4. Find PQ
N
Р
5x + 16
S
R.
9x - 32
Q

The value of the missing side QT using the similar triangles concept is;

QT = 6

We are given;

TU is parallel to QR.

TS = 12

QR = 18

Now, TU is 6 more than QT, Thus;

TU = QT + 6

From the concept of similar triangles, we can say that;

QS/TS = QR/TU

Plugging in the relevant values gives us;

(12 + QT)/12 = 18/(QT + 6)

(12 + QT)(QT + 6) = 18*12

QT² + 18QT + 72 - 216 = 0

QT² + 18QT - 144 = 0

Solving this using online quadratic equation calculator gives;

QT = 6

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Answer: y = -x + 5

(0, 5), (1, 4), (2, 3), (3 2) ...

Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.

What is Random Variable?

A continuous random variable is a random variable where the data or value can assume infinitely many values ( meaning it’s a continuous set of data. )

For example a random variable measuring the time taken for someone to cook rice is continuous since there are an infinite number of possible times that can be done.

a) If the random variable Y has a uniform distribution on the interval (0, 1), then the probability density function (PDF) of Y is given by:

[tex]f_Y(y) = 1 for 0 < y < 1[/tex]

= 0

If we let W = Y, then the PDF of W is simply the same as the PDF of Y, since W and Y are equal. Therefore, the PDF of W is given by:

[tex]f_W(w) = 1 for 0 < w < 1[/tex]

= 0

b) If we let W = VY, where V is a constant, then the PDF of W is given by:

[tex]f_W(w) = f_Y(w/V) / |V|[/tex]

Substituting in the expression for the PDF of Y, we get:

[tex]f_W(w) = 1/|V| for 0 < w/V < 1[/tex]

= 0

If V > 0, then this reduces to:

[tex]f_W(w) = 1/V for 0 < w < V[/tex]

= 0

If V < 0, then the range of w is reversed and the PDF becomes:

[tex]f_W(w) = -1/V for V < w < 0[/tex]

= 0

The normalization factor [tex]|V|[/tex] is necessary because the transformation

W = VY stretches or compresses the original uniform distribution on the interval (0, 1) by a factor of [tex]|V|[/tex].

Hence, Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.

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The total distance a baseball player travels is 0 meter from his starting point in the first case when he runs 3 meters forward and then runs 3 meters in the opposite direction.

What is distance ?

A measurement of how far away two things or points are might be quantitative or occasionally qualitative.

If an object covers the same distance in the forward and opposite direction, it will cover 0 meter from his starting point.

It happens because when it covers a distance say 5 Km in forward direction and then, when it goes in the opposite direction with equal distance, it reaches to its starting point from where it was started.

Hence, If the player runs 3 meters forward and then runs 3 meters in the opposite direction, h will be at his starting point or we can say, he will cover 0 meter from his starting point.

However, in all other cases, the distance is not equal in both forward and opposite direction.

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The value of y is less than or equal to 0 (y ≤ 0).

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

4y + 1/5 ≤ 4/5

We have to find the value of y.

Subtract 1/5 from both sides,

4y + 1/5 - 1/5 ≤ 4/5 - 1/5

               4y ≤ 3/5

Multiply both sides by 1/4

4y x 1/4 ≤ 3/5 x 1/4

y ≤ 3/20

y ≤ 0.15

Hence, the value of y is less than or equal to 0 (y ≤ 0).

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Answer

-15

Step-by-step explanation: your welcome

Given curves:

See the attached, where both curves and their intersection is shown.

According to this we have:

Answer:

x = 96.05 bushels

p = $2.84

Step-by-step explanation:

Graph the two equations (see attachment).

The market equilibrium is the point of intersection of the graphs for x > 0.

From inspection of the graph, the point of intersection is (96.05, 2.84).

Therefore:

c. √49  and  d. _³√125  are irrational numbers .

RATIONAL NUMBERS

A rational number is a number that can be written in the form p/q , where p and q are integers and  q ≠ o.

IRRATIONAL NUMBER

An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.

a.  √27 = 5.196152.

Do you think the decimal part stops after 5.196152? No, it is never-ending. Therefore, it is a non-terminating decimal with non-repeating numbers.

The number 5.1961524227... can't be written in p/q form. So √27 is an irrational number.

b . The number 5.1961524227... can't be written in p/q form. So it is an irrational number.

c. The number √49 can be written in p/q form as 7/1 . So √49 is an irrational number.

d. The number 3√125 can be written in p/q form as 5/1 . So it is an irrational number.

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Answer:

[tex] \sf \: 4 \frac{4}{8} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: 2 \frac{3}{8} + 2 \frac{1}{8} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: 2 \frac{3}{8} + 2\frac{1}{8} [/tex]

[tex] \sf \rightarrow \: \frac{19}{8} + \frac{17}{8} [/tex]

[tex] \sf \rightarrow \: \frac{(19 + 17)}{8} [/tex]

[tex] \sf \rightarrow \: \frac{36}{8} [/tex]

[tex] \sf \rightarrow \: 4 \frac{4}{8} [/tex]

Hence, the answer is 4 4/8.

