4306)

Therefore, the new confidence interval at a 90% confidence level would be approximately (0.369, 0.431) when rounded to three decimal places.

b) Standard Error = \(\sqrt{(p_{hat} * (1 - p_{hat})) / n}\)

where \(p_{hat}\) is the sample proportion and n is the sample size.

Given that the sample size increases to 255 while the sample proportion remains the same, the new sample proportion is:

\(p_{hat}\) = 68 / 255 ≈ 0.267

Standard Error = sqrt((0.267 * (1 - 0.267)) / 255) ≈ 0.028

For a 98% confidence level, the critical value is \(Z_{98}\) ≈ 2.326.

New Margin of Error = \(Z_{98}\) * Standard Error = 2.326 * 0.028 ≈ 0.065

New Confidence Interval = (\(p_{hat}\) - New Margin of Error, \(p_{hat}\) + New Margin of Error)

                     = (0.267 - 0.065, 0.267 + 0.065)

                     ≈ (0.202, 0.332)

Therefore, the new confidence interval with a sample size of 255 would be approximately (0.202, 0.332) when rounded to three decimal places.

c) From the standard normal distribution table, we find:

\(Z_{99}\) ≈ 2.576

New Margin of Error = Margin of Error * (\(Z_{99}\) / \(Z_{98}\)) = 0.0435 * (2.576 / 2.326) ≈ 0.0482

New Confidence Interval = (Mean - New Margin of Error, Mean + New Margin of Error)

                     = (0.4 - 0.0482, 0.4 + 0.0482)

                     ≈ (0.3518, 0.4482)

Therefore, the new confidence interval at a 99% confidence level would be approximately (0.352, 0.448) when rounded to three decimal places.

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10.5 small boxes equals the same amount of cereal in a large box

From the information given, let:

n is the number of smaller boxes

We know that:

Then,

12 + 7.6n = 6 + 8n

collect like terms

8n - 7. 6n = 12 - 6

0. 4n = 6

n = 6/ 0. 4

n = 15

The amount of cereal in a large box is;

6 + 8n = 6 + 8 (15) = 126 ounces

The amount of cereal in the smaller box is 12 ounces

Divide the volume of the larger box by the volume of the smaller box;

= 126/ 12

= 10. 5 smaller boxes

Hence, 10.5 small boxes equals the same amount of cereal in a large box

The complete question:

A cereal box manufacturer changes the sizeof the box to increase the amount of cereal it contains. The equations 12 + 7.6n and 6 + 8n, where n is the number of smaller boxes, are both representative of the amount of cereal that the new larger box contains. How many smaller boxes equal the same amount of cereal in the larger box?

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As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

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The length of the rectangle whose area is 7 units larger than its perimeter is 13 units.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

Given, Area of a rectangle is 7 units larger than its perimeter.

Assuming the length of the rectangle to be 'l' and the width to be 'w',

and the width is 3 units.

∴ (l×w) = 2(l + w) + 7.

(l×3) = 2(l + 3) + 7.

3l = 2l + 6 + 7.

l = 13 units.

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For the relaxation test, the response of the following models, including the initial (elastic) stress and the final stress after a very long time, are given as follows:

Model A: Two Springs in Parallel, The equation of the model is given as F = F1 + F2. The two springs are in parallel to each other, so they have the same extension x. Therefore, the force in the first spring is F1 = k1x, while the force in the second spring is F2 = k2x, so the total force F is given by F = k1x + k2x = (k1 + k2) x. The relaxation test is carried out by applying a constant load to the system, allowing it to reach its equilibrium position, and then removing the load. The system then relaxes back to its initial state. The initial (elastic) stress is given by σ0 = F/A, where F is the initial load applied and A is the cross-sectional area of the specimen. The final stress after a very long time is given by σ∞ = 0.

Model B: Maxwell Model ,The Maxwell model consists of a spring and a dashpot connected in series, as shown below. The spring has a spring constant k, and the dashpot has a viscosity coefficient η. The deformation of the spring results in a force F = kx. The dashpot resists the deformation with a force proportional to the velocity of the deformation, which is given by F = ηv.The relaxation test is carried out by applying a constant load to the system, allowing it to reach its equilibrium position, and then removing the load. The system then relaxes back to its initial state. The relaxation time constant for this model is given by τ = η/k.The initial (elastic) stress is given by σ0 = F/A, where F is the initial load applied and A is the cross-sectional area of the specimen. The final stress after a very long time is given by σ∞ = 0.

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Answer:

a) 52  

b)115

Step-by-step explanation:

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Answer:

x = 14, y = 37

Step-by-step explanation:

The angle vertical to (9x + 12 )° and 3x are same- side interior angles and are supplementary, sum to 180°, then

9x + 12 + 3x = 180

12x + 12 = 180 ( subtract 12 from both sides )

12x = 168 ( divide both sides by 12 )

x = 14, so

3x = 3 × 14 = 42

3x and 4y - 10 are adjacent angles and supplementary, then

3x + 4y - 10 = 180

42 + 4y - 10 = 180

4y + 32 = 180 ( subtract 32 from both sides )

4y = 148 ( divide both sides by 4 )

y = 37

A hiker is standing on one bank of a river. The height of the tree is approximately 159.45 feet.

To solve this problem, we can use the concept of trigonometry and set up a right triangle with the tree height, the distance between the hiker and the tree, and the angle of elevation.

Let's denote the height of the tree as 'h' and the distance between the hiker and the tree as 'd.' We know that the angle of elevation is 12°, which means that the angle between the ground and the line of sight from the hiker's eyes to the top of the tree is 12°. Therefore, we can set up a right triangle as follows:

    /|

   / |

h /  |d

/   |

/θ___|

where θ represents the angle of elevation (12°).

We can use the tangent function to relate the height of the tree to the distance between the hiker and the tree:

tan θ = opposite/adjacent = h/d

Rearranging this equation gives:

h = d tan θ

Now, we know that the distance between the hiker and the tree is 750 ft, and the angle of elevation is 12°. Plugging these values into the equation above, we get:

h = 750 tan 12°

Using a calculator, we can find that tan 12° is approximately 0.2126. Therefore,

h = 750 * 0.2126 ≈ 159.45

So the height of the tree is approximately 159.45 feet.

Therefore, the height of the tree is approximately 159.45 feet.

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Step-by-step explanation:

= 7 × 4/3

= (7 × 4)/3

= 28/3

7 × 4/3 = 28/3

Answer:

\( \sf 9 \frac{1}{3} \)

Step-by-step explanation:

\( \sf = 7 \times \frac{4}{3} \)

\( \sf = \frac{7}{1} \times \frac{4}{3} \)

\( \sf = \frac{28}{3} \)

\( \sf = 9 \frac{1}{3} \)

Answer:

its 5 5+4=9

Step-by-step explanation:

Answer:

7 and 7√3

Step-by-step explanation:

It's a rule in a triangle with 30°, 60° and 90°

Side opposite to 30° is x

Side opposite to 60° is x√3

Side opposite to 90° is 2x (diagonal)

So,

2x = 14

x = 7 (side with 30°)

x√3 = 7√3

Answer:

\({ \rm{ - 2x + 4 = 15x}}\)

-2 & 15

Coefficients (in -2x+4=15x):

What are coefficients?

Coefficients are the constants in an equation.  

Answer:

6

Step-by-step explanation:

1+3=4

8÷4=2

Kindergarten = 2×1 =2

Other class = 2×3=6

Ratio of kindergarten classes to other classes is 2:6

Step-by-step explanation:

Sn= a+[n-1]d

S2= a+[2-1]d

8.5 = a+d _______Equation 1

S5 = a+[5-1]d

13=a+4d ________Equation 2

Subtract Equation 1 from Equation 2

13=a+4d

-

8.5= a+d

________

4.5= 3d

d=1.5

Substituting d=1.5 in equation 1

8.5=a+1.5

a=8.5-1.5

a=7

Sum of terms of an A.P =

Sn= n/2[2a+(n-1)d]

292= n/2[2×7+(n-1)d]

292=n/2[14+(n-1)1.5

292×2=n[14+(n-1)1.5]

584=n[14+1.5n-1.5]

584= 14n+1.5n²-1.5n

584= 1.5n²+12.5n

1.5n²+12.5n-584

1.5n²-24n+36.5n-584

1.5n(n-16)+36.5(n-16)

(1.5n+36.5)(n-16)

**n-16=0

n=16

Answer:

I think you copied this wrong

Step-by-step explanation:

Most likely g = 2

Therefore (2) + 6(11)

2+66=68

Recently, the Town of Aberdeen announced they were going to acquire a large parcel of land for a new park initiative.

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The inequality that represents the possible elevations of climbers in the death zone on Mount Everest is 8000 < x ≤ 8850

The given parameter is'

Height = About 8850 meters

Death zone = Location above 8000 meters

Let the height be represented with x

So, the inequality that represents x is

Death zone  < x ≤ Height

This gives

8000 < x ≤ 8850

Hence, the inequality that represents the possible elevations of climbers in the death zone on Mount Everest is 8000 < x ≤ 8850

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Answer:

Step-by-step explanation:

You want to know the price per bushel for wheat, corn, and rye, given the sales ...

Using x, y, and z for price per bushel of wheat, corn, and rye, respectively, the given sales tell us ...

The easiest way to solve a system of equations like this is to make use of the matrix manipulation capabilities of a calculator. The attached calculator display shows the reduction of the augmented matrix of coefficients to "reduced row-echelon form". That puts the solution in the last column:

  x = y = 3.61, z = 1.91

The price per bushel for wheat and corn is the same: $3.61; the price per bushel for rye is $1.91.

__

Additional comment

The second attachment shows a solution using a graphing calculator. In this solution, an expression for z based on the first equation is used in the remaining two equations, which then tell us the values of x and y.

If you add all of the equations, you get 10x +10y +10z = 91.30, which gives you ...

  x + y + z = 9.13

This can be solved for any variable you may want to substitute into any pair of the equations. This approach avoids any messy fractions.

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Solution

We can use the following identity:

Solving for x we got:

Answer:

hmmmmmmmm

Step-by-step explanation:

yea i really dont know