Let P(x,y) be a point on the graph of y=√x
Express the distance d from P to the point (0,0)(0,0) as a function of x
(a) d=√x2+x
(b) d=x2+x
(c) d=√x2+3x+1
(d) d=x2+3x+1
(e) None of the above.

The value of angle m∠FCG is 27.5.

x = 25

x = 35

We have,

1.

GCH and ECD are alternate angles.

This means,

GCH = 125 = ECD

And,

ECG and DCH are alternate angles.

This means,

ECG = DCH = x

Now,

GCH + ECD + ECG + DCH = 360

125 + 125 + x + x = 360

250 +2x = 360

2x = 360 - 250

2x = 110

x = 55

Now,

ECG = ECF + FCG

55 = ECF + FCG

ECF and FCG are equal.

So,

m∠FCG = 55/2 = 27.5

2.

The straight angles are formed by (5x + 20) and (2x - 5).

So,

5x + 10 + 2x - 5 = 180

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 25

3.

2x + 43 and 2x - 3 are on the same side of the parallel lines.

So,

2x + 43 + 2x - 3 = 180

4x + 40 = 180

4x = 180 - 40

4x = 140

x = 35

Thus,

The value of angle m∠FCG is 27.5.

x = 25

x = 35

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The rule that represents the dilation of the original triangle with a scale factor of 12 centered at the origin is (x, y) → (12x, 12y).

The coordinates of the vertices of the original equilateral triangle can be found by dividing the perimeter by the length of each side, which is 4/3. Thus, each vertex is located at a distance of 4/3 units from the adjacent vertices.

Let's assume that the original triangle is centered at the origin (0,0) and its vertices are (2/3, 0), (-1/3, √3/3), and (-1/3, -√3/3).

Multiply the x and y coordinates of each vertex by the scale factor of 12.

Thus, the vertices of the dilated triangle would be:

(2/3) × 12, 0 × 12 = (8, 0)

(-1/3) × 12, √3/3 × 12 = (-4, 2√3)

(-1/3) × 12, -√3/3 × 12 = (-4, -2√3)

So, the rule that represents the dilation of the original triangle with a scale factor of 12 centered at the origin is:

(x, y) → (12x, 12y)

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The given numbers in order from least to greatest is 0.44, 0.442 and 0.445.

The given numbers are 0.442, 44.5% and 11/25.

Here, 44.5% = 44.5/100

= 0.445

11/25=0.44

Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

Now, 0.44<0.442<0.445

Therefore, the given numbers in order from least to greatest is 0.44, 0.442 and 0.445.

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The graph and table show weight changes of two Chihuahua puppies over time; B's weight can be expressed as a function of A's weight plus 3 ounces.

The graph and table show the weight of two Chihuahua puppies, A and B, over a 10-week period. We can use the graph to determine the change in weight of Puppy B from week 2 to week 9.

This change in weight can be expressed in various ways, including as the rate at which Puppy B gained weight per week

(B(9) - B(2) divided by 7),

the amount of weight Puppy B gained in ounces during the seven-week interval ending at

t=9 (B(9) - B(2)),

or simply as the difference in height between the two points on the graph representing weeks 2 and 9.

The equation B(t) = A(t) + 3

It represents the relationship between Puppy B's weight and Puppy A's weight at any given time t. Specifically, Puppy B weighs three more ounces than Puppy A at time t.

This equation can be used to calculate Puppy A's weight at any given time if we know Puppy B's weight, or vice versa.

It can also be used to compare the weights of the two puppies at any given time, as the difference between their weights will always be

3 ounces.

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Some alkenes have geometric cis-trans isomers because of the presence of a double bond between two carbon atoms. In a carbon-carbon double bond, the carbon atoms are connected to two different groups of atoms, which can be oriented differently in space. In the cis configuration, the two substituent groups on each carbon atom are on the same side of the double bond, while in the trans configuration, the two substituent groups on each carbon atom are on opposite sides of the double bond.

