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The DE is the ray with end point E and the ray GA and ray DF will not intersect

From the given diagram

Consider the ray DE,

The starting point of the ray DE = D

Then the end point of the ray DE = E

The D is the starting point and E is the end point of the ray DE

Therefore DE is the ray with end point E

Consider the ray GA and DF, those rays are not in contact and going opposite direction, therefore it will not intersect

The GA and DF will not intersect

Hence, the DE is the ray with end point E and the ray GA and ray DF will not intersect

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The height of the model of the lighthouse in inches is 20 inches

The real height of the lighthouse = 160 feet

The scale model of the light house has scale of

1 inch : 8 feet

Consider the height of the model of the lighthouse is x

Then the proportion of the scale model of the lighthouse and the actual height will be

1 inch / 8 feet = x inches / 160 feet

Cross multiply the terms

1 × 160 = 8x

Multiply the terms

8x = 160

Divide both side of the equation by 8

8x / 8 = 160 / 8

x = 20 inches

Hence, the height of the model of the lighthouse in inches is 20 inches

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Answer:

49.7

Step-by-step explanation:

FORMULA : A = (b1 + b2)h/2

base 1 = 4.2

base 2 = 10

4.2 + 10 = 14.2

height = 7

14.2 x 7 = 99.4

99.4/2 = 49.7

Answer:

18

Step-by-step explanation:

Answer:

18 pounds

Step-by-step explanation:

5x 3 3/5= 18

If the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds

The quantity of fuel releases from the container = 5 gallon per second

Consider the fuel remaining in the container = y

Consider the number of seconds that have passed since the fuel started dispensing = x

Then x and y satisfy a linear relationship

The quantity of fuel in the tank at the beginning = 103 gallon

Time taken = 2 seconds

Then the equation will be

y = 103 - 5x

Time taken is x = 2

y = 103 - 5× 2

y = 103 - 10

y = 93 gallon

Hence, if the tank begins with 103 gallons, then 93 gallon will remain after 2 seconds

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Answer:

Step-by-step explanation:

formula of a linear line - y=mx+c

so y=

m= gradient x =x coodinate c=y-intercept

c= -3

m = 0

which is y=-3

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Answer:

Step-by-step explanation:

Points given:

This is a horizontal line with constant y - value of - 3.

So it equation is y = - 3.

Answer:

2 hours

Step-by-step explanation:

time it took on the first day = x

speed = d/t

time it took on second day = x + 1

75 = d/x

50 = d/x + 1

75x = d

50 = 75x/(x + 1)

50(x + 1) = 75x

50x + 50 = 75x

50 = 25x

x = 50/25

x = 2

Answer:

width = 9 m

Step-by-step explanation:

the diagonal divides the rectangle into 2 right triangles.

using Pythagoras' identity on one of the triangles

with legs 12 and width (w) and hypotenuse (diagonal) 15 , then

w² + 12² = 15²

w² + 144 = 225 ( subtract 144 from both sides )

w² = 81 ( take square root of both sides )

w = [tex]\sqrt{81}[/tex] = 9

that is the width of the rectangle is 9 m

The equation that relating the total length of the road L and the number of days D is L = 54 + 4d, the length of the road after 37 days is 202 miles

The length of the road at starting = 54 miles

The rate of lengthening the road per day = 4 miles per day

Where L is the total length of the road in miles

D is the number of days the crew has worked

Then the equation will be

L = 54 + 4D

The number of days = 37 days

Substitute the value of D

L = 54 + 4×37

L = 54 + 148

L = 202 miles

Hence, the equation that relating the total length of the road L and the number of days D is L = 54 + 4d, the length of the road after 37 days is 202 miles

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Answer: t=1

Step-by-step explanation:

1. Distribute the -3

-18t=-3t-15

2. Move the -3t to the other side

-15t=-15

3. Divide by -15 to solve for t

t=1

The square of a number is increased by 5 times the number [tex]6x^{2} +5x-4=0[/tex]

What is quadratic equation?
A quadratic equation is a second order equation written as a[tex]x^{2}[/tex] + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.

Product of 6 and the square of a number is increased by 5 times the number, he result is 4.

