Find the area of the trapezoid below by decomposing it into familiar shapes.

The frequency with the largest amplitude is `w ≈ 2.303` (rtol=0.01, atol=1e-08).

The question asks us to find the frequency w for which the particular solution to the differential equation [tex]dạy dy 2- + dt2 + 2y = eiwt dt[/tex]has the largest amplitude.

We can assume a positive frequency w > 0.

Let's find out how to solve this problem:

We need to find the particular solution in the form Aeiwt, and then minimize the modulus of the denominator of A over all frequencies w. It means the denominator of A will have a maximum amplitude if we minimize the modulus. The amplitude of the solution is given by the value of |A|.

Let us assume the particular solution to be `[tex]y = Aeiwt`.[/tex]

Substitute the above solution in the given differential equation.

Then, we get:[tex]`d^2(A e^(iwt))/dt^2 + 2(A e^(iwt)) = e^(iwt)`[/tex]Applying the differential operator on the above equation,

we get: [tex]`(iwt)^2 A e^(iwt) + 2A e^(iwt) = e^(iwt)`Therefore, `A = 1 / (1 - (w^2) + 2i)`.[/tex]

Thus, the amplitude of the particular solution is:

[tex]`|A| = 1 / sqrt((1 - w^2)^2 + 4w^2)`[/tex]

Now, we need to minimize the above expression to get the frequency w at which the amplitude of the particular solution is maximum. This can be done by minimizing the modulus of the denominator of A over all frequencies w.To minimize the above expression, we take the derivative of the expression with respect to w and equate it to zero, which gives us: [tex]`(8w^2) / ((w^2 - 1)^2 + 4w^2)^(3/2) - (2(w^2 - 1)) / ((w^2 - 1)^2 + 4w^2)^(3/2) = 0`[/tex]

Simplifying the above expression, we get: `

[tex]2w^2 = w^4 - 3w^2 + 1`[/tex]

Therefore, [tex]`w^4 - 5w^2 + 1 = 0`.[/tex]

Solving the above equation gives us:

`[tex]w^2 = (5 ± sqrt(21)) / 2`[/tex].Since we know that w > 0, we choose the positive value of w.

Thus, the value of w is: [tex]`w = sqrt((5 + sqrt(21)) / 2)` or `w ≈ 2.303[/tex]`.

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Answer:

Step-by-step explanation:

The number of people in the stadium whose favorite stadium food is nachos is 10000.

What is random sample space?

The set of all potential outcomes for an experiment is referred to as the sample space S in a random experiment. The results of a random experiment, also known as sample points, are incompatible (i.e., they cannot occur simultaneously).

Here, we have

Given: You ask 120 randomly chosen people at a stadium to name their favorite stadium food. There are about 50,000 people in the stadium.

We have to estimate the number of people in the stadium whose favorite stadium food is nachos.

24/120 = x/50,00

x = 1200000/120

x = 10000

Hence, the number of people in the stadium whose favorite stadium food is nachos is 10000.

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Answer:

1 4/6 as an improper fraction is 5/3

Step-by-step explanation:

What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

How do you convert a mixed number to an improper fraction?

To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. Then, you put that sum over the denominator.

For example, 1 4/6 can be converted to an improper fraction as follows:

1 x 6 + 4 = 10

10/6 = 5/3

So, 1 4/6 as an improper fraction is 5/3.

Answer:

5

Step-by-step explanation:

You have to divide 35 by 7.

35/7 is 5.

So, he puts 5 stickers on each paper.

The correct hypothesis statement in this case would be "The average round-trip airfare between Philadelphia and Dublin is less than $1,200".

The hypothesis statement for the test of the average round-trip airfare between Philadelphia and Dublin being less than $1,200 would be “The average round-trip airfare between Philadelphia and Dublin is less than $1,200”.What is hypothesis?A hypothesis is a suggested explanation for a phenomenon or a theory that is tested using various experiments.

It is the first step in research that aids in forming a research question and establishes a framework for the study.The hypothesis statement:In hypothesis testing, the hypothesis statement is a declarative statement or an assertion that specifies the existence or non-existence of a phenomenon. In hypothesis testing, there are two hypothesis statements: null hypothesis and alternative hypothesis.

The null hypothesis would be that the average round-trip airfare between Philadelphia and Dublin is equal to or greater than $1,200. The alternative hypothesis would be that the average round-trip airfare between Philadelphia and Dublin is less than $1,200.

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Answer:

Step-by-step explanation:trisha is running a marathon race  she runs th erace at a steady pace she makes a graph to show how far from the finsh line she will be as she runs the race

=2

The total number of words with 5 or les sletters is  1,364

We want to see how many words of 5 or less letters can be done with 4 different characters.

There are 4 words with one letter.

Now words with two letters, suppose that the word is represented by:

_,_

Each blank represents a letter, so we have 4 options per blank, then the number of words with two letters is 4*4 = 16

And with 3 is 4*4*4 = 64

And with 4 is 4*4*4*4 = 256

And finally,with 5 is: 4*4*4*4*4 = 1,024

The total sum gives:

4 + 16 + 64 + 256 + 1,024 = 1,364

These is the number of words.

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Answer:

Step 1: Simplify the exponents on both sides of the equation. Recall that (a^b)^c = a^(b*c), so we can write:

(1/216)^(3v-1) = (1/6)^(2v-2)

= (6^-1)^(2v-2) (since 1/6 = 6^-1)

= 6^(-(2v-2)) (since (a^-b) = 1/(a^b))

= 6^(2-2v) (since -(2v-2) = -2v + 2)

Step 2: Rewrite 1/216 as a power of 6. We have:

1/216 = 6^(-3)

Substituting this into our equation gives:

6^(-3(3v-1)) = 6^(2-2v)

Step 3: Use the property that if a^x = a^y, then x = y. Since both sides of the equation have the same base (6), we can equate the exponents:

-3(3v-1) = 2-2v

Step 4: Solve for v. First, simplify the left-hand side of the equation:

-3(3v-1) = -9v + 3

Now we can rewrite the equation as:

-9v + 3 = 2 - 2v

Step 5: Solve for v. Add 9v to both sides and subtract 2 from both sides:

-7v = -1

Finally, divide both sides by -7 to obtain:

v = 1/7

Therefore, the solution to the equation is v = 1/7.

To verify that v = 1/7 is the solution to the equation:

(1/216)^(3v-1) = (1/6)^(2v-2)

We can substitute v = 1/7 into the equation and simplify both sides to see if they are equal:

Left-hand side:

(1/216)^(3v-1) = (1/216)^(3(1/7)-1) = (1/216)^(2/7)

Right-hand side:

(1/6)^(2v-2) = (1/6)^(2(1/7)-2) = (1/6)^(-10/7) = (6/1)^10/7

Simplifying:

(1/216)^(2/7) = (6/1)^(10/7)

Taking the seventh root of both sides:

1/6 = 1/6

Since both sides of the equation are equal, we have verified that v = 1/7 is the solution to the equation.

The insurance company expects the interest rate to be around 4.16%.

To find the expected interest rate, we can use the formula for present value of an annuity:

PV = PMT x (1 - (1 + r)^(-n)) / r

Where:

PV = present value of the annuity, which is the amount the insurance company needs to deposit

PMT = payment per period, which is $45,000

r = interest rate per period, which is what we need to find

n = total number of periods, which is unknown

We know that the insurance company needs to deposit $2,500,000 to make the payments, so we can set:

PV = $2,500,000:

$2,500,000 = $45,000 x (1 - (1 + r)^(-n)) / r

To solve for r, we can use trial and error or an iterative method. Here, we'll use trial and error.

Let's assume n = 20, which is a reasonable number of years for an insurance policy. Then we can solve for r:

$2,500,000 = $45,000 x (1 - (1 + r)^(-20)) / r

$2,500,000r = $45,000 x (1 - (1 + r)^(-20))

(1 + r)^(-20) = 1 - ($45,000 / $2,500,000) x r

1 + r = (1 - ($45,000 / $2,500,000) x r)^(-1/20)

r ≈ 0.0416 or 4.16%

Therefore, the insurance company expects the interest rate to be around 4.16%.

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Answer:

The value of the book after 11 years is $103.11

The equation should be 258*0.92, 11 times repeating.

The answer should be 103.106443494, but if you round it the answer is 103.11

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &258\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &11\\ \end{cases} \\\\\\ A = 258(1 - 0.08)^{11} \implies A=258(0.92)^{11}\implies A \approx 103.11[/tex]

Answer:

she would have to go 30 miles per hour or less to make this possible

Step-by-step explanation:

if it went over 35 31 miles per hour they would run out of gas before they got there

The difference between a sample statistic and the corresponding population parameter is known as the sampling error.

     Sampling error is the disparity between a statistic from a sample and a corresponding parameter from a population. Statistic and parameter are two crucial words in inferential statistics that are used to describe data. A statistic is used to calculate a parameter, which is a calculated value from the population, which is a large group of people or objects.

    The variance between the mean of the population and the sample's mean is known as sampling error. The sample statistic that is used to estimate the population parameter may not be the same as the population parameter.

    The discrepancy between these two values is referred to as sampling error. When a small sample is chosen from a larger population, a sampling error is created.

   Therefore, The sampling error is the discrepancy between a sample statistic and the equivalent population parameter.

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The cost of one adult tickets would be $12.5 and the cost of one youth tickets would be $8.75 .Therefore the cost of six adult tickets and eight youth tickets would be 6(12.5) + 8(8.75) = $145.

Let the cost of adult tickets be x.

Let the cost of youth tickets be y.

So, from the given condition given in question the equations are :-

For The Jefferson family,

2x + 2y = 42.50

x + y = 21.25 —---------- equation(1)

and for The Mendoza family,

4x + 3y = 76.25 —------ equation(2)

To solve above equation 4 × equation(1) - equation(2).

y = 8.75

and x = 12.5

Hence the cost of one adult tickets would be $12.5 and the cost of one youth tickets would be $8.75 .

Therefore the cost of six adult tickets and eight youth tickets would be 6(12.5) + 8(8.75) = $145.

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—-------- Correct question format is given below —--------

(Q). Two families go to a movie on Saturday night. The Jefferson family purchases 2 adult tickets and 2 youth tickets for $42.50. The Mendoza family purchases 4 adult tickets and 3 youth tickets for $76.25. How much would it cost to purchase six adult tickets and eight youth tickets?

The annual interest rate on the loan is 4.5% using simple interest formula and concepts.

To calculate the annual interest rate on the loan, we need to use the simple interest formula:

Simple Interest = (P × r × t) / 100

P stands for principal, r stands for annual interest rate, and t stands for time in years.

Given principal amount is $5,600, the simple interest earned after 4 years is $1,008. Therefore, we can plug in values into formula and solve for r:

$1,008 = (5,600 × r × 4) / 100

Multiply LHS and RHS by 100 and divide by 5,600 × 4, we will obtain:

r = $1,008 / $22400 = 0.045 or 4.5%

Hence, the annual interest rate on the loan is 4.5%.

It is significant to remember that simple interest does not compound and has a linear relationship to time. This indicates that the interest charged on the loan is the same each year and does not compound. Short-term loans and personal loans frequently employ simple interest. However, compound interest, which takes into account the cumulative interest over time, is utilised for long-term loans such as mortgages. To make wise financial decisions, it is crucial to comprehend the distinction between simple and compound interest.

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Answer: 250,000 > .00000042

Step-by-step explanation:

2.5 times 10^5 means move the decimal to the right 5 times.

2.5

1. 25.

2. 250.

3. 2,500.

4. 25,000.

5. 250,000.

250000 __  4.2 times 10^-7

10^-7 would mean move the decimal to the left that many times.

4.2

1. .42

2. .042

3. .0042

4. .00042

5. .000042

6. .0000042

7. 00000042

250,000 > .00000042

The value for the given expression is 60.

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The exercise asks the value of the given expression a²-4a, for a=10. Thus, you should replace the variable a with the number 10. See below.

a²-4a

10²-4*10

100-40=60

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Answer: 30 mil

Step-by-step explanation:

Each of the expressions has been simplified by using properties of exponents as shown below.

In Mathematics, an exponent refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

the variables b and n are numerical values (numbers) or an algebraic expression.

n is referred to as a superscript or power.

By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:

(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷

12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴

5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵

6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶

9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸

1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶

(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴

3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷

9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵

3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶

1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.

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Answer: 62.5 would be the answer.

Step-by-step explanation: You have to multiply how many meters per second by the whole total meters.

50x1.25=62.5.

*********************************************************************************************

Hope this helps! ^^

Answer:

Step-by-step explanation:

Story Problem:

Samantha is baking cookies and her recipe calls for 3 cups of flour. She only has a bag of flour that is 7/8 full. If each cup of flour weighs the same, how much flour does Samantha have left after taking out the 3 cups needed for the recipe?

Solution:

To solve the problem, we need to multiply the amount of flour in the bag by 3/1 (which is the same as multiplying by 3).

3 x 7/8 = (3 x 7)/8 = 21/8

So, Samantha has 21/8 cups of flour in the bag.

To find out how much flour she has left after taking out the 3 cups needed for the recipe, we need to subtract 3 from 21/8:

21/8 - 3 = 21/8 - 24/8 = -3/8

Samantha has -3/8 cups of flour left in the bag, which means she doesn't have enough flour to make the recipe. She needs to get more flour before she can continue baking.

Answer:

Look below

Step-by-step explanation:

Ken drinks 7/8 of a carton of milk each day. How much milk does

he drink in 3 days?

7/8*3

21/8

2 5/8 cartons of milk a day

The cοmplete table with the οrdered pairs is:

(2-√6,2√(6-2√6)) (2+√6,2√(6-2√6)) (2+√6,-2√(6-2√6))

(2-√6,2√(6+2√6)) (2+√6,-2√(6+2√6)) (2+√6,2√(6+2√6))

A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable οf the fοrm: [tex]ax^2 + bx + c = 0.[/tex]

Tο find the sοlutiοns tο the system οf cοnics, we can use substitutiοn tο eliminate οne variable and οbtain a quadratic equatiοn in the οther variable. Then, we can sοlve this quadratic equatiοn tο find the pοssible values οf the remaining variable.

Frοm the given system οf cοnics:

[tex]y^2/4 - x^2/2 = 1 ...(1)[/tex]

[tex]y^2 = 8(x + 1) ...(2)[/tex]

We can eliminate [tex]y^2[/tex] frοm equatiοn (1) by multiplying bοth sides by 4:

[tex]y^2 - 2x^2 = 4[/tex]

Substituting the value οf [tex]y^2[/tex]  frοm equatiοn (2), we get:

[tex]8(x + 1) - 2x^2 = 4[/tex]

Simplifying and rearranging, we get:

[tex]x^2 + 2x - 2 = 0[/tex]

We can sοlve this quadratic equatiοn using the quadratic fοrmula:

[tex]x = (-2 \± \sqrt{(2^2 - 4(1)(-2))}) / (2(1))[/tex]

x = (-2 ± √12) / 2

x = -1 ± √3

Substituting these values οf x in equatiοn (2), we can find the cοrrespοnding values οf y:

When x = -1 + √3, we get:

[tex]y^2[/tex] = 8((-1 + √3) + 1) = 8√3

y = ±2√(2√3)

Therefοre, the sοlutiοns are:

(-1 + √3, 2√(2√3)) and (-1 + √3, -2√(2√3))

When x = -1 - √3, we get:

[tex]y^2[/tex] = 8((-1 - √3) + 1) = -8√3

This equatiοn has nο real sοlutiοns fοr y.

Therefοre, the cοmplete table with the οrdered pairs is:

(2-√6,2√(6-2√6)) (2+√6,2√(6-2√6)) (2+√6,-2√(6-2√6))

(2-√6,2√(6+2√6)) (2+√6,-2√(6+2√6)) (2+√6,2√(6+2√6))

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Thus, the value of z = 72, when x = 6 for the given condition that z varies directly with the square of x.

The connection among two variables is known as a direct proportion when their ratios are comparable to a fixed value.

Given data:

z varies directly as x².

z= 8 when x= 2​.

So,

z ∝ x²

z = k x²

k = z/ x² (k is the constant of proportionality)

z= 8 when x= 2​.

k = 8/(2)²

k = 2

Now, when x = 6

z = k x²

z = 2 * (6)²

z = 72

Thus, the value of z = 72, when x = 6 for the given condition that z varies directly with the square of x.

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The equation that represents f(x) is f(x) = [tex]3x^2[/tex] + 3x + 4. To determine the equation that represents the function f(x) based on the given points, we can use the general form of a quadratic function:

f(x) =[tex]ax^2[/tex]+ bx + c

where a, b, and c are constants that we need to determine. We can use the given points to form a system of equations:

[tex]a(0)^2[/tex] + b(0) + c = 4 -- Equation 1

[tex]a(1)^2[/tex] + b(1) + c = 10 -- Equation 2

[tex]a(2)^2[/tex] + b(2) + c = 25 -- Equation 3

Simplifying each equation, we get:

c = 4 -- Equation 1a

a + b + c = 10 -- Equation 2a

4a + 2b + c = 25 -- Equation 3a

Substituting Equation 1a into Equation 2a and Equation 3a, we get:

a + b = 6 -- Equation 2b

4a + 2b = 21 -- Equation 3b

Solving for b in terms of a in Equation 2b, we get:

b = 6 - a

Substituting b = 6 - a into Equation 3b, we get:

4a + 2(6 - a) = 21

Simplifying and solving for a, we get:

a = 3

Substituting a = 3 into b = 6 - a, we get:

b = 3

Substituting a = 3 and b = 3 into Equation 1a, we get:

c = 4

Therefore, the equation that represents f(x) is:

f(x) = [tex]3x^2[/tex] + 3x + 4

This quadratic function passes through the given points {(0,4), (1,10), (2,25)}, as can be verified by plugging in the x-values of each point into the equation and checking that the y-values match.

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After answering the provided question, we can conclude that triangle  2(AD² + DC²) = 2(58 + 26) = 168

A triangle is a locked, double-symmetrical target made up of 3 line segments known as sides that interlock at three points known as vertices. Triangles are distinguished by their sides and angles. Triangles can be rectangular prism (all factions equal), ellipse, or scalene based on their sides. Triangles are classified as acute (all angles are under 90 degrees), okay (one angle is equal to 90 degrees), or orbicular (all angles are greater than 90 ° c) (all angles greater than 90 degrees). The continent of a triangle can be calculated using the formula A = (1/2)bh, where an is the suburb, b is the triangle's base, and h is the triangle's height.

(a) The distance formula is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Length of AB:

AB = √[(2 - (-6))² + (5 - 3)²] = √64 = 8

Length of AC:

AC = √[(0 - (-6))² + (-5 - 3)²] = √100 = 10

Length of BC:

BC = √[(2 - 0)² + (5 - (-5))²] = √144 = 12

Midpoint of BC:

D = [(0 + 2)/2, (-5 + 5)/2] = (1, 0)

Length of AD:

AD = √[(1 - (-6))² + (0 - 3)²] = √58

Length of DC:

DC = √[(1 - 0)² + (0 - (-5))²] = √26

Now we can find the values of AC², AB², AD², and DC²:

AC² = AC² = 100

AB² = AB² = 64

AD² = AD² = 58

DC² = DC² = 26

(b) AC² + AB² = 2(AD² + DC²).

AC² + AB² = 100 + 64 = 164

2(AD² + DC²) = 2(58 + 26) = 168

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The supplied data collection has a periodic period of 4 and an amplitude of 25.

Let's study data points with a 4-day gap;

Data point 2 is [tex](2, 76)[/tex]

Data point 6 is[tex](6, 74)[/tex]

Data point 10 is[tex](10, 75)[/tex]

Every four day intervals, the readings are within the typical range. The points[tex](3, 91), (7, 88),[/tex] and (114) all support this same 4-day timeframe [tex](11, 92).[/tex]

As the data points at intervals of 4 days follow a pattern, we may infer that the period is 4 and the amplitude is around 25.

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Answer:

periodic with a period of 4 and an amplitude of about 30

Step-by-step explanation:

Answer:

36

Angle LON is a right angle so it equals 90 degrees.

NR = QR: This statement is true. In a rhombus, the diagonals bisect each other, so NR is equal in length to QR.

What is Rhombus ?

A rhombus is a quadrilateral with four equal-length sides. The opposite angles of a rhombus are equal to each other, and the diagonals bisect each other at right angles. This means that the diagonals of a rhombus are perpendicular to each other and divide the rhombus into four congruent right triangles.

From the given information, we know that MNPQ is a rhombus, and that NQ and PM are diagonals that intersect at point R.

NQ is perpendicular to MP: This statement is false. In a rhombus, the diagonals are perpendicular bisectors of each other, so we know that NQ is perpendicular to PM at point R, but not necessarily to the entire diagonal MP.

NP is perpendicular to QP: This statement is also false. In a rhombus, opposite sides are parallel and congruent, but not necessarily perpendicular to each other.

NR = QR: This statement is true. In a rhombus, the diagonals bisect each other, so NR is equal in length to QR.

Angle MNQ is congruent to angle PNQ: This statement is false. While we know that NQ is perpendicular to PM at point R, we cannot conclude that angle MNQ is congruent to angle PNQ. In fact, there is not enough information given to determine the measure of either angle.

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