The cis-trans isomerism arises due to the restricted rotation around the carbon-carbon double bond. In the case of cis isomers, the substituent groups are too bulky to rotate around the double bond, and they remain on the same side of the double bond. In contrast, in the trans isomers, the substituent groups are oriented on opposite sides of the double bond, which allows them to rotate freely around the bond.

The presence of cis-trans isomers has important consequences for the physical and chemical properties of alkenes, including their reactivity, solubility, and melting points. The two isomers can have different properties and can exhibit different biological activities, making them important targets for drug design and synthesis.

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The values of the equations are 1) 3 × 10⁴ and 2) 8.132 × 10⁵.

Given that are equations in scientific notation, we need to simplify them,

1) 2.4 × 10⁴ + 5.57 × 10³

So,

= 2.4 × 10 × 10³ + 5.57 × 10³

= 24 × 10³ + 5.57 × 10³

= 10³(24+5.57)

= 10³(29.57)

= 10³ × 29.57 × 10 / 10

= 2.957 × 10⁴

≈ 3 × 10⁴

2) 8.14 × 10⁵ - 7.8 × 10²

= 8.14 × 10³ × 10² - 7.8 × 10²

= 8140 × 10² - 7.8 × 10²

= 10²(8140-7.8)

= 10²(8132.2)

= 8132.2 × 10²

= 8132.2 × 10² × 10³ / 10³

= 8.132 × 10⁵

Hence the values of the equations are 1) 3 × 10⁴ and 2) 8.132 × 10⁵.

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Answer. The correct option is (E). 9.5 and 14.5

Explanation for step 1This is because 95% of the mean weights from samples of size 100 cats from this population will fall between 9.5 and 14.5 pounds. The other answers are incorrect because they do not fall within the range of 95% of the mean weights from samples of size 100 cats from this population

About 95% of the mean weights from samples of size 100 cats from this population would fall between approximately 11.51 pounds and 12.49 pounds.

To determine the range within which 95% of the mean weights from samples of size 100 cats would fall, we can use the concept of the confidence interval.

Given:

Population mean weight (μ) = 12 pounds

Population standard deviation (σ) = 2.5 pounds

Sample size (n) = 100 cats

Since the population distribution is assumed to be approximately normal, the sampling distribution of sample means will also be approximately normal. To calculate the range, we can use the formula for the confidence interval:

Confidence Interval = sample mean ± (z * standard error)

The standard error can be calculated using the formula:

Standard Error = σ / √n

Using a 95% confidence level, the corresponding z-value is approximately 1.96 (obtained from standard normal distribution table).

Plugging in the values:

Standard Error = 2.5 / √100 = 0.25

Confidence Interval = 12 ± (1.96 * 0.25)

Calculating the values:

Lower limit = 12 - (1.96 * 0.25) ≈ 11.51 pounds

Upper limit = 12 + (1.96 * 0.25) ≈ 12.49 pounds

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1 gram is equal to 0.001 kilogram.
To convert grams to kilograms, divide grams by 1000.

Answer: An angle that measures 180° would be a straight angle.

Step-by-step explanation:

This question is asking to identify an angle that measures 180°. To find if this angle is acute, obtuse, right, or straight is to measure them each.

Acute Angle - Acute angles are angles that measures less than 90° degrees

Obtuse Angle - Obtuse angles are any angles that greater than 90° with the exception of an 180° angle

Right Angle - Right angles are angles that are exactly equal to 90°

Straight Angle -  Straight angles are defined angles that are exactly 180 ° degrees.

Since a straight angle is 180° degrees. Therefore, this angle would be defined as a straight angle. Hope this helps!

The number of ways is 1 billion.

We are asked to determine the possible number of ways of the social security number that is 9 digits if the numbers can be repeated.

In this case, using fundamental counting, there are 10 possible numbers in each digit that is from zero to nine.

Thus, the number of ways is 10*10*10*10*10*10*10*10*10 equal to 1 billion ways.

