The area of the triangle below is 30m2
. If you positioned a congruent triangle, as shown by the dotted triangle, to make a parallelogram, what would the area of the parallelogram be?

There are irrational values of x and y for which their sum, x + y, is a rational number.

Assume \($\sqrt{2}$\) is irrational.

Therefore,\($\sqrt{2}+\sqrt{2} = 2\sqrt{2}$\) is irrational

Since \($\sqrt{2}$\) is irrational, and the product of a non-zero rational number and an irrational number is irrational.

Let \($x= \sqrt{2}$\) and \($y = -\sqrt{2}$\).

Since x and y are irrational,

\($x+y = \sqrt{2}-\sqrt{2} = 0$\) is rational.

Consequently, we have proved that there exist irrational numbers x and y such that x + y is rational.

Note: Any two irrational numbers are not necessarily a good choice for this question.

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you have a fair die, with six faces containing the numbers 1,2,3,4,5,6. are the two events a and b then A and B are exhaustive.

Given

A= { 1,2,4}

B= { 2,3,4,5,6}

C= { 3,4}

D= { 2,4,5}

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

S= P(X n Y)

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

AnB= { 1,2,3,4,5,6}

and the sample space is:

S= {1,2,3,4,5,6}

By comparison;

A n B= S

Hence, A and B are exhaustive.

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Answer:

77

Step-by-step explanation:

11- 6(x – 8)

f(-3)

11-6(-3-8)

11+18+48

=77

The solution to the equation "16 more than s is at most -80" in interval notation is (-∞, -96].

To solve the equation "16 more than s is at most -80," we need to translate the given statement into an algebraic expression and then solve for s.

Let's break down the given statement:

"16 more than s" can be translated as s + 16.

"is at most -80" means the expression s + 16 is less than or equal to -80.

Combining these translations, we have:

s + 16 ≤ -80

To solve for s, we subtract 16 from both sides of the inequality:

s + 16 - 16 ≤ -80 - 16

s ≤ -96

The solution for s is s ≤ -96. However, since the inequality includes "at most," we use a closed interval notation to indicate that s can be equal to -96 as well. Therefore, the solution in interval notation is (-∞, -96].

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Answer:

x < 4

Step-by-step explanation:

Step 1: Write inequality

5x < 20

Step 2: Solve for x

Here we see that any number less than 4 will work. So numbers like 3, 0, or even -12587235897 would work.

The frequency of a repeated event is its number of instances for every unit of time. In below given way frequency table can be constructed.

The frequency of a repeated event is its number of instances for every unit of time. It differs from angular frequency and is sometimes made reference to as temporal resolution for clarification. The unit of frequency is hertz (Hz), or one occurrence per second.

The time elapsed between events is measured by the period, which is the opposite of the frequency. For instance, the period, T—the time between beats—is equal to half a second if a heart beats 120 times per minute. Frequency tables to represent the morning and afternoon dogs as two sets of data are:

range        frequency

0- 9             2

10- 19           3

20-29         1

30-39         2

40-49         1

50-59         1

Therefore, in above given way frequency table can be constructed.

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Answer:

Step-by-step explanation:

One

If there are 12 dogs and cats in the vet's office, then if they were the same, there would be 6 dogs and 6 cats. Since there are are more dogs than cats, the number of dogs would have to be at least 7 to get more cats than dogs. If there were 7 dogs, there could only be 5 cats so that the total would be 12.

Two

The question is becoming more general. The answer is C.  Notice that's exactly what happened in part one.

Answer:

=11p-5r

Step-by-step explanation:

3p+(-q)-7r-(-8p)-q+2r=

3p-q-7r+8p-q+2r=

3p+8p-q-q-7r+2r=

11p-5r=

The calculated value of the side length in the triangle is 144

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

The simiar triangles

Using the theorem of corresponding sides, we hav

GH = 2JK

So, we have

10x - 36 = 2 * 4x

Multiply

So, we have

10x - 36 = 8x

Evaluate

2x = 36

So, we have

x = 18

This means that

GK = 4 * 18

GK = 144

Hence, the indicated side length in the triangle is 144

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If It is estimated that only 9/20 of the people who attempt to climb a certain mountain actually reach the summit. If 140 people attempt the​ climb, The number of people that are  expected to reach the​ summit is 63.

Let x present the expected number of people to reach the summit

Hence,

9  /20 = x  /140

Cross multiply            

20x = 1260

Divide both side by 20x

x = 1260 / 20

x =  63 people

Therefore the number of people are 63 people.