Consider x as the number,

The question can be written as:

[tex]6(x^{2} )+5(x)=4[/tex]

[tex]6(x^{2} )+5(x)-4=0[/tex]

Hence, the answer for the given question is [tex]6x^{2} +5x-4=0[/tex].

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Answer: x = -1

Step-by-step explanation:

Since, you know y = 2, substitute that y-value into the other function:

[tex]2=2x+4\\\\2x=2-4=-2\\\\x=\frac{-2}{2} =-1[/tex]

Answer:

Desmos is a free graphing and teaching tool for math available on the web as well as on iOS and Android. In addition to plotting equations, classroom activities are available to help students learn about a variety of math concepts.

A definition of Desmos has been given below

What is Desmos?
Desmos can be applied in a variety of contexts. Students can avoid spending $100 on a graphing calculator by using it for free. It can be used by teachers to create stunning images for tests and presentations. But Desmos really shines in the classroom exercises. Teachers can use Desmos to assist students in making the connection between mathematical concepts and actual, concrete shapes and images. It's simple to begin an activity with your students: Just instruct the children to enter the website's activity code. Try the student preview of an activity before assigning it. In the teacher moves section at the bottom of each activity, you can find specific ways to guide your children while they work. The teacher dashboard allows for the tracking of progress.

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Answer: 62.5

Step-by-step explanation:

To break even, profit equals zero.

[tex]1.60n-100=0\\\\1.60n=100\\\\n=62.5[/tex]

Answer:

3,500 Millimeters

Step-by-step explanation:

1 Meter = 1,000 Millimeters so,

3.5 meters = 3,500 Millimeters

Answer: The sequence has a common difference between consecutive terms

14 - 18 = 10 - 14 = - 4

This indicates it is an arithmetic sequence with a common difference - 4

Step-by-step explanation:

The volume of the model of the air balloon is 1000m³.

So, the volume of the model:

So, calculate the volume of the model as follows:

Therefore, the volume of the model of the air balloon is 1000m³.

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Answer: USE the forumla

Step-by-step explanation:

Consider a frustum of radii 'R' and 'r', and height 'H' which is formed by a cone of base radius 'R' and height 'H + h'. Its volume (V) can be calculated by using: V = πh/3 [ (R3 - r3) / r ] (OR) V = πH/3 (R2 + Rr + r2)

Answer:

19x − y = 0

__

The rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.

What is rate in mathematics?

A rate is the ratio of two related quantities expressed in different units. the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable. One unit of one of these quantities is used to represent the ratio's denominator, and if it can be altered consistently, then the ratio can be stated as follows: (i.e., is an independent variable).

The rate can be configured as.

Rate = [tex]\frac{1/3}{5/6}[/tex]

Rate = [tex]\frac{2}{5}[/tex]

Hence, the rate at which the pail is collecting the water is [tex]\frac{2}{5}[/tex] of an inch per minute.

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3 pounds 9 ounces of rutabagas would cost $2.28

The question is a percentage problem

The trim loss percent for rutabagas is 19%

= 19 percent

= 19 / 100

= 0.19

trim loss factor = 1 - 0.19 = 0.81

selling price of rutabagas  = $0.79 * 0.81 = 0.6399

converting all the unit in pounds

3 pounds 9 ounces: if 1 pound is 16 ounces then 9 ounces will be

3 pounds 9 ounces: 9/16 ounces = 0.5625

therefore we have 3.5625 pounds of rutabagas

3.5625 pounds of rutabagas will cost

= 3.5625 * 0.6399

= $2.28

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The estimate, a predicted time of 81.54 minutes, is both reliable and reasonable. the correct option is (A).

Given that,

The projected amount of time spent with family for someone who spent 36 minutes playing video games is 81.54 minutes, according to the line of best fit.

To find :

Is it appropriate to make the aforementioned forecast using this line of best fit

According to the  "line of best fit" it is that along which the sum of squares of deviation is minimum. This means the line of best fit minimizes the deviation or we can say error due to which it gives better estimate than other method.so, the predicted number of minutes spent with family is both reliable and reasonable.

