The length of segment AE is 5 centimeters. a. what is the length of segment CD? b. what is the length of segment AB? c. Name a segment that had the same length ...

The set which is equivalent and equal to the given set; {1, 2, 3, ...} is; Z+.

It follows from the task content that the set which is equivalent to the given set; {1, 2, 3, ...} is to be determined.

Since the numbers in the set are all integers and which happen to be positive integers.

Hence, the best representation of a set which is equivalent to the given set as given in the task content is; Z+.

The set of positive integers is represented as Z+. It implies all the integers greater than 0.

Hence, the set which is equivalent to the given set; {1, 2, 3, ...} is; Z+.

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The value of x will be 15 and the value of y will be 4.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

Here in the image, we have a triangle having sub-triangles. The value of x is calculated by considering two right-hand triangles.

x / ( x + 5 ) = 18 / ( 18 + 6 )

x / ( x + 5 ) = 18 / 24

24x = 18x + 90

6x = 90

x = 15

The value of y will be calculated by considering the two left-hand triangles.

12 / ( 12 + y) = 15 / 20

240 = 180 + 15y

15y = 60

y = 60 / 15

y = 4

Therefore, the value of x will be 15 and the value of y will be 4.

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The probability of selecting two students (a and b) randomly is found as 1/380.

The formula for evaluating the Probability is-

Probability = Favourable outcomes / Total outcomes.

As, per the given question.

Total number of students = 20.

The probability for selection of 'a' is 1/20.

Now, the total students left is 19.

Thus, the probability for selection of 'b' is 1/19.

The total probability for selection of both is -

Probability(a and b) = 1/20×1/19

Probability(a and b) = 1/380

Thus, the probability of selecting two students ( a and b) randomly is found as 1/380.

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The number of perennials flower from 60 flowers seen by the students with of which 70% were perennials flowers is 42.

Perennials Flowers are plants that live more than two years.

To calculate the amount of perennial flowers seen by the students, we use the techniques of percentage.

Using the formula,

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the number of perennials flower is 42.

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Step-by-step explanation:

[tex](3x + 2) + x = 180 \\ 3x + x = 180 - 2 \\ 4x = 178 \\ x = 44.5[/tex]

Answer:

x° = 44.5°

Step-by-step explanation:

x° and (3x + 2)° are supplementary angles, which means they add up to 180°.

Equation: x + 3x + 2 = 180

Step 1: Combine like terms.

[tex]\implies 4x + 2 = 180[/tex]

Step 2: Subtract 2 from both sides.

[tex]\implies 4x + 2 - 2 = 180 - 2[/tex]

[tex]\implies 4x = 178[/tex]

Step 3: Divide both sides by 4.

[tex]\implies \dfrac{4x}{4}=\dfrac{178}{4}[/tex]

[tex]\implies x = 44.5[/tex]

Step 4: Substitute 44.5 as the value of x in (3x + 2) to find its measure.

[tex]\implies 3(44.5)+2[/tex]

[tex]\implies 135.5[/tex]

Therefore, the measure of x° is 44.5°, and the measure of (3x + 2)° is 135.5°. Together, they add up to 180°.

An equation is a collection of variables and constants. The value of x and y for the system of the equation as -2x - 4y = -18 and x = y will be x = 3 and y = 3.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given system of equations,

-2x - 4y = -18 and x = y

Substitute, x = y

-2(y) - 4y = -18

-6y = -18

y = 3 and x = 3

Hence "The value of x and y for the system of the equation as -2x - 4y = -18 and x = y will be x = 3 and y = 3".

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The number of students that went on the field trip is 137.

Let s represent the number of seventh grade students that went on the field trip.

Total number of participants = number of students + number of teachers

a + 19

Number of participants that rode the larger bus : 2/3 x (a + 19) = 104

In order to determine the value of a, take the following steps:

Multiply both sides of the fraction by 3 / 2

a + 19 = 104 x 3 / 2

a + 19 = 156

Subtract 19 from both sides of the equation:

a = 156 - 19

a = 137

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In order pair (4,9), 9 is the y- coordinate while 4 is the x-coordinate.