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If the cost of the PC is less than the cost of time saved, it is worth purchasing. Thus yes, it should be purchased

To determine whether it is worth purchasing a new personal computer (PC) based on time savings, we need to make some assumptions. Let's consider the following assumptions:

Now, let's calculate the total time saved and the cost associated with the PC over the 5-year period.

Total Time Saved:

In a day, the PC saves 3 minutes per use, and it is used 10 times. Therefore, the total time saved per day is 3 minutes * 10 = 30 minutes.

In a year, the total time saved would be 30 minutes/day * 250 working days/year = 7500 minutes.

Over 5 years, the total time saved would be 7500 minutes/year * 5 years = 37500 minutes.

Cost of PC:

To determine the cost of the PC, we need to consider the labor cost associated with the time saved. Let's calculate the cost per minute:

Cost per Minute:

The labor cost per hour is $X. Therefore, the labor cost per minute is $X/60.

Cost of Time Saved:

The total cost of time saved over 5 years would be the total time saved (37500 minutes) multiplied by the labor cost per minute ($X/60).

Comparing Costs:

To determine whether it is worth purchasing the PC, we need to compare the cost of time saved with the cost of the PC. If the cost of the PC is less than the cost of time saved, it is worth purchasing.

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Answer:

It’s c. -37 and -3

Step-by-step explanation:

The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.

According to the statement

we have given that the

Jody earns $10 per hour babysitting And jody earns $15 per hour doing yardwork.

And she worked 34 hours and earned $410

and we have to express in the linear equation terms.

So, For this purpose,

Let x represents the number hours she babysat

Let y represents the number of hours she did yardwork

And the equations become

x + y = 34.

10x + 15y = 410

And with the help of these linear equations we find the hours which are x and y.

So, The above written equations perfectly express the given conditions in the statement.

The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.

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Step-by-step explanation:

because VW || YZ, the 2 triangles are similar.

this is given by the rules of equal angles of intersecting lines with parallel lines. Z to V and Y to W would be such intersecting lines.

and therefore, the angle at W is the angle at Y, the angle at V is the angle at Z. and therefore both angles at A are equal.

so, for similar triangles the scaling factor between corresponding pairs of sides is the same for all sides.

e.g. the same scaling factor that converts 7.2 to 12, converts then also x to x+4.

7.2 × f = 12

f = 12/7.2 = 12/ 72/10 = 120/72 = 10/6 = 5/3

x × 5/3 = x + 4

5x = 3x + 12

2x = 12

x = 6

A to Y = x = 6

W to A = x + 4 = 6 + 4 = 10

Answer:

3805kg

Step-by-step explanation:

2400 ≥ 2350

1460 ≥ 1455

2400 + 1460≥ 2350 + 1455 = 3805

The lower bound is 3805kg

The total distance from Nina's house to the school to the community center (20 units) is greater than the total distance from Nina's house to the school to the grocery store (18 units).

Part a: To calculate the distance in units from Nina's house to her school using absolute values, we need the coordinates of both locations. Let's assume Nina's house is located at point A (x1, y1) and her school is located at point B (x2, y2). The distance between these two points can be calculated using the distance formula:

Distance = |x2 - x1| + |y2 - y1|

Let's say Nina's house is at coordinates (3, 5) and her school is at coordinates (-2, -1). Plugging these values into the formula:

Distance = |(-2) - 3| + |(-1) - 5|

        = |-5| + |-6|

        = 5 + 6

        = 11 units

Therefore, the distance from Nina's house to her school is 11 units.

Part b: To determine whether the total distance from Nina's house to the school to the grocery store is greater than the total distance from Nina's house to the school to the community center, we need the distances between these locations. Let's assume Nina's house is point A, her school is point B, the grocery store is point C, and the community center is point D.

Let's say the distance from Nina's house to the school is 11 units, the distance from the school to the grocery store is 7 units, and the distance from the school to the community center is 9 units.

Total distance from Nina's house to the school to the grocery store = 11 + 7 = 18 units

Total distance from Nina's house to the school to the community center = 11 + 9 = 20 units

Therefore, the total distance from Nina's house to the school to the community center (20 units) is greater than the total distance from Nina's house to the school to the grocery store (18 units).

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Answer:

congruent

Step-by-step explanation:

1.congurent

2.corresponding angle

3.11x+1=10x+10

11x-10x=10-1

or,X=9

To calculate the chances of success for each student, the school would likely use logistic regression analysis.

Logistic regression analysis is a statistical technique used to model the relationship between a binary outcome variable (in this case, success or failure) and one or more predictor variables (such as academic performance, attendance, or socio-economic factors). The goal of logistic regression is to estimate the probability of a specific outcome occurring based on the given predictors. In this scenario, the school would be interested in determining the likelihood of success for each student based on various factors. Logistic regression allows for the calculation of the probability of success and can provide insights into the factors that significantly contribute to or hinder student success. By analyzing the relationship between the predictor variables and the binary outcome of success, the school can gain valuable information to make informed decisions and interventions to support student achievement.

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If cholesterol level were changed to being measured in grams instead of milligrams, the correlation between fat content and cholesterol level would not be affected.

This is because correlation is a measure of the strength and direction of the linear relationship between two variables, and converting the units of measurement does not change the underlying relationship between the variables. So, the correlation coefficient of 0.75 would remain the same whether cholesterol level is measured in milligrams or grams.

The correlation between fat content and cholesterol level for the 20 different brands of American cheese slices is 0.75. If you change the measurement of cholesterol level from milligrams to grams (1 gram = 1000 milligrams), it will not affect the correlation. The correlation coefficient will remain 0.75, as it is unit-less and only represents the strength and direction of the relationship between the two variables.

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Answer:

21,952.6

Step-by-step explanation:

20÷4=5

5+109,758= 109,763

109,763÷5 = 21,952.6

Answer:

21952.6

Step-by-step explanation:

Since there are 4 people in total, you divide 20 by 4 giving you 5. By adding 109,758 you will get 109,763. Dividing that by 5 then gives you the answer: 21,952.6

The expression for the total cost is given as

y=30+19.99x

Step-by-step explanation:

Initialization of variables

let y be the total charges

and let x be the number of hours

given that the parties fee is $30

and $19.99 per hour

we can model the expression as '

y=30+19.99x

Therefore the expression for the cost is given as

y=30+19.99x

Answer:

0

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

The y is the variable.

There’s a imaginary -1 in front of the y

Answer:

33.33%

Step-by-step explanation:

since there are 12 months in a year, that means there are 24 months in 2 years

8/24 = 1/3

Just multiply a fraction by 100% to convert it to percentage form.

100*1/3

33.33%

to check if correct

33.33% × 24 = 7.9992 or 8

7.9992 rounded to the nearest whole number is 8

Answer:

D : $105

Step-by-step explanation:

I use Proportional Reasoning.

part    percent

whole   100  is the formula.

We are looking for the part so we will keep that as "x"

x       35

300   100

100 x 3 is 300. So 35 x 3 is 105. Thats the answer!

(a) The probability that both Anderson and Box will be selected is 0.1

(b) The probability that at least one of the two members whose name begins with C is selected is 0.7

(c) The probability that the two chosen representatives have a total of at least 17 years teaching experience there is 0.6

(a) You will have to consider the 10 different outcomes. Each combination of "A−B","B−Cox", "B−Cramer",... is equally likely to be drawn.

There are \(\left \{ {{5} \atop {2}} \right. =10\)

10 ways to choose 2 people from a group of 5. Since we are only considering 1 possibility, the answer will be 1/10=0.1

(b), there are a few possibilities where at least 1 "C" member gets selected. Consider

"Cox−A", "Cox−B", "Cox−Cramer", "Cox−F"

and

"Cramer−A", "Cramer−B", "Cramer−Cox", "Cramer−F"

Notice that "Cox−Cramer" appears twice, so one needs to be eliminated. Turns out there are 7 different possibilities out of 10...so we have 0.7

(c), I'd personally recommend taking the "compliment" of events. ie, how many combinations have LESS than 17 years? Turns out there are 4 combinations - (3,6),(3,7),(3,10),(6,7).

You can use the answer from (a) and evaluate this to become

1−4/10=0.6.

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If He rides back home, taking the same route, on a bus that travels at a rate of 40mi/hr. The entire trip takes 3.5 hrs. How far along this route is Terrence’s house from the theater is : 50 mile.

Movie time = 2hrs and 15mins

Let convert the movie time

2hrs and 15mins = 2 15/60 h = 2 1/4 h = 2.25 h

Now let calculate the bus time and the distance

Bus time = Entire time - Walking time

Bus time = 3.5 h - 2. 25 h

Bus time =  1.25 h

Now let calculate the distance

Distance = Speed × Time

Distance =  40mi/hr ×  1.25 h

Distance = 50 mile

Therefore the distance is 50 mile.

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Answer:

the answer is "A"

The Reason:

1. it's equal so the circle is going to be shaded

2. and it less than 5 so it will be  to the right