Hence the number of ways is 1 billion.

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The missing values of x in the triangle are 66.8, 16.6, 10, 51.8

For A

Cos(x) = Adjacent / hypotenuse

Cos(58) = x/126

x = Cos(58) × 126

x = 66.8

For B :

Sin(x) = opposite/ hypotenuse

sin(x ) = 8/28

sin(x) = 0.2857

x = 16.6°

For C:

Tan(x) = opposite/ adjacent

Tan(x) = 6/34

Tan(x) = 0.176

x = 10°

For D:

sin(x) = opposite/ hypotenus

sin(18) = 16/x

x = 16/sin(18)

x = 51.8

Therefore, the missing values of x are 66.8, 16.6, 10, 51.8

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The probability that a student picked at random would pick a room filled with cupcakes or computers using probability concept is 0.26.

Probability is the ratio of required outcome to the total possible outcomes.

Mathematically,

Probability = Required outcome / Total possible outcomes

Room filled with computers or cupcakes = Number of rooms filled with computers + Number of rooms filled with cupcakes = 12 + 3 = 15

Total number of rooms = 12+3+12+3+29 = 59

P(computers or cupcakes) = 15/59 = 0.259

Therefore, the probability that a student picked at random would pick a room filled with cupcakes or computers is 0.26.

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Answer:

9 1/10th m/s2 :)

Step-by-step explanation:

The reason it is 1/10 is because the Number is 81 not 80, therefore 1/10 because there it is 1 left in 80 making it a fraction not a whole :) i hope this helps sorry if the explanation is too complicated...

Answer:

9.8596

Step-by-step explanation:

The depth of the water in the cylinder container is 120.9inches.

Given:

The frustum's vertical depth (h) is 30 cm.

Top frustum radius (r1) = 18 cm

Frustum's bottom radius (r2) is 28 cm.

The following formula determines the volume of a cone's frustum:

[tex]V = \frac{1}{3}* \pi * h * (r1^2 + r2^2 + (r1 * r2))[/tex]

calculating the frustum's volume

V=[tex]\frac{1}{3} *\pi *30(18^2+28^2+18*28)\\[/tex]

V=50642.5[tex]in^3[/tex].

The following formula determines a cylinder's volume:

Volume of cylinder = [tex]\frac{1}{3} \pi r^2h[/tex]

[tex]50642.5 = (1/3) *\pi *20^2*h[/tex]

h=[tex]50642.5*\frac{3}{\pi *20^2}[/tex]

h= 120.9 inches

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To determine the amount of salt in the tank after 60 minutes, we need the concentration of salt in the solution entering the tank.

The information provided, which is the salt concentration in terms of "zib salt /gal," is incomplete and does not specify the actual value of zib.

If you can provide the concentration of salt in the solution entering the tank (in terms of a specific numerical value), I can help you calculate the amount of salt in the tank after 60 minutes.

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a tank contains 100 gal of pure water inirially. a solution containing zib salt /gal enters into the tank at the vate of 3 gal/min. also a drain is open so that qhe volume of the solution is constant. tow much after salt is in the tank after 60 mins?

A ratio is a comparison of two or more quantities expressed as a fraction. For example, if we say that the ratio of apples to oranges is 2:3, it means that for every two apples, there are three oranges. Ade received an amount of 1500 from the total sum of 4000 .

In order to find out the amount Ade received, we need to first understand the concept of ratio. A ratio is a comparison of two or more quantities expressed as a fraction. For example, if we say that the ratio of apples to oranges is 2:3, it means that for every two apples, there are three oranges.

In this problem, we are given that Ade and Ola share a sum of 4000 in the ratio of 3:5. This means that the total ratio is 3+5 = 8.

To find out the amount Ade received, we need to first find the fraction of the total sum that belongs to Ade. We can do this by dividing Ade's ratio by the total ratio.

Ade's ratio is 3, so the fraction of the total sum that belongs to Ade is 3/8.

Now, we can find the amount Ade received by multiplying this fraction by the total sum:

Amount Ade received = (3/8) x 4000 = 1500.

1.Add the ratio parts: 3 (Ade's part) + 5 (Ola's part) = 8 total parts.

2. Divide the total sum (4000) by the total parts (8): 4000 ÷ 8 = 500. This gives us the value of one part.

3. Multiply Ade's ratio part (3) by the value of one part (500): 3 × 500 = 1500.

So, Ade received an amount of 1500 from the total sum of 4000.

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If α ,β are the roots of the equation then  (1 - α)(1 - β) - 50 is equal to -26.

Given that the equation

[1 25]

[0 1 2 -1 1 2] 5 [1 -1 2 0] 10 [0 1 2 -1 1 2] 5 [x^2 - 5x + 20x + 2] = [40]

is satisfied by α and β as the roots, we can rewrite the equation as follows:

[1 25]

[0 1 2 -1 1 2] 5 [1 -1 2 0] 10 [0 1 2 -1 1 2] 5 [(x - α)(x - β)] = [40]

Expanding and simplifying the equation, we get:

(x - α)(x - β) - 26 = 0

Substituting x = 1, we have:

(1 - α)(1 - β) - 26 = (1 - α)(1 - β) - 50 + 24 = -26.

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Answer:

Condition:

If a series converges, then the terms of the series approach 0.

Converse:

If the terms of a series approach 0, then the series converges.

Answer:

y = 2 sin (2x)

Step-by-step explanation:

the general form of a sine function is:

y = A sin (Bx + C) + D

where:

- A is the amplitude

- B is related to the period by the formula: period = 2pi/B

- C is the phase shift

- D is the vertical shift

Since you want an amplitude of 2, you can set A = 2. Since you want a period of pi, you can set B = 2pi/pi = 2.

y = 2 sin (2x)

Deb has 75 different combinations to choose from for her workout.

Deb has 25 different combinations to choose from. This is because she has 5 activities she can do and 5 different locations she can do them in, which gives her a total of 25 possible combinations. Once she's done with her activity, she has 3 different exercises she can do, so she has a total of 75 (25 x 3) different combinations to choose from for her workout.
The total number of combinations Deb has for her workout, we need to multiply the number of choices she has for each part of her workout.
1. Activity: Deb can choose from 5 activities (hike, walk, skate, bike, or run).
2. Location: Deb can choose from 5 locations (over the hills, around the lake, along the river, into the valley, or up the mountain).
3. Exercise: Deb can choose from 3 exercises (jumping jacks, sit-ups, or pull-ups).
Now, we'll multiply the number of choices for each part of the workout:
Total combinations = (Activities) x (Locations) x (Exercises) = (5) x (5) x (3) = 75
Deb has 75 different combinations to choose from for her workout.

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The rhombus-shaped cookie cutter has diagonals of 10 centimeters and 6.7 centimeters. We can use the formula for the area of a rhombus, which is A = (d1 * d2)/2, where d1 and d2 are the lengths of the diagonals.

So, the area of the cookie cutter is A = (10 * 6.7)/2 = 33.5 square centimeters.  Since Alejandro wants to ice the tops of 16 cookies, we need to find the total area of the tops of the cookies. If we assume that each cookie is a rhombus with the same shape as the cookie cutter, then each cookie has an area of (10 * 6.7)/2 = 33.5/2 = 16.75 square centimeters.  Therefore, the total area that needs to be covered in icing is 16 * 16.75 = 268 square centimeters. Rounded to the nearest square centimeter, the total area is 268 square centimeters.

