What is the measure of angle QRS in this figure?A:78B:120C:132D:175

The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

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a. The value of P(2) is 0.022

b. The value of P(2 or fewer) is 0.027

From the question; n = 15, p = 0.4

a. We have to determine P(2).

P(X = x) = ⁿCₓ·Pˣ·(1 - P)ⁿ⁻ˣ

P(X = 2) = ¹⁵C₂·(0.4)²·(1 - 0.4)¹⁵⁻²

We can write ⁿCₓ = \(\frac{n!}{x!(n - x)!}\)

P(X = 2) = \(\frac{15!}{2!(15 - 2)!}\) · (0.16) · (0.6)¹³

P(X = 2) = \(\frac{15\times14\times13!}{2\times1\times13!}\) · (0.16) · (0.6)¹³

P(X = 2) = (15 × 7) · (0.16) · (0.6)¹³

After simplification

P(X = 2) = 0.022(approx)

b. We have to determine P(2 or fewer).

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)

P(x ≤ 2) = ¹⁵C₀·(0.4)⁰·(1 - 0.4)¹⁵⁻⁰ + ¹⁵C₁·(0.4)¹·(1 - 0.4)¹⁵⁻¹ + ¹⁵C₂·(0.4)²·(1 - 0.4)¹⁵⁻²

After simplification like above

P(x ≤ 2) = 0 + 0.005 + 0.022

P(x ≤ 2) = 0.027

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Answer:

A. 4 units

Step-by-step explanation:

The inequality in interval notation is  [ -1, ∞ ) from the given equation x ≥ - 3

Given data :

x ≥ - 3

x is greater than or equal to - 3, so - 3 is our smallest value of the interval so it goes on the left. Since there is no upper endpoint (it is ALL values greater than or equal to 3),

we put the infinity symbol on the right side. The boxed end on 3 indicates a closed interval.

In interval notation it is [ -1, ∞ )

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The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.

To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.

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To show that the Directed Disjoint Paths Problem is NP-complete, we can use a reduction from the well-known NP-complete problem of Hamiltonian Path, which is defined as follows: given a graph G and a starting node s, does G contain a simple path that visits every node exactly once and ends at s?

We can reduce the Hamiltonian Path problem to the Directed Disjoint Paths Problem as follows. Given a graph G and a starting node s for the Hamiltonian Path problem, we can construct a new graph G' as follows:

Now, consider the k pairs of nodes (s1,t1), (s2,t2), ..., (sk,tk) in G', where si and ti are the corresponding nodes in G' for the ith node in G. We can see that G contains a Hamiltonian path from s to s if and only if G' contains k node-disjoint paths from si to ti for all i.

Since the Hamiltonian Path problem is NP-complete, and we have shown that it can be reduced to the Directed Disjoint Paths Problem in polynomial time, it follows that the Directed Disjoint Paths Problem is also NP-complete.

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Answer:

The circle is increasing at a rate of 1.76π or about 5.5292 square centimeters per second.

Step-by-step explanation:

We want to determine the rate at which a circle's area is increasing given that its radius is increasing at a rate of 0.02 cm/s at the instant when its radius is 44 cm.

In other words, we want to find dA/dt when dr/dt = 0.02 cm/s and r = 44.

Recall that the equation of a circle is given by:

\(\displaystyle A = \pi r^2\)

Take the derivative of both sides with respect to t:

\(\displaystyle \frac{d}{dt}\left[ A\right] = \frac{d}{dt}\left[ \pi r^2\right]\)

Implicitly differentiate:

\(\displaystyle \frac{dA}{dt} = 2\pi r \frac{dr}{dt}\)

dr/dt = 0.02 and r = 44. Substitute and evaluate:

\(\displaystyle \begin{aligned} \frac{dA}{dt} & = 2\pi (44\text{ cm})\left(0.02\text{ cm/s}\right) \\ \\ & =1.76\pi \text{ cm$^2$/s} \\ \\ &\approx 5.5292 \text{ cm$^2$/s} \end{aligned}\)

In conclusion, the circle is increasing at a rate of 1.76π or about 5.5292 square centimeters per second.

Answer:

Step-by-step explanation:

Plug in 6 for x for g(x) and f(x)

f(6) = 2(6)⁵ = 15,552

g(6) = 10 x 4⁶ = 40,960

15,552 < 40,960

f(6) < g(6)

The number of points to be removed from the graph is 2

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

The graph

From the graph, we can see that

2 points have the same y coordinates

Another 2 points have the same y coordinates

For it to be a function, one of the 2 points must be removed each

So, we have the number of points to be removed from the graph is 2

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The pattern is empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

Given that, there are 6 pails in a row. The first 3 pails are filled with water.

The easiest way to solve this problem is to empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty. This will create the desired pattern of full, empty, full, empty, full, empty.

Therefore, empty the second pail, leaving the first and third pail full and the fourth and sixth pails empty.

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The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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Answer:

d

Step-by-step explanation:

1 kg has 1000 g

Then 2,5 kg has 2,5 × 1000 = 2500 g

You can also make a proportion:

1 kg - 1000 g

2,5 kg - x g

Use the property of the proportion to find x (cross-multiply):

x = 2,5 × 1000 / 1 = 2500 g

We will investigate how to determine the constant of proportionality for specific relationship between two variables.

We are given the respect proportionality between two variables ( x and y ) on a cartesian coordinate plane as such:

We are to determine the constant of proportionality ( k ) for the relationship expressed between the two variables.

A general proportional relation between ( x ) and ( y ) is expressed as follows:

Where,

We will use the given data point ( x , y ) and the general expression for direct proportions to determine the value of the constant of proportionality ( k ) as follows:

We plugged in the respective quantities of the variables ( x ) and ( y ) and evaluated for the constant of proportionality ( k ):

The required rate of simple interest is 1.75%.