Hannah drove 450 miles to her brother's house at an average speed of 60 miles per hour. How long did she take? (Time)

[tex]t=\dfrac{Distance}{Speed}[/tex]

[tex]t=\dfrac{450}{60}[/tex]

[tex]t=7.5hours[/tex]

Remember, time must be converted to seconds as it is the unit for time.

7.5 hours to seconds

1 hour = 3600 seconds

3600 seconds * 7.5 hours

[tex]=\fbox{27000 seconds}[/tex]

Surface area of the cylinder is 211.5 [tex]cm^{2}[/tex]

The entire area that is occupied by the flat surfaces of the cylinder's bases and its curving surface is known as the surface area of a cylinder.

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

Diameter is 9 cm, and height is 19 cm,

therefore r = 4.5 cm and height is 19 cm.

A = 2 r² π + 2 r π h

A = 2 * 4.5*4.5 π + 2 ·* 4.5* 19 π

A = 40.5 π + 171 π

A = 211.5 [tex]cm^{2}[/tex]

Surface area of the cylinder is 211.5 [tex]cm^{2}[/tex]

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The solution of the equation 4x - 3  = 5 is not extraneous .

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Therefore, let's solve the equation to know whether it is extraneous solution.

Hence,

4x - 3  = 5

add 3 to both sides of the equation

4x - 3 + 3 = 5 + 3

4x = 8

divide both sides of the equation by 4

4x / 4 = 8 / 4

x = 2

Therefore, it is not extraneous solution.

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Answer:

YES

Step-by-step explanation:

The function that expresses the area of the 160 square feet carpet remaining after t minute is; A(t) = 160 - 9·t

A function is a rule that maps the elements of a set known as the input of the function, to the elements of another set, known as the output of the function, such that each element of the input is mapped to exactly one element of the output set.

The area Julian's carpet covers = 160 square feet

The area the Carpet Pro cleaning service is able to clean every minute = 9 square feet.

A table of values showing the area of the carpet remaining after each minute of cleaning by Carpet Pro, can be presented as follows;

Time, t (minute)    [tex]{}[/tex]    Area remaining to be cleaned (square feet), A(t)

0          [tex]{}[/tex]                              160

1          [tex]{}[/tex]                               151

2          [tex]{}[/tex]                              142

3          [tex]{}[/tex]                              133

4          [tex]{}[/tex]                              124

5          [tex]{}[/tex]                              115

The change in the area of the carpet remaining is a constant and therefore, the first difference of the values in the above table is a constant which indicates that the relationship is a linear relationship, with an equation of the form y = m·x + c

Where;

m = The slope = (151 - 160)/(1 - 0) = -9

c = The y-intercept  The value of the function when the input (time) is zero, which is 160

c = 160

x = The number of minutes that elapse, t

y = The number of square feet remaining after t minutes, A(t)

Plugging in the above value, we get;

A(t) = -9·yt + 160

The function that expresses the number of square feet remaining A(t) after t minutes from the time the carpet cleaner began cleaning the carpet is; A(t) = 160 - 9·t

The possible options based on a similar question posted online and the 160 square feet area of the carpet specified in the question are;

A(t) = 160 - 9·t

A(t) = 160 - 0.1^t

A(t) = 160·(0.1)^t

A(t) = 160·(0.9·t)

A(t) = 160 - 0.9·t

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Answer:

b=4

Step-by-step explanation:

[tex]a^{2}+b^{2}=c^{2}[/tex]

[tex]3^{2}+b^{2}=5^{2}[/tex]

[tex]9+b^{2}=25[/tex]

[tex]b^{2}=16[/tex]

[tex]\sqrt{b^{2}} = \sqrt{16}[/tex]

b=4

Based on the definition of isosceles triangle, the value of x is: 25.

An isosceles triangle has two base angles that are equal and are opposite two equal sides.

The image shows an isosceles triangle that is inscribed in the circle. Therefore, the two base angles will each equal (2x - 5).

To find the value of x, create the equation below:

2(2x - 5) + 90 = 180

4x - 10 + 90 = 180

4x + 80 = 180

Subtract 80 from both sides:

4x + 80 - 80 = 180 - 80

4x = 100

Divide both sides by 4:

4x/4 = 100/4

x = 25

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The student has completed in Rhythm will be 57.7%

What is probability ?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.

To find,

a) The student has competed in none of the categories is 10.3%

b) The student has competed in all three of these categories is 14.1%

c) The student has competed in Smooth or Standard, but not Rhythm

d)  The student has competed in Rhythm and Standard, but not Smooth is 17.9%

The student has completed in Rhythm will be 57.7%

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Answer: 6y = 7x - 40

Step-by-step explanation:

Step-by-step explanation:

To find out how much you need to deposit in an account now to have a certain amount after a certain number of days, you can use the formula:

P = F / (1 + r * t)

where:

P is the present value or the amount you need to deposit now.

F is the future value or the amount you want to have in the account after a certain number of days.

r is the annual interest rate, expressed as a decimal.

t is the number of years for which the money will be invested.