The coordinates are the pair of numbers that describe the position of some point in a plane using the horizontal x-axis and the vertical y-axis as the point of reference. The representation of this coordinate is usually done by (x,y) where x represents the point's reference with respect to the x-axis and y represents the point's reference with respect to the y-axis. There are four quadrants in the graph which are named quadrant 1, quadrant 2, quadrant 3, and quadrant 4. In quadrant 1 both the x and y-axis is positive, in quadrant 2 x-axis is negative and the y-axis is positive, in quadrant 3 both the x and y-axis are negative, and in quadrant 4 x-axis is positive while the y-axis is negative.

I hope this answer helps

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Answer:

9

Step-by-step explanation:

Remember that all points have the form, [tex](x,y)[/tex].

Soo in this problem,

                    [tex]\begin{cases}\text{4 is the x-coordinate}\\\text{9 is the y coordinate}\end{cases}[/tex]

Thus, The y-coordinate is 9!!

Answer:

Δ = b² - 4ac

Step-by-step explanation:

do math

Answer:

3/4,. it's means for every 4 games there's a $3 fee

Step-by-step explanation:

3/4

it's means for every 4 games there's a $3 fee

The null hypothesis is rejected thus there is a significant difference in the incidence of lung cancer in all four groups.

When the p-value is less than 0.05, the null hypothesis that there is no difference between the means is rejected, and we come to the conclusion that there is a significant difference. The existence of a significant difference cannot be inferred if the p-value is higher than 0.05.

The null hypothesis in the given scenario was that all four groups will have the same incidence rate of lung cancer which is rejected.

An assertion that there is no correlation between two population measures is referred to as a null hypothesis. To prepare the ground for additional experimentation or study that explains the position of interest, researchers reject or refute the null hypothesis.

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Answer:

Square root 19 comma, 5,8,30

Answer:5,8,30

Step-by-step explanation: i took a test

From the diagram, A is the major arc

                               B is the minor sector

                               C is the major segment.

What do you mean by major arc, minor sector, and a major segment of a circle?

      1. Major arc: A significant arc is one that is larger than 180 degrees in measure.

      2. Minor sector: A circle's intercepted arc and two of its radii define a region known as a sector. The center angle is the intersection of the two radii. A minor sector is defined as having a center angle of less than 180°.

The major arc is A significant arc is one that is larger than 180 degrees in measure. So, A is the major arc. The minor sector is defined as having a center angle of less than 180°. So, B is the minor sector. And C has the maximum portion of length so C is a major segment.

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The neighbour us an amount of $160 for the work that we did for him.

As per the agreement the never will pay 20 dollars were every hour that we work.

We worked for a total of 8 hours on Saturday.

So, according to the unitary method,

Total amount of money owned by the neighbour = number of hours for which we work x the amount received for working per hour.

Total amount of money owned by the neighbour = 8 × 20

Total amount of money owned by the neighbour = 160 dollars.

The total amount of money owned by the neighbour to us is 160 dollars.

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The confidence interval is (233.8436; 271.0564).

What is a confidence interval?

The likelihood that a population parameter will fall between a set of values for a specific percentage of the time is referred to as the confidence interval. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

What is the margin of error?

In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.

We have,

Sample mean = 252.45

Sample standard deviation = 74.50

n = 64

α = 0.05

By applying the margin of error formula, we get

Margin of Error = tα/2 * s/√n

df = n - 1 = 64 - 1 = 63

t(α/2, df = 63) = 1.998

Margin of Error = 1.998 * 74.50/√64

Margin of Error = 18.6064

The confidence interval = 252.45 ± 18.6064

= (233.8436; 271.0564)

Hence, the confidence interval is  (233.8436; 271.0564).

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The probability that a designer does not prefer red is 0.77.

Probability (event) = favorable outcome / total outcome

Total primary color designers = 400.

The number of opinions for red = 92

The probability for designer prefer red = 92 /100

The probability for designer prefer red = 0.23

Then, the probability that a designer does not prefer red = 1 - 0.23

The probability that a designer does not prefer red = 0.77

Thus, the probability that a designer does not prefer red color = 0.77.

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The correct question along with table is attached-

Answer:

111%

Step-by-step explanation:

£3 × 60 = £180

(35 × £8) + ( 25 × £4) = £380

£380 ‐ £180 = £200

200/180 × 100% = 111% (nearest whole number)

we use the pooled proportion when we calculate the standard error for the difference in proportions when performing a hypothesis test  whne When the variances of both populations are the same

The standard error for the distinction within the proportions is calculated utilizing the population proportions but in cases where the population proportions are unknown, we utilize the test proportions to calculate the standard error. In the case of hypothesis testing, we are mindful of the population proportions whereas in evaluating the confidence interval for the distinction between the proportions we have no thought of the population proportions. So, the standard error for a hypothesis test of distinction in two proportions is distinctive from the standard error for a certain interval of the difference in two proportion.

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An equation is a mathematical statement showing the equality of two

opposite variables

How to determine the equation of the circle using coordinates?

The equation of a circle is determined by the function r²=(x-x1)² +(y-y1)²

where :

then, the last thing is to write the equation of the circle and input the values of the coordinates to arrive at your answer,

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The probability that there will be no repeats on the digits is 0.504.

What is meaning of probability?

The ratio of favorable outcomes with the total number of outcomes is known as probability of that event.

The number of digits of the password is 4.

The numbers from 0 to 9 is 10.

If the digit can repeat, then we can chose first digit in 10 ways, the second digit in 10, third digit in 10 ways and fourth digit in 10 ways.

The total number of ways is 10 × 10 × 10 × 10 =10000.

If the digit can't repeat, then we can chose first digit in 10 ways, the second digit in 9 (because we can't use first digit) , third digit in 8 ways (because we can't use first digit and second digit) and fourth digit in 7 ways(because we can't use first digit, second digit, and third digit).

The total number of ways is 10 × 9 × 8 × 7 =5040.

The favorable outcomes for this event is 5040.

The total number of outcomes is 10000.

The required probability is 5040/10000 = 0.504.

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The equation of a line parallel to x - 4y = 36 is x - 4y = 16.

If the two lines are parallel then their slope must be equal. Two parallels lines have different intercepts but same slope. The slope intercept form of a line is y = mx + c. Where m is the slope and c is the intercept.

Now, writing the given equation in slope-intercept form,

x - 4y = 36

4y = x - 36

[tex]y=\frac{1}{4}x-9[/tex]

By comparing it with slope-intercept form, we get

[tex]m=\frac{1}{4}[/tex]

c = -9

Now, Finding the equation of line passing through (-4,-5) with slope as [tex]\frac{1}{4}[/tex],

[tex]m=\frac{y-y_1}{x-x_1} \\\\\frac{1}{4}=\frac{y-(-5)}{x-(-4)}\\\\ \frac{1}{4}=\frac{y+5}{x+4}\\x+4=4y+20\\x-4y=16[/tex]

The equation of parallel line is x - 4y = 16.

Hence, the equation of a line parallel to x - 4y = 36 is x - 4y = 16.

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The value of x that is a counterexample to the student's conjecture is (a) x = -1/4

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

x = Non-negative number

Student's conjecture:

x + 4 < x²

Using the options, we have:

(a) x = -1/4

x + 4 < x²

-1/4 + 4 < (-1/4)²

3.75 < 1/16 -- false

(b) x = -4

x + 4 < x²

-4 + 4 < (-4)²

0 < 16 -- true

(c) x = 1

x + 4 < x²

1 + 4 < (1)²

5 < 1 -- false

This cannot be used because x is non-negative

(c) x = 4

x + 4 < x²

4 + 4 < (4)²

8 < 16 -- true

The false statements are the counterexamples

Hence, the value of x is (a) x = -1/4

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Complete question

Given that x is a nonnegative number, a student conjectured that x + 4 < x². Which value of x is a counterexample to the student's conjecture?

