What is the area of the triangle?
Write your answer as a fraction or as a whole or mixed number.
2 height
3 2/3 base

Answer:

X < 4

Step-by-step explanation:

3rd one.

The required values of x,y for the two triangles are (15√2,15√2) & (√10,2√5)

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c2.

Given here : Two special triangles

1) Clearly the given triangle is a right isosceles triangle as  a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.

Thus x=y

Now using pythagoraes theorem we get

[tex]x^2+x^2=30^2\\2x^2=900\\x^2=450\\x=15\sqrt{2}[/tex]

Thus x=y=15√2

2) Again the given triangle is an isosceles triangle and thus x=√10

[tex]\sqrt{10}^2+\sqrt{10}^2 =y^2\\y^2=20\\y=2\sqrt{5}[/tex]

Hence,  The required values of x,y for the two triangles are (15√2,15√2) & (√10,2√5)

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The formula for the geometric sequence above is Tₙ= 5. (-3⁽ⁿ⁻¹⁾)

In geometric sequence, the general formula of geometric sequence is:

Tₙ= ar⁽ⁿ⁻¹⁾

Information:

Tₙ = the n-th term

a = first term

r = ratio

n = the number of terms

In the question above,

a= 5

r= T2/T1=-15/5=-3 (This is the ratio)

Substitute the value of a and r to the formula of Tₙ:

Tₙ= ar⁽ⁿ⁻¹⁾

Tₙ= 5. (-3⁽ⁿ⁻¹⁾)

So the formula of Tₙ for the sequence above is Tₙ= 5. (-3⁽ⁿ⁻¹⁾)

In the above formula there is a ratio of geometric sequences. In a geometric sequence, two successive terms have the same ratio. Comparisons to geometric sequences are referred to as ratios (r). This is where the quotient of adjacent terms will be obtained.

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Answer: Jan 11

Step-by-step explanation:

You subtract two weeks (14 days) from Jan 25.

25-14=11

The last pay day was January 11.

The number of boys and girls in the family would be = 2 and 3 respectively.

The siblings are Mike and Emily which are brother and sister. That is 1:1 = boy : girl

The number of brothers Mike has = number of sisters he has. That is ; number of brothers= number of sisters.

The number of brothers Emily has = 3× number of girls

Let the number of girls in the family be x.

Let the number of boys in the family be y.

Also the number of brothers Emily has is equal to 1 less than the number of boys in the family, i.e. (y - 1).

One less because Steve himself is excluded.

Hence, 3(y-1)= X

3y -3 = x ---> equation 1

Also, it is given that Mike has as many brothers as sisters.

Now, the number of brothers Mike has is equal to the number of boys in the family, i.e., y. Also, the number of sisters Mike has is equal to 1 less than the number of girls in the family, i.e. (x-1). One less because Emily herself is excluded.

Hence, y = x- 1 ---> equation 2

Putting, the value of x from the first equation into the second equation, we get:

y= (3y-3)-1

y = 3y-4

2y = 4

y = 4/2 = 2

Therefore X = y+1 = 2+1 = 3

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The answer is [tex]L = 624 cm^2; S = 944 cm^2[/tex]  where L is the lateral area and S is the surface area of a right rectangular prism.

The lateral area of a right rectangular prism is given by the formula:

[tex]L = 2(lw + bh)[/tex]

where l and b are the length and width of the base, and h is the height of the prism.

The surface area is given by the formula:

[tex]S = 2(lb + bh + lh)[/tex]

For the given prism with a base of 12 cm by 10 cm and a height of 16 cm, the lateral area is:

[tex]L = 2((12 cm)(10 cm) + (12 cm)(16 cm)) \\= 2(120 cm^2 + 192 cm^2)\\= 2(312 cm^2)\\= 624 cm^2.[/tex]

The surface area is:

[tex]S = 2((12 cm)(10 cm) + (10 cm)(16 cm) + (12 cm)(16 cm))\\ = 2(120 cm^2 + 160 cm^2 + 192 cm^2) \\ = 2(472 cm^2) \\ = 944 cm^2.[/tex]

So the answer is [tex]L = 624 cm^2[/tex] ; [tex]S = 944 cm^2[/tex] .

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Answer:

The correct answer is L=704 cm^2 ; S-944 cm^2

Step-by-step explanation:

p=2l+2w

P=2(12)+2(10)=24+20=44cm

L=(44)(16)=704 cm^2

So the lateral area is 704 cm^2

B=(12)(10)=120cm^2

S=704+2(120)=704+240=944cm^2

So the surface area is 944 cm^2

The father age is now 168 years old and the son is now 24 years old.

Father's age = 7 times the son's age

7x = (Father's age) - (son's age)

7x = 168 - 24

7x = 144

x = 144/7

x = 24

Therefore, the father is 168 years old and the son is 24 years old.