In this case, you want to have $5,000 in the account in 697 days, which is equivalent to 697 / 365 = 1.91 years. The annual interest rate is 0.0375. Plugging these values into the formula, we get:

P = 5000 / (1 + 0.0375 * 1.91)

Solving this equation, we find that you would need to deposit $4,921.15 in your account now to have $5,000 in the account in 697 days.

Answer:

a) 3193.75

b)39,693.75

Step-by-step explanation:

0.05 = 2a + 5b

0.2 = 8a + 2b

the trick is to multiply the equations with contacts, so that an addition or subtraction of the equating can be made, and one variable is eliminated in that result, which allows us then to solve for the second variable.

and then we use one of the original equations to solve for the first variable.

in our case, multiplying the first one by 4 and then subtracting the second one sends to be the simplest approach :

0.2 = 8a + 20b

- 0.2 = 8a + 2b

-------------------------

0 = 0 + 18b

b = 0/18 = 0

0.05 = 2a + 5b = 2a + 5×0 = 2a

a = 0.05 / 2 = 0.025

a = 0.025

b = 0

Answer:

140.69

Step-by-step explanation:

I hope this helps

The required linear equation that represents the table is y = -x + 4.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

The values of x are 0, 1, 2, 3,

And values of y are 4, 3, 2, 1.

The linear equation that represents the values, can be written as,

y = -x + 4

When the values of x are substitute in the above equation, the values of y are,

At x = 0, the value of y = 4

At x = 1, the value of y = 3

At x = 2, the value of y = 3

And at x = 3 the value of y = 1

Hence, the required linear equation is y = -x + 4.

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The interest rate should be 6.4116% to achieve the required goal.

What is simple interest?

The daily interest rate, the principal, and the number of days between payments are multiplied to determine simple interest. Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest. Simple-interest loans are frequently used for auto loans and short-term personal loans.

Given data:

A = 4176 + 1071 = $5247

t = 4 years

P = $4176

r = ?

By using the formula,

  A = P(1 + rt)

  r = (1/4)((5247/4176) - 1)

    = 0.06411638

   r = 0.06411638

Converting r decimal to R a percentage

R = 0.06411638 * 100

  = 6.4116% per year

Hence, the interest rate should be 6.4116% to achieve the required goal.

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Answer:

It's 6 and -5.

Step-by-step explanation:

:D

The probability that the child will choose a number that is not a multiple of 9 is 90%.

Probability refers to the chance or likelihood that an expected outcome occurs when multiple developments or events could have happened.

Probability describes the ratio between expected favorable outcomes and possible outcomes.

Probability as a ratio is described as a fractional value when it is not 100% certain or uncertain.

In such cases, probability hovers between zero and 1.

The multiples of 9 from 1 through 50 are five (9, 18, 27, 36, and 45).

The other numbers from 1 to 50 are 45 (50 - 5).

The probability of choosing a multiple of 9 is 10% (5/50 x 100).

The probability of choosing a number that is not a multiple of 9 is 90% (45/50 x 100) or (1 - 0.05).

Thus, the probability that the child chooses a non-multiple of 9 between 1 and 50 is 90%.

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Answer:

y = x - 3

Step-by-step explanation:

1. slope-intercept form: y = mx + b
given: m = 1;  (-4, -7)

2. plug in the values from the given point [(x, y) --> (-4, -7)] into the linear equation of the slope-intercept form.
y = mx + b
-7 = 1(-4) + b
-7 = -4 + b
b = -3

3. construct the final equation in slope-intercept form.
y = mx + b
y = x - 3

Answer:

x=3

Step-by-step explanation:

7-3=4 or 4+3=7

For country A , the doubling time = 26

For country B , the growth rate = 1.5

Define growth rate?

The growth rate is the fractional change per unit time, ∆x. x. ∆t , the fractional change divided by the length of the time period.

For Country A :

      Formula for doubling time,

      T = [tex]\frac{log 2}{log (1 + \frac{k}{100} )}[/tex]

The given growth rate , k% = 2.7%

T = [tex]\frac{log 2}{lod (1 + \frac{2.7}{100} )}[/tex]

  = [tex]\frac{log 2}{log (1 + 0.027)}[/tex]

  = [tex]\frac{log 2}{log (1.027)}[/tex]

  = 26.017

  ≅ 26

Therefore, the doubling time (T) = 26 years

For Country B :

        Formula for growth rate

           k = 100 [tex][2^{1/T} - 1][/tex]

k = 100 [tex][2^{1/46} - 1 ][/tex]        (Since T = 46 years)

k = 100 [1.01518 - 1]

k = 100 [0.01518]

k = 1.518

k ≅ 1.5

Therefore, the growth rate is 1.5 % per year.

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Answer:

f and g share no roots in common

Step-by-step explanation:

The roots of [tex]f(x)=0[/tex] are [tex]x=\pm 3[/tex].

From the graph, the roots of [tex]g(x)=0[/tex] are where the graph of [tex]g(x)[/tex] intersects the [tex]x[/tex] axis, which are at [tex]x=2, 10[/tex].