Here, we have,

(Principal + Interest) is a straightforward interest equation.

A = P(1 + rt)

Where: A is the sum of the accrued principal and interest.

Principal Amount is P.

I is the interest rate.

r is the annual percentage rate of interest, or R/100.

R is the annual percentage rate of interest; R = r * 100 t is the length of time involved in months or years.

Since I = Prt,

the initial formula A = P(1 + rt) evolved from A = P + I to A = P + Prt,

which may be represented as A = P(1 + rt).

Given: Principal is $1,300

Rate is 7% and the amount earned that is A-P is $159.25.

A = P(1 + rt)

Therefore substituting the values in the above mentioned equation, we get:

159.25= 1300(1+r×7)

On solving we get,

r= 1.75%

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complete question:

At the Blue Bank, Barry would earn $159.25 in simple interest in 7 years after depositing $1,300.

What rate of simple interest is offered at the

Blue Bank?

Answer:

12 im pretty sureeee

Step-by-step explanation:

Answer:

1-1/6

Step-by-step explanation:

3/6+2/6=5/6

This is out of one pound

So there is 7/6 pounds left

Or 1-1/6

Answer: 930,925

Step-by-step explanation:

N is somewhat close to 900,000.

The only number that matches this is 930,925.

Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

\(x_1 = -4, x_2 = 5, x_3 = 12\)

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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Answer:

1260 sq yds

Step-by-step explanation:

slope side  +     vertical side  +     bottom side   +          both ends

(32x15)       +     (32x12)           +        (32x9)         +          (9x12x0.5)(2)=

480+384+288+108=1260

Answer:

Step-by-step explanation:

If you add the lengths of two sides, 12 and 14, you will get 28. Using the above theorem, the third side cannot be greater than or equal to 28. Therefore, the greatest possible whole-number length of the unknown side is 27.

Answer:

Step-by-step explanation:

7 or C

Using compound interest, it is found that it will take 11.28 years for the the account to grow to $4500.

The compound interest formula is given by:

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

A(t) is the amount of money after t years.

P is the principal(the initial sum of money).

r is the interest rate(as a decimal value).

n is the number of times that interest is compounded per year.

t is the time in years for which the money is invested or borrowed.

In this problem:

We have to solve for t when \(A(t) = 4500\), thus:

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

\(4500 = 3000(1 + \frac{0.036}{12})^{12t}\)

\((1.003)^{12t} = 1.5\)

\(\log{(1.003)^{12t}} = \log{1.5}\)

\(12t\log{1.003} = \log{1.5}\)

\(t = \frac{\log{1.5}}{12\log{1.003}}\)

\(t = 11.28\)

It will take 11.28 years for the the account to grow to $4500.

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The evaluated function values are g(-3) = 11, g(5) = 11, g(a) = 11 and g(a+h) = 11

A composite function is a function that results from combining two or more functions. It is created by using the output of one function as the input of another function.

The function g(x) is defined as g(x) = 11, which means that the output of the function is always 11, no matter what value of x is inputted.

i.e. the function g(x) = 11 always returns the value 11, regardless of the input.

Therefore, we have:

g(-3) = 11

g(5) = 11

g(a) = 11

g(a+h) = 11

So, regardless of the value of a or h, the function g(x) will always return 11.

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Answer: I believe it's A

Hope this helped

Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

The range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

The range of function g depends on the range of the function f.

Let's start by assuming that we know the range of f.

If the range of f is Rf, then the range of -2f is the set {-2y | y ∈ Rf}, which is just the set of all numbers that can be obtained by multiplying an element of Rf by -2.

Finally, we add 1 to each of these values to get the range of g. Therefore, the range of g is:

Rg = {1 - 2y | y ∈ Rf}

In other words, the range of g is obtained by taking the range of f, multiplying each element by -2, and adding 1 to each result.

If we don't know the range of f, we can still say something about the range of g. Specifically, we know that g(x) can never be greater than 1 (since the largest value that -2f(x) can take is 0, and adding 1 to 0 gives us 1), and g(x) can never be less than 1 - 2M, where M is the largest possible value that f(x) can take on. In other words, the range of g is bounded between 1 - 2M and 1, but it may not include all values in that interval, depending on the range of f.

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Answer: \(9.38\times10^{33}\)

Step-by-step explanation:

Given: Molecules in a liter of water = \(3.35\cdot10^{25}\)

A certain river discharges about \(2.8\cdot10^8\) liter of water every second.

Molecules in river = \(3.35\cdot10^{25}\times2.8\cdot10^8\)

\(=3.35\cdot2.8\cdot10^{25}\cdot10^8\\\\= 9.38\times10^{25+8}\ \ \ \ [a^m\cdot a^n=a^{m+n}]\\\\= 9.38\times10^{33}\)

Hence, there are \(9.38\times10^{33}\) does the molecules in river per second.

The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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Answer:

The way adolescents spend their time can strongly influence their health later in life. For youth to maintain a healthy future, they need plenty of sleep; good nutrition; regular exercise; and time to form relationships with family, friends, and caring adults. Additionally, the time adolescents spend in school and in after-school activities with peers and adults can advance healthy academic, emotional, social, and physical development. The amount of time they spend on screens and in social media may also influence adolescents’ overall well-being.

The American Time Use Survey, collected by the U.S. Bureau of Labor Statistics, contains detailed information about how individuals ages 15 and older use their time and provides a picture of a typical weekday and weekend day for a high school teen during the school year. Here we specifically analyze how adolescents ages 15-19 who are enrolled in high school spend their time.

Step-by-step explanation: