Increase £16470.45 by 3.5%
Give your answer rounded to 2 DP

Answer: 63

Step-by-step explanation:

The given arithmetic sequence is defined by the formula:

ak = 3 + 4(k - 1)

To find the 16th term, we can substitute k = 16 into this formula and simplify:

a16 = 3 + 4(16 - 1)

a16 = 3 + 4(15)

a16 = 3 + 60

a16 = 63

Therefore, the 16th term of the arithmetic sequence is 63.

The required average density of the giant envelope is equal to 3.30 x 10^9  kg/m^3.

Average density of the giant's envelope, required the mass and volume of the envelope.

Let us assume that the giant is a sphere with a radius of 0.6 AU,

the volume of the envelope is ,

V = (4/3)πr³

  = (4/3)π(0.6 AU)³

  = (4/3)(3.14)(0.6 × 149.6 ×10⁶ )³

To convert this volume to units of cubic meters,

Multiply by the conversion factor by,

1 AU = 149.6 x 10⁶m

⇒1 AU³ = (149.6 x 10⁶ km)³

⇒1 AU³ = 3.35 x 10³³ m³

Now ,calculate the density of the giant's envelope using the formula,

density = mass / volume

Giant's envelope has a mass of 0.5 solar masses,

which is equivalent to,

M = 0.5 x 1.99 x 10³⁰ kg

   = 9.95 x 10²⁹ kg

Average density of the giant's envelope is equals to,

⇒ density = 9.95 x 10²⁹ kg / (4/3)(3.14)(0.6 × 149.6 ×10⁶ )³

                = 3.30 x 10^9 kg/m^3

Therefore, the average density of the giant's envelope is approximately 3.30 x 10^9  kg/m^3.

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Lattice permutation is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1.

In mathematics, a lattice permutation group is a type of permutation group, also known as a Coxeter group, which acts on a set of vectors in a lattice.

A lattice permutation group is a special type of finite group that can be used to generate symmetries in a lattice structure. They are related to Coxeter groups, which are groups that act on a set of points in a Euclidean space, and are generated by reflections.

Lattice permutation groups are generated by permutations of the lattice points, and can be used to study the symmetry of a lattice. These groups are important in the study of crystallography, and can be used to classify the symmetry of a lattice.

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The complete question is:

______ is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1.

Answer:

D, 12 cm.

Step-by-step explanation:

First, draw out the circle with a hexagon in it. I did this by dividing the circle into thirds and then halving each of those because it was easier to visualize. I ended up with something like the image below. Now, we know that the sum of all of the angles that come together at the center of the circle is going to be 360. We can divide 360 by 6 to get 60. The top angle of the triangle, the angle closest to the center, is 60 degrees. We also know that the length of all of these legs that are going out will be the same, because the radius of the circle is constant. This makes each triangle an isosceles triangle. Given the isosceles base angle theorem, both base angles of the triangle must be the same. The sum of all angles in a triangle is 180 degrees. So the equation for x, one of the angles, would be  60 (angle closest to center) + 2x = 180. Let's subtract 60 from both sides to get 2x = 120. Divide both sides by two to get x = 60. Okay, so now we know that all angles in the triangle are 60 degrees. By the equilateral triangle theorem, we know these triangles must be equilateral because all of their angles are 60 degrees. Equilateral triangles also have the same side lengths. Because 12 is one side length, then all side lengths = 12. Therefore, the length of one side of the hexagon is 12.

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The decimal number 555 is written as 4210 in base-5.

Answer:  [tex]555_{10} =4210_{5}[/tex]

Step-by-step explanation:

Decimal to base five conversion

here

                                    D   Q            Remainders

                                    5  |555               0

                                     5  |111                   1

                                      5  |22                  2

                                       5  |4                     4

                                             0  

In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.

In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v

We use the following formula to create a confidence interval around the population mean u:

CI = x ± z*(s/√n)

where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.

Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.

CI = 18.1 ± 1.96*(4.1/√34)

CI = 18.1 ± 1.96*(0.704)

CI = 18.1 ± 1.38

Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.

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Answer: 2 meters

Step-by-step explanation:

The length of one train car is 80 millimeters. Therefore, the length of the entire train is:

25 cars × 80 mm per car = 2000 mm

To convert millimeters to meters, we need to divide by 1000:

2000 mm ÷ 1000 = 2 meters

Therefore, Venell's model train is 2 meters long.

The shape of the resultant matrix of the multiplication of a "2 by 4" matrix and a "4 by 3" matrix will be a "2 by 3" matrix, the correct option is (d).

We know that the general rule for matrix multiplication, which is If matrix A is "m by n" matrix (it has m rows and n columns) and the matrix B is "n by k" matrix (it has n rows and k columns),

Then the product AB is an "m by k" matrix, which means, that the resulting matrix will have "m" rows and "k" columns.

In this case, the "2 by 4" matrix means that matrix has 2-rows and 4-columns, and

The "4 by 3" matrix means the matrix has 4-rows and 3-columns.

Since the number of columns in the first matrix (4) matches the number of rows in the second matrix (4), we can perform the multiplication.

The resulting matrix will have 2 rows and 3 columns,

Therefore, the shape of the resultant matrix is (d) 2 by 3.

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The given question is incomplete, the complete question is

Please identify from the following choices which has the shape of the resultant matrix of multiplication of a "2 by 4" and "4 by 3" matrices.

(a) 3 by 2

(b) 2 by 4

(c) 4 by 4

(d) 2 by 3

Answer:

Step-by-step explanation:1.4 -1, 1 2, -1

The points on the surface z² = xy+ 1 which are closest to the point

(7, 11, 0) is x = 2 and y = 10.

The distance of any point on the surface from the point (7, 11, 0)  is

D(x, y) = { [ x -7]2 + [ y -11 ]2 + [ z -0 ]2 } 1/2

D(x, y) = { [ x -7]2 + [ y -11 ]2 +  z 2 } 1/2

D(x, y) = { [ x -7]2 + [ y -11 ]2 + z 2 } 1/2

D(x, y) = { [ x -7]2 + [ y -11 ]2 + x y +1 } 1/2

Now,

To minimize D  suffices to minimize

d (x ,y ) =  [ x -7]2 + [ y -11 ]2 + x y +1

∂ d / ∂ x =2 x + y - 14

∂ d / d y = 2 y +x - 22

Solving the system:

2x + y - 14 = 0   and    2y +x - 22 = 0   we get  for

x = 2  and for y = 10

The Hessian being 3 > 0  and  d²x  and  d²y positive makes sure that the points ( 2 , 10, √21 )  and   ( 2 , 10, -√21 )  are the points of interest

Complete Question:

Find the point(s) on the surface z2=xy+1 which are closest to the point

(7, 11, 0). List points as a comma-separated list, (e.g., (1,1,-1), (2, 0, -1),

(2,0, 3)).

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The equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.

A line that meets a curve at a point and has the same slope as the curve there is said to be the tangent line to that curve. A line that is perpendicular to the tangent line at a given position is the normal line to a curve at that location. In other words, the normal line's slope equals the tangent line's slope's negative reciprocal. The normal line is helpful for determining the direction of greatest change of the curve at a place whereas the tangent line gives information about the instantaneous rate of change of the curve at that point.

The given function is f(x) = 1/x.

The slope of the function is the derivative of the function thus,

f(x) = 1/x

f'(x) = -1/x²

f'(7) = -1/49

The equation of the line is given as:

y - y1 = m(x - x1)

where, m is the slope of the equation.

The equation of the tangent line is:

y - f(7) = f'(7)(x - 7)

y - 1/7 = -1/49(x - 7)

y = (-1/49)x + 8/49

b. The equation of the normal line to the graph is given as:

The slope of the normal line is negative and opposite of the tangent line.

That is,

m = 49.

y - f(7) = 49(x - 7)

y - 1/7 = 49(x - 7)

y = 49x - 342

Hence, the equation of the tangent line is y = (-1/49)x + 8/49. 2. The equation of the normal line is y = 49x - 342.

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Answer:

To find the domain and range of (fog)(x), we need to first find (fog)(x):

(fog)(x) = f(g(x)) = f(x-3) = e^(x-3)

The domain of (fog)(x) is all real numbers because there are no restrictions on the input x that would make e^(x-3) undefined.

To find the range of (fog)(x), we need to determine the possible outputs of e^(x-3). Since e^x is always positive, e^(x-3) is positive for all x. Therefore, the range of (fog)(x) is y > 0.

So, the answer is: D. domain: all real numbers | range: y > 0

The fraction of the students in the class are women is  one-third (1/3)

If there are 16 men in the class of 24 students, we can find the number of women by subtracting the number of men from the total number of students:

Number of women = Total number of students - Number of men

Number of women = 24 - 16

Number of women = 8

Therefore, there are 8 women in the class.

To find the fraction of students in the class who are women, we divide the number of women by the total number of students:

Fraction of students who are women = Number of women / Total number of students

Fraction of students who are women = 8 / 24

Fraction of students who are women = 1/3

So, one-third (1/3) of the students in the class are women.

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Your question is incomplete. The complete question is: Which of the graphs below illustrates water boiling in Denver, Colorado? (Altitude 1,600 meters.)

Answer:

Explanation:

The normal boiling point of water is 100°C. That is the temperature at which water boils when the atmospheric pressure is 1 atm, i.e. at sea level.

The liquids boil when its vapor pressure equals the atmospheric pressure; so the higher the atmospheric pressure the higher the boiling point, and the lower the atmospheric pressure the lower the boiling point.

Since, it is stated that the altitude of Denver, Colorado is 1,600 m, the atmospheric pressure (the pressure exerted by the column of air above the place) is lower than 1 atm (atmospheric pressure at sea level).

Hence, water boiling point in Denver is lower than 100°C.

The graphs shown represent the temperature (T °C) as water is heated. Since when liquids boil their temperature remains constant during all the phase change, the flat portion of the graph represents the time during which the substance is boiling.

In the graph A, the flat portion is below 100°C; in the graph B, the flat portion is at 100 °C; in the graph C the flat part is above 100ªC, and, in graph D, there is not flat part. Then, the only graph that can illustrate water boiling in Denver, Colorado is the graph A.

Answer:

A right angled triangle is similar to triangle ABC

Step-by-step explanation:

If you tilt the triangle and put it straight, you'll see that angle C is equal to 90°

And if a triangle has one angle of 90° then it is a right angled triangle

Hope you understand :)

The pieces of information would prove that the polygon trig is a parallelogram is GI || TR (option b).

Now, suppose you have a quadrilateral named TRIG. The question asks which of the given information would prove that TRIG is a parallelogram. Let's examine each option to determine which one satisfies the conditions of a parallelogram.

a) GT || IR: This option tells us that GT is parallel to IR. However, we cannot conclude that TRIG is a parallelogram from this information alone.

b) GI || TR: This option states that GI is parallel to TR. Again, we cannot immediately conclude that TRIG is a parallelogram from this information.

c) GO ≅ OR, TO ≅ OI: This option tells us that GO is congruent to OR and TO is congruent to OI. However, this information alone does not prove that TRIG is a parallelogram.

d) GR ≅ TI: This option states that GR is congruent to TI. Similarly, we cannot conclude that TRIG is a parallelogram from this information.

e) GO ⊥ OI: This option tells us that GO is perpendicular to OI. Unfortunately, this information alone does not prove that TRIG is a parallelogram either.

f) GT ≅ TR: This option states that GT is congruent to TR. However, this information alone does not prove that TRIG is a parallelogram.

The answer is option (b) GI || TR. If GI is parallel to TR, then by definition, TRIG has opposite sides parallel, which means it is a parallelogram.

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Complete Question:

Polygon TRIG is a quadrilateral.

Which of the following pieces of information would prove that TRIG is a parallelogram?

a) GT || IR

b) GI || TR

c) GO ≅ OR, TO ≅ OI

d) GR ≅ TI

e) GO ⊥ OI

f) GT ≅ TR

Answer: D: 2mn

Step-by-step explanation:

To simplify the expression 14m^2n^2 / 7mn, we can cancel out the common factors in the numerator and denominator.

We can cancel out 7 in both the numerator and denominator to get:

14m^2n^2 / 7mn = 2m * n / 1 = 2mn

Therefore, the expression 14m^2n^2 / 7mn is equivalent to 2mn. The answer is option D.

All rules towards each statement shown in table below.

The relationships between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It entails the study of trigonometric functions like sine, cosine, and tangent, which connect a triangle's angles and side lengths.

Rules towards each statement:

                                                                  Statements

Rule1.     Cos x/ Sin x  (Sec 2x - 1)             Pythagorean identity

Rule2.    Cos x/Sin x  (Tan 2x)                  Algebra

Rule3.    Cos x/Sin x (Sin 2x/Cos 2x)       Reciprocal

Rule4.    Sin x/Cos x                                 Odd/ Even

Rule5.    Tan x                                           Quotient

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As per trigonometric functions, rules towards each statement are:

Rules towards each statement:

                                                                 Statements

Rule1.     Cos x/ Sin x (Sec 2x - 1)             Pythagorean identity

Rule2.    Cos x/Sin x (Tan 2x)                  Algebra

Rule3.    Cos x/Sin x (Sin 2x/Cos 2x)       Reciprocal

Rule4.    Sin x/Cos x                                 Odd/ Even

Rule5.    Tan x                                           Quotient

Trigonometry is a branch of mathematics that focuses on the relationships between triangles' sides and angles. It requires studying the trigonometric functions that link the angles and side lengths of a triangle, such as sine, cosine, and tangent.

Rules towards each statement:

                                                                 Statements

Rule1.     Cos x/ Sin x (Sec 2x - 1)             Pythagorean identity

Rule2.    Cos x/Sin x (Tan 2x)                  Algebra

Rule3.    Cos x/Sin x (Sin 2x/Cos 2x)       Reciprocal

Rule4.    Sin x/Cos x                                 Odd/ Even

Rule5.    Tan x                                           Quotient

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The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.

An employee who earned $20,000 will contribute $260 to the welfare fund.

To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.

The first $1000 will have a contribution rate of 4%.

Contribution for the first $1000 = 4% of $1000 = $40.

The next $1000 will have a contribution rate of 3%.

Contribution for the next $1000 = 3% of $1000 = $30.

The next $1000 will have a contribution rate of 2%.

Contribution for the next $1000 = 2% of $1000 = $20.

The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.

Contribution for the remaining amount = 1% of $17,000 = $170.

Now, let's sum up the contributions for each tier:

$40 + $30 + $20 + $170 = $260.

Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.

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Step-by-step explanation:

7eh8heusvush0wio0w92726 2is 3the world ydgugd8jd8djkd0jd9jd8hd7hd

Let's break down this question. How many students were in each grade? In grades 9-10, there were 122 students, and in grades 11-12, there were 123 students. What kind of bands were the students asked to choose from? Were they given a list of bands to choose from, or were they simply asked to suggest a band they would like to see?

Answer:

To convert 49% to a fraction, we can simply write it as 49/100. This is because a percentage is a way of expressing a number as a fraction of 100. So 49% means 49 out of 100, which can be written as the fraction 49/100.

Answer:

49/100

Step-by-step explanation:

Percent means out of 100.

49%

49/100

Answer:

k = -5

Step-by-step explanation:

According to the Remainder Theorem, when we divide a polynomial f(x) by (x − c), the remainder is f(c).

Therefore, if we divide polynomial f(x) = x³ + kx + 9 by (x - 2) and the remainder is 7 then:

To find the value of k, simply substitute x = 2 into the function, equate it to 7 and solve for k.

[tex]\begin{aligned}f(2)=(2)^3 + k(2) + 9 &= 7\\8+2k+9&=7\\2k+17&=7\\2k&=-10\\k&=-5\end{aligned}[/tex]

Therefore, the value of k is -5.

35 is a reasonable prediction of the number of times he will select 2 yellow socks?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.

In the given question,

The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:

P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25

So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.

To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:

E(X) = n * p

where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.

In this case, n = 175 and p = 1/25. So,

E(X) = 175 * (1/25) = 7

Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.

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Find the percent of each number :-

1.) 64% of 75 tiles :

[tex] \implies \sf \: \dfrac{64}{100} \times 75 \\ \\\implies \sf \:0.64 \times 75 \\ \\ \implies \sf \: 48 \\ [/tex]

Hence, 64% of 75 tiles is 48 tiles.

2.) 20% of 70 plants.

[tex] \implies \sf \: \dfrac{20}{100} \times 70 \\ \\\implies \sf \:0.2 \times 70 \\ \\ \implies \sf \: 14 \\ [/tex]

Hence, 20% of 70 plants is 14 plants.

3.) 32% of 25 pages .

[tex] \implies \sf \: \dfrac{32}{100} \times 25 \\ \\\implies \sf \: 0.32 \times 25 \\ \\ \implies \sf \: 8 \\ [/tex]

Hence, 32% of 25 pages is 8 pages.

4.) 85% of 40 e -mails.

[tex] \implies \sf \: \dfrac{85}{100} \times 40 \\ \\\implies \sf \:0.85 \times 40 \\ \\ \implies \sf \: 34 \\ [/tex]

Hence, 85% of 40 e -mails is 34 e-mails.

5.) 72% of 350 friends.

[tex] \implies \sf \: \dfrac{72}{100} \times 350 \\ \\\implies \sf \:0.72 \times 350 \\ \\ \implies \sf \: 252 \\ [/tex]

Hence, 72% of 350 friends is 252 friends.

6.) 5% of 220 files.

[tex] \implies \sf \: \dfrac{5}{100} \times 220 \\ \\\implies \sf \:0.05 \times 220 \\ \\ \implies \sf \: 11 \\ [/tex]

Hence, 5% of 220 files is 11 files.

Rolling a six-sided die 80 times and recording the number of l's rolled and it is a Binomial Distribution.

The binomial distribution is a probability distribution used in statistics that summarizes the probability that a value will take on one of two independent values ​​given a set of parameters or assumptions. The binomial distribution is calculated by multiplying the probability of success by the power of the number of successes and by multiplying the probability of failure by the power of the difference between the number of successes and the number of trials. The product is then multiplied by the combination of trials and successes.

For example, suppose a casino develops a new game where participants bet on the number of heads or tails in a specified number of coin tosses. Suppose a contestant wants to bet $10 that 20 coin tosses will result in exactly 6 heads. The participants wanted to calculate the probability of this happening, so they used calculations from the binomial distribution.

The probability is calculated as :

(20! / (6! × (20 - 6)!)) × (0.50)⁶ × (1 - 0.50)⁽²⁰⁻⁶⁾. Therefore, the probability of getting exactly 6 heads out of 20 coin tosses is 0.037, or 3.7%.

In this case, the expected value is 10 heads, so the contestant made a bad bet.

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The probability of each of the events of {at most three lines are in use}, {fewer than three lines are in use}, {at least three lines are in use, {between two and five lines, inclusive, are in use}, {between two and four lines, inclusive, are not in use} and {at least four lines are not in use} are 0.70, 0.45, 0.55, 0.80, 0.35 and 0.40 respectively.

The problem involves finding probabilities of different events for a mail-order company with six telephone lines. The probability mass function (pmf) is given, and we use it to calculate the probabilities of different events such as "at most three lines are in use" or "between two and five lines, inclusive, are in use".

To calculate these probabilities, we use basic probability formulas such as the addition rule, subtraction rule, and the complement rule.

P(X ≤ 3) = 0.10 + 0.15 + 0.20 + 0.25 = 0.70

P(X < 3) = 0.10 + 0.15 + 0.20 = 0.45

P(X ≥ 3) = 1 - P(X < 3) = 1 - (0.10 + 0.15 + 0.20) = 0.55

P(2 ≤ X ≤ 5) = P(X ≤ 5) - P(X < 2) = (0.10 + 0.15 + 0.20 + 0.25 + 0.20) - 0.10 = 0.80

P(2 ≤ X ≤ 4) = 0.20 + 0.25 + 0.20 = 0.65, so P(2 ≤ X ≤ 4)ᶜ = 1 - 0.65 = 0.35

P(X ≥ 4) = 0.20 + 0.05 + 0.05 = 0.30, so P(X ≤ 3) = 1 - P(X ≥ 4) = 0.70 - 0.30 = 0.40

These formulas are applied based on the given events to determine the probabilities.

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Answer: D) Angle R is 65 degrees

Step-by-step explanation:

In the given figure, we have a right-angled triangle PQR.

Using the property of angles in a triangle, we know that the sum of angles in a triangle is 180 degrees. Therefore,

∠QRP + ∠QPR + ∠PRQ = 180 degrees

Since ∠PRQ is a right angle (90 degrees), we have:

∠QRP + ∠QPR = 90 degrees

Now, we are given that ∠QPR is 25 degrees. Substituting this in the above equation, we get:

∠QRP + 25 = 90 degrees

Solving for ∠QRP, we get:

∠QRP = 90 - 25 = 65 degrees

Therefore, the measure of angle R is 65 degrees, which is option (D).

Answer:

Answer is D

Step-by-step explanation:

SPiDerMom is so hot bTw

The simplification of the given expression

[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]

is y = 7

[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]

find the square root of 25

[tex]y =( \sqrt{47 + \sqrt{9 - 5} } [/tex]

simplify root 9 - 5

[tex]y = ( \sqrt{47 + \sqrt{4} } [/tex]

find the square root of 4

[tex]y = ( \sqrt{47 + 2)} [/tex]

Add root 47 and 2

[tex]y = ( \sqrt{49} )[/tex]

Find the square root of 49

y = 7

Therefore, the solution to the given expression is y = 7

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