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The calculated equation of the line L is y = -4x  + 5

Given that

We have the partition to be

m : n = 2 : 3

The coordinate is then calculated as

M = 1/(m + n) * (mx₂ + nx, my₂ + ny₁)

So, we have

M = 1/5 * (2 * 11 + 3 * -9, 2 * 12 + 3 * 7)

Evaluate

M = (-1, 9)

The slope of line PQ is

Slope = (12 - 7)/(11 + 9)

So, we have

Slope = 1/4

The slopes of perpendicular lines are opposite reciprocals

So, the slope of L is

m = -4

The equation of line L is then calculated s

y - 9 = -4(x + 1)

So, we have

y = -4(x + 1) + 9

Evaluate

y = -4x  + 5

Hence, the equation of line L is y = -4x  + 5

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According to the information, the most suitable prism for cereals would be #1 because it has more comfortable dimensions for buyers who would need fewer materials.

To find the area of the prisms we must find the area of each of their faces as shown below:

option 1

5 * 4 = 20

20 * 2 = 40

6 * 5 = 30

30 * 2 = 60

6*4=24

24 * 2 = 48

60 + 40 + 48 = 148

option 2

option 3

On the other hand, if we want to find the volume of the boxes we must multiply all their sides as shown below:

According to the above, we can infer that the three packages have the same volume. However, the most appropriate for this product would be #1 because it has more comfortable dimensions for buyers because they need fewer materials and its value would be lower.

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Answer:

The period of this graph is 7.

3 is the slope of the line between the pairs of points in each of the tables. Third table represents a linear function.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The word m is frequently used to represent slope; the reason for this is unclear, but it can be found in O'Brien's (1844)[2] and Todhunter's (1888) versions of the equation for a straight line, respectively, where it is written to be "y = mx + b" or "y = mx + c". The percentage of the "vertical difference" with the "horizontal change" among (any) two unique points on a line is used to compute slope. The ratio may occasionally be written as a quotient.

1)slope = y₂-y₁/x₂-x₁

         = -24/-8

         =3

2)slope = y₂-y₁/x₂-x₁

         = 13/3

         =3

Third table represents a linear function.

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Your question is incomplete but most probably your full question was,    

There are 7 multiples of 3 in the range 100₃ to 1000₃

From the question, we have the following parameters that can be used in our computation:

Multiples of 3 from 100₃ to 1000₃

Convert the numbers to base ten using the product rule

Such that each digit is multipled by the 3 to the exponent of the position of the number

And the sum of each product is taken

So, we have

100₃ = 1 * 3² = 0 * 3¹ + 0 * 3⁰ = 9

1000₃ = 1 * 3³ + 0 * 3² +  0 * 3¹ + 0 * 3⁰ = 27

The multiples of 3 from 9 to 27 are

9, 12, 15, 18, 21, 24 and 27 i.e. 7 numbers

Hence, the number of multiples of 3 in the range are 7

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Manova (Multivariate Analysis of Variance) tests whether mean differences among groups on a combination of dependent variables (DVs) are statistically significant. If there is at least 20 cases in the smallest cell, the test is robust to violations of the assumption of multivariate normality.

In Manova, multiple dependent variables are analyzed simultaneously to determine if there are significant differences among groups. The test examines whether the mean vectors of the groups are equal across the DVs. The assumption of multivariate normality implies that the data should follow a multivariate normal distribution.

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The height of the tabletop is 45.5 centimeters.​

In Mathematics and Geometry, the area of a trapezoid can be calculated by using this mathematical equation (formula):

Area of trapezoid, A = ½ × (a + b) × h

Where:

a and b represent the base areas of a trapezoid.

h represent the height of a trapezoid.

By substituting the given side lengths into the formula for the area of a trapezoid, we have the following:

4,732 = ½ × (85 + 123) × h

4,732 = 104h

Height, h = 4732/104

Height, h = 45.5 cm.

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The volume of the cylinder is given as 3053.63 cubic units

V=πr²h

Where the V = volume

r = radius

h = height

We have to apply the values to the formula

In this case, the radius (r) is 9, and the height (h) is 12.

Now, we can plug the radius and height into the volume formula:

Volume = π * (9)² * 12 ≈ 3.1416 * 81 * 12

3053.63 cubic units

The volume of the cylinder is given as 3053.63 cubic units

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