Therefore, the estimate, a predicted time of 81.54 minutes, is both reliable and reasonable

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The question was incomplete. Check below the complete question.

is it reasonable to use this line of best fit to make the above prediction? select the correct answer below:

a. 81.54minutes

b. 50.25minutes

c. 23minutes

d. 36minutes

The IQR for Jacob's data set is determined as: 2 seconds.

To find the interquartile range (IQR) of a Data set, find the third quartile value and the first quartile value. Their difference is the Interquartile Range (IQR) of the data.

Interquartile Range (IQR) = third quartile - first quartile.

In the box plot given, we can deduce that:

Third quartile = 15.5

First quartile = 13.5

Interquartile Range (IQR) = 15.5 - 13.5

Interquartile Range (IQR) = 2 seconds

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Answer: 2 seconds

Step-by-step explanation:

For the height and arm span of a sample of 50 teenagers explanatory variable and the response variable for this relationship is the explanatory variable, height of teenagers, helps explain the response variable, arm span of teenagers. (Option C)

An explanatory variable refers to the variable that can be manipulated in experiment by the researcher and is the independent variable whereas a response variable refers to the variable that is modified as a result and is the dependent variable. In the given case, the height is the explanatory variable while the arm span is the response variable as a teenager's arms spread is influenced by their height.

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The scale factor k=5

corresponding parts are:

AL--> TD

TK---> AH

DK---> LH

angle A-----> angle T

angle D-----> angle L

angle H-----> angle K

What is scale  factor?

The difference in scale between an original object's scale and that of a new, smaller representation is known as a scale factor (bigger or smaller). By multiplying each side by a certain number, say 2, we can increase the size of a rectangle with sides of 2 cm and 4 cm.

The letter H lies on the line TK

Scale factor k

=( side length of new image)/ ( corresponding side length of new image)

=TD/AL=15/3=5

k=5

From the figure, corresponding parts are as below:

AL--> TD

TK---> AH

DK---> LH

angle A-----> angle T

angle D-----> angle L

angle H-----> angle K

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Standard deviation - The value of x is 1.96.

What is standard normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

As given, for a standard normal distribution, 95% of the data points are contained in the interval [ -x , x ].

The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean and standard deviation are both equal to 1. By transforming its values into z-scores, any normal distribution can be standardised. Z-scores indicate how far away from the mean each number is from.

Hence, from the standard normal table, the value of x = 1.96 for 95% confidence level.

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The scenario that represents a greater speed is scenario 1, which is 60 miles per hour.

Speed can be defined as the time it takes a moving object or body to cover a specific distance. In order words, it is calculated as:

Speed = distance/time.

In scenario 1, using one point on the graph, (1, 60), we can find the unit rate which is the speed in miles per hour:

Speed = y/x = distance/time = 60/1

Speed for scenario 1 = 60 miles per hour.

In scenario 2, we are given the equation, y = 55x:

55 is the unit rate which is the speed.

Speed for scenario 2 = 55 miles per hour.

The greater speed is 60 miles per hour.

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Answer: 13 markers and one pen

Step-by-step explanation:

14/2 = 7

7+6=13 markers

Which means there is only one pen left

From the obtained equation, there are 4 pens and 10 markers.

Given that, there are 14 pens and markers.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of pens be p.

Then, the number of markers will be p+6

Now, the equation is p+p+6=14

⇒ 2p+6=14

⇒ 2p=8

⇒ p=4

Thus, p+6=10

Therefore, from the obtained equation, there are 4 pens and 10 markers.

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Answer:

380 ft²

Step-by-step explanation:

diameter = 22 ft

radius = diameter/2 = 22 ft/2 = 11 ft

area = πr²

area = 3.14 × (11 ft)²

area = 379.94 ft²

Answer: 380 ft²

Answer:

[tex]38=4c+2m[/tex]

Step-by-step explanation:

I will use the letter c to represent bags of chips, and the letter m to represent pounds of meat.

The total cost of c bags of chips is 4 times c. The total cost of m pounds of meat is 2 times m. The total amount that he spends is $38. Therefore, this equation can be written.

[tex]38=4c+2m[/tex]