The father is currently 168 years old and the son is 24 years old. This is because the father is seven times older than his son and 24 years older than his son.

The complete question is :

A father is seven times older than his son and his son is 24 years younger than his father. How old is each now?

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Answer:

I do not see a correct answer posted...see below

Step-by-step explanation:

20 % OFF means you pay 80 %   ( 80% is .80 in decimal)

.80 * 28 = $ 22.40   after discount (before tax)

  now you need to add the 6%  tax

      .06 * 22.40 = 1.34     added to the 22.40 = $ 23.74   AFTER TAX

Answer: 1/4.

Step-by-step explanation:

The probability of selecting a nickel first and then a dime is calculated as follows:

Step 1: Determine the number of successful outcomes. There are 4 nickels and 9 dimes in the bag, so there are 4 successful outcomes of selecting a nickel first.

Step 2: Determine the number of possible outcomes. Since David is selecting 2 coins from the bag one at a time without replacement, the number of possible outcomes is 16 (9 + 4 + 3).

Step 3: Calculate the probability. The probability of selecting a nickel first and then a dime is 4/16 = 1/4.

So, the probability that David will select a nickel first and then a dime is 1/4.

the price at each level of demand can be calculated by p = D(q) = 28 - 2.25q.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, Given a function that defines the price for a certain model of a youth wristwatch is related by p = D(q) = 28 - 2.25q.

Thus,

A) The demand function is p = 28 - 2.25q.

When demand q is 0,

price is p = 28 - 2.25*0 = $28

B) When demand q is 400,

price is p = 28 - 2.25*4 = $19.

C) When the price is 10,

we have 10 = 28 - 2.25q or 2.25q = 18.

This gives q = 800 or 8 in hundreds

D) Graph of the demand function will have a vertical intercept of 28 (When q = 0, the value of p is 28) and a horizontal intercept of 12.44.

Here the first graph in part A is correct because it fits the intercepts

E) Supply function is p = 1.25q.

When the price is 0,

the quantity supplied is 0.

F) When the price is 17,

quantity supplied is 17 = 1.25q or q* = 13.6 of 1360 in hundreds

G) The vertical intercept is 0.

The graph will be similar to the one in option A because it matches both demand and supply equations.

H) Equilibrium occurs when demand and supply are equal

28 - 2.25q = 1.25q

28 = 3.5q

q* = 28/3.5 = 8 or 800 watches

price is p = 1.25*8 = $10.

therefore,  the price at each level of demand is solved above.

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Complete question:

The equation to represent the situation is y = 12.5x + 35

Angela belongs to a baking club. After receiving 4 recipes, Angela had spent $85. After receiving 10 recipes, she had spent $160.

The situation represent a linear equation. Therefore, the equation to represent the situation is as follows;

Using slope intercept form,

y = mx + b

where

Therefore,

using (4, 85) and (10, 160)

slope = m = 160 - 85 / 10 - 4

m = 75 / 6

m = 12.5

Therefore, let's find y-intercept using (10, 160)

160 = 12.5(10) + b

160 - 125 = b

b = 35

Hence, the equation is y = 12.5x + 35

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The required solution of the given simultaneous equations y = 1/5x + 6 and 4x + 5y = 5 is (-5, 5).

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Given equation,
y = 1/5x + 6,
4x + 5y = 5

Graph the given equation on the coordinate plane,
As we can see both lines intersect each other at (-5, 5), which is the solution of the system of the equation given.

Thus, the required solution of the given simultaneous equations y = 1/5x + 6 and 4x + 5y = 5 is (-5, 5).

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The domain of each function is given as follows:

11. All real values except x = -2 and x = 4.

12. All real values except x = -1 and x = 1.

13. All real values except x = -2.

The domain of a function is the set that contains all the possible input values for the function.

The functions in this problem are rational functions, meaning that all the values of x that make the denominator zero are excluded from the domain.

Then the excluded values are obtained as follows:

11. x² - 4 = 0 -> x = -2 and x = 2.

12. x² - 1 = 0 -> x = -1 and x = 1.

13. x + 2 = 0 -> x = -2.

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this is therefore a second order reaction  Rate = k [a]²

first lets tabulate the data

                [a]                              rate  (m/s)

             0.10                           10.010

             0.01                            0.024

             0.40                             0.096          

x - order of reaction with respect to a

since a is the only reactant, the order with respect to a is the order of the reaction

rate equation;

Rate = k [a]ˣ

where k - rate constant

substituting rate values and [a]

0.010  = k[0.15 ]ˣ----1)

0.040  = k [0.30]ˣ----2)

divide 2 by 1

4 = 2ˣ

x = 2

therefore order with respect to a is 2

this is therefore a second order reaction

Rate = k [a]²

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Answer:

Trina

Step-by-step explanation:

Trina is 85.6 below sea level

Jessie is 87.9 above

distance wise 85.6 is shorter

The speed of the car is 0.8 miles per hour when the skid mark is 100 feet.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The speed of a car in miles per hour is √(20)L, Where 'L' is the length in feet of its skid mark.

We know, 1 mile is equal to 5280 feet.

So, The speed of the car is √(20)×(L/5280) miles.

Therefore, The speed of the car when the skid mark is 100 feet is,

=  √(20)×(100/5280) miles.

= √20×0.019 miles.

= 0.8 miles per hour.

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True. A counting process {N(t)} is a Poisson process(PP) if and only if it is a renewal process in which the interarrival times have an exponential distribution function.

A counting process is a mathematical model used to count the number of events that occur over time. A Poisson process is a specific type of counting process in which the number of events occurring in any given time interval is independent of the number of events that have occurred in any previous interval.

A renewal process is a type of counting process in which the arrival of events resets the process so that the future events are independent of the past events. The interarrival time between two events in a renewal process is the time between the arrival of one event and the arrival of the next.

Complete Question:

T/F. a counting process {nt} is a pp if and only if it is a renewal process in which the interarrival times have an exponential distribution function.

C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school.

C(X,Y) is a statement that means a student X from the school is enrolled in class Y which is one of the classes offered by the school. The domain for X consists of all students in the school and the domain for Y consists of all classes being offered. To explain this statement further, firstly it should be noted that the statement is saying that a student (X) is enrolled in a class (Y). Secondly, the term “domain” refers to the set of all possible values that can be used for a given variable. In this case, the domain for X consists of all students in the school, while the domain for Y consists of all classes being offered at the school. Therefore, the statement C(X,y) is saying that a student from the school is enrolled in one of the classes offered by the school.

The complete question: Let C(X,Y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being

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Answer:

47500

Step-by-step explanation:

5 x 19=95

95 x 25=2375

2375 x 4=9500

9500 x 5= 47500

hope this is correct :)

Answer:

SAS

Step-by-step explanation:

When a recipient not-for-profit entity receives a gift for transfer to another charitable entity, it records it as revenue upon receipt.

If the donor retains the right to revoke or redirect the gift, it's recognized as a "Contribution Receivable" liability until the restrictions lapse or are fulfilled. Consult accountants for proper accounting.

When a recipient not-for-profit entity receives a gift that will be transferred without restriction to another charitable entity,

The accounting treatment typically involves two steps:

Recognition on Receipt:

The recipient not-for-profit entity should recognize the gift as revenue or contribution in its financial records upon receipt.

This is because the organization has legal control and possession of the gift, even if it intends to transfer it to another charitable entity.

The accounting entry will depend on the nature of the gift received ( cash, securities, in-kind donation).

Classification as a "Contribution to be Transferred":

The second step involves classifying the received gift as a "Contribution to be Transferred" on the recipient's balance sheet.

This classification reflects that the entity intends to pass the gift along to another charitable entity

and that the funds are not restricted for use within the recipient organization.

If the donor retains the right to revoke or redirect the gift,

The recipient not-for-profit entity should follow the guidelines for recognizing contributions subject to donor restrictions.

Until the restrictions lapse or are fulfilled, the contribution should be recorded as a liability ( "Contribution Receivable").

Accounting for contributions with donor-imposed restrictions can be complex,

and the specific treatment will depend on the terms of the gift and applicable accounting standards.

It's essential for the not-for-profit organization to consult with its accountants

or financial advisors to ensure compliance with relevant accounting principles and reporting requirements.

Also, it's important to note that accounting standards and regulations may vary across different countries or regions,

so organizations should adhere to the accounting principles applicable in their specific jurisdiction.

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The values in the table do not represent the function.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A data table.

The table does not represent the function.

Because the input value of -3 connected to two points 1 and 0.

Therefore, it is not a function.

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Option C. A random sample of attendees would be a group of attendees selected in a systematic and unbiased manner, such that each attendee has an equal chance of being selected to participate in the survey.

This ensures that the opinions represented in the survey are representative of the opinions of the entire attendee population. For example, the organizers could randomly select every 10th attendee, or they could use a random number generator to select a certain number of attendees. The important thing is that the selection process is not influenced by any extraneous factors and is done in a way that ensures each attendee has an equal chance of being selected.

Finally, it is also important to ensure that the survey questions are clear, unbiased, and relevant to the topic being studied. This will help ensure that the responses obtained are meaningful and accurately reflect the opinions of the attendees.

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The organizers of a conference want to survey attendees about the registration fee. Which of the following best describes a random sample of attendees?

A. The organizers form groups of 20 attendees based on the day the attendees registered. Then, the organizers randomly choose 4 groups and select all of the attendees in these groups.

B. The organizers select the first 80 attendees who register for the conference because these attendees are easily accessible.

C. The organizers assign each attendee a different number. Using a random number table, the organizers draw 80 of those numbers at random. Then, organizers select the attendees assigned to the drawn numbers. Every set of 80 attendees is equally likely to be drawn using the random number table.

Answer:

5

Step-by-step explanation:

A Pythagorean triple using Euclid's rule is (3, 4, 5).

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

Given:

Pythagorean triples consist of the three positive numbers a, b, and c, where a²+b² = c².

The symbols for these triples are (a, b, c).

Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.

The example of triplets is (3,4,5).

Therefore, the example of triplets is (3,4,5).

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The merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons.

The merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons. This is because we must compare each element in both lists in order to sort them. So a total of m+n comparisons are required in the worst case scenario.

This can be visualized by using a formula: n + m = m+n. This formula can be used to calculate the total number of comparisons required.

For example, if m = 10 and n = 15, then 10 + 15 = 25. This means that 25 comparisons would be required in order to sort the two lists.

Thus, the merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons. This is because we must compare each element in both lists in order to sort them.

The merging of two sorted lists of sizes m and n into a sorted list of size m+n requires O(m+n) comparisons.

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The equation is an identity because it always works to find the zeros of a quadratic equation regardless of the coefficients.

The equation in Exploration 4.1.1 problem 3 is an identity because it was derived from the general quadratic equation [tex](ax^2 + bx + c = 0)[/tex]. Therefore, it always works when given the coefficients of a quadratic equation. This is demonstrated by using the formula for the quadratic equation, which is [tex]x = (-b ±√(b^2 - 4ac))/2a[/tex]. Plugging in the coefficients of a quadratic equation, the result is always the zeros of the quadratic equation. For example, for the equation[tex]6x^2 - 4x + 3 = 0[/tex], the zeros are found by plugging in a = 6, b = -4, and c = 3 into the formula. This gives us[tex]x = (-(-4) ±√((-4)^2 - 4(6)(3))/2(6) = (4 ±√(16 - 72))/12 = (4 ±√(-56))/12 = (4 ±√(7i))/12[/tex]which corresponds to the two zeros of the equation,[tex]x = -2 ± 3i[/tex]. This demonstrates that the equation is an identity because it always works to find the zeros of a quadratic equation regardless of the coefficients.

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The total amount that he will owe after the loan period of 25 weeks is; $806.25

The formula to calculate simple interest is;

I = PRT/100

Where;

P is principal

R is rate

T is time

We are given;

P = $780

R = 7%

T = 25 weeks = 25/52 years

Thus;

I = (780 * 7 * 25/52)/100

I = $26.25

Total payoff = $780 + $26.25

= $806.25

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There is a 95% chance that the true mean number of hours of sleep per day for all students in the school falls within this range

To calculate the 95% confidence interval for the mean number of hours of sleep per day of a random sample of 50 students from a large high school, you would need to follow these steps:

Calculate the mean of the sample by adding up all the hours of sleep reported and dividing by the sample size (n).

Calculate the standard deviation (σ) of the sample by taking the square root of the sum of squares of the differences between the sample values and the mean divided by n1.

Calculate the standard error (SE) by dividing the standard deviation by the square root of n.

Calculate the margin of error (ME) by multiplying the standard error by the critical value of 1. 96.

Calculate the confidence interval by adding and subtracting the margin of error from the mean. This will give you the lower and upper bounds of the confidence interval.

Therefore, the 95% confidence interval for the mean number of hours of sleep per day of a random sample of 50 students from a large high school is (6. 73, 7. 67). This means that there is a 95% chance that the true mean number of hours of sleep per day for all students in the school falls within this range

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If x must be a number. The same outcome is obtained by increasing x by 20% as well as by decreasing that product of four with x by 5. x has the value of 25/14.

Let's look up an expression for raising x by 20%. This might be shown as x + 20%. x = x + 0.2x = 1.2x = 6x/5.

The two expressions must now be set to be equal to each other.

6x/5 = 4x - 5

Add 6x/5 to both sides and subtract. To make 4x and 6x/5 have a similar denominator, we can rephrase 4x as 20x/5.

0 = 20x/5 - 6x/5 - 5 = 14x/5 - 5

0 = 14x/5 - 5

We can now increase both sides by five.

5 = 14x/5

Now that we have the reciprocal of 14/5, 5/14, we may multiply either sides by this number.

5(5/14) = (14x/5)(5/14) = x

25/14 = x

Thus, the solution is 25/14.

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