Responses

A. ​ x=−1/4 ​

​B. ​ x=−4 ​ ​

C. x = 1

D. x = 4

Using the principle of proportional relationship, you can go 165km farther after the trip of 360km with 42L gasoline in the tank.

Consumption rate =[tex]8L[/tex] for [tex]100 km[/tex]

So, per  number of Km per Litre is

[tex]8L = 100km[/tex]

[tex]1 L = x[/tex]

so,

[tex]8x = 100[/tex]

[tex]x=8 \div 100\\[/tex]

[tex]x= 12.5[/tex] kilometer per Litre

Number of kilometers for [tex]42 L[/tex]

[tex]12.5 km = 1 L[/tex]

[tex]y=42L[/tex]

On, Cross multiplying

[tex]y = 12.5\times42[/tex]

[tex]y = 525 km[/tex]

The difference in the distance [tex]= 525 - 360 = 165 km[/tex]

Therefore, the gas can go for a further [tex]165 km[/tex]

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The difference between an independent sample and a dependent sample is that the dependent sample for one set of items is paired measurement while measurements made on two samples are termed an independent sample.

In statistics, while considering two samples and conducting a hypothesis test, one should be aware of which type of test should be conducted based on samples whether they are dependent or independent. If the value of another sample is affected by any one sample then the samples are dependent. If no information can be deduced from the other sample using one sample then the samples are independent.

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The speed of the wind is 50 mph.

Speed, expressed in terms of meters per second, is the rate at which an object's position changes. A thing moves one metre in one second, for instance, if it starts at the origin and moves three metres in three seconds. The formula for speed is as straightforward as dividing a distance by a time.

Given,

250 mph for the plane's speed when there is no wind

v is the wind speed.

Think about how the plane will move against the wind:

V' = the rate of flight of the aircraft against the wind = V + v = 250 + v

300 miles is the distance travelled in d'.

T is the passage of time over the distance.

The distance's travel time is specified as

t' = d'/V'

t' = 300/(250 + v) eq-1

Think about how the plane moves when flying against the wind:

V" is the speed of a plane travelling against the wind and equals V - v. This equals 250 - v.

D" = 200 miles of distance travelled

t" is the passage of time over the distance.

The distance's travel time is specified as

t'' = d''/V''

t'' = 200/(250 - v) eq-2

Due to this:

travelling time of 300 time required to drive 200 miles in miles

t' = t''

using eqs 1 and 2

300/(250 + v) = 200/(250 - v) (250 - v)

3/(250 + v) = 2/(250 - v) (250 - v)

750 - 3 v = 500 + 2 v

5 v = 250

v = 50 mph

The speed of the wind is 50 mph.

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Answer:

Step-by-step explanation:

Distance equation:

If cars move in opposite directions their speeds add up, then the distance between them after 1.5 hours is:

Answer:

After 1.5 hr, they are 3s - 7.5 mi away.

Step-by-step explanation:

Forming the expression,

→ 1.5 × (s + s - 5)

Now the required solution will be,

→ 1.5 × (s + s - 5)

→ 1.5 × (2s - 5)

→ 1.5(2s - 5)

→ 3s - 7.5

Hence, answer is 3s - 7.5 miles.

No. of par-3 holes be represented by = 5

No. of par-4 holes be represented by = 8

No. of par-5 holes are represented by = 5

Total number of courses in the club= 18 (given in the question)

Total shot taken by golfer=72 (given in the question)

Let par-3 holes be represented by t

Let par-4 holes be represented by f

Let par-5 holes be represented by v

forming equations:

f+2=2v

t=v

f + v + t = 18

f+2=2v

f=2v-2 -(i)

t=v -(ii)

f + t + v=18

putting values from (i) and (ii)

(2v-2) + v + v=18

2v-2+2v=18

4v=18+2

4v=20

v=20/4

v=5

Number of par-5 holes=5

from (i)

f=2v-2

putting value

f=2(5)-2

f=10-2

f=8

Number of par-4 holes=8

from (i)

t=v-

putting value

t=5

t=5

Number of par-3 holes=5

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