Find an equation of variation for the given situation.
y varies directly as x, and y = 0.1 when x = 0.5.

The Decimal point is a fraction whose denominator is a power of ten and whose numerator is expressed by figures placed to the right of the decimal point.

Given information:

Expanded Form of 6.02

\(6.02 = (6 \times 100) + (2 \times \frac{1}{102} )\\6.02 = (6 \times 1) + (2 \times \frac{1}{100} )\\6.02 = 6 + \frac{2}{100}\\ 6.02 = 6 + 0.02\)

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The value of x is 93.

What is the exterior angles property of a quadrilateral?

The total of a quadrilateral's outside angles is 360°. Since all convex polygons share this property, their total exterior angles will always add up to 360 degrees.

In the given figure,

The sum of all outside angles=360°

x-11+x+10+31+2x-42=360

4x-12=360

4x=360+12=372

x=372/4 =93

So, the value of x is 93.

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Answer:

(5,1)

Step-by-step explanation:

A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate. An equation that produces such a set of ordered pairs defines a function.

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Answer:

1. diameter=5.54m

2. radius=9.55cm

3. area=11.46feet²

Step-by-step explanation:

1. The formula of the area of a circle is: A=\(\pi r^{2}\)

   A: area of the circle=25m²  

    \(\pi\) : Pi≈3.14

    r: radius of the circle= unknown

   Solve the equation to find r:

   25=(3.14)r²

    r²=\(\frac{25}{3.14}\) =7.69m²

    r= √7.69= 2.77m

   diameter d= 2 x r =2 x 2.77 =5.54m

2. The formula of the perimeter of a circle is: P=2\(\pi r\)

   P: perimeter of the circle= 30cm

    \(\pi\) : Pi≈3.14

   r: radius of the circle= unknown

   Solve the equation to find r:

   30=(3.14)r

   r= \(\frac{30}{3.14}\) = 9.55cm

   radius r = 9.55cm

3. First we have to find r (radius) from  the equation of perimeter:

    P=2\(\pi r\)

     r= \(\frac{P}{2\pi }\) = \(\frac{12}{2(3.14)}\) = \(\frac{12}{6.28}\) =1.91 feet

     Substitute r in the equation of area to get the area:

     A=  \(\pi r^{2}\) = 3.14 (1.91)² = 3.14(3.65) = 11.46 feet²

The expected value of PX is 2.Therefore(Y) = E(PX) / 100= 2 / 100= 0.02The mean of the random variable Y, where Y is equal to the number of kilowatt hours expended annually is 0.02. Therefore, the correct option is (D) 0.02.

Why The expected value of PX is 2?

The given problem states that the total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one year is a continuous random variable X that has the density function  f(x)=x, 0 < x < 1, f(x) = 2 – x, 1 ≤ x < 2 and f(x) = 0, elsewhere. We need to evaluate the mean of the random variable where Y is equal to the number of kilowatt hours expended annually.

The total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one year is given as X. Let us calculate the expected value of the random variable Y which is equal to the number of kilowatt hours expended annually.The number of kilowatt hours expended annually Y is calculated as follows:Y = Power consumed × Hours of use per yearLet Power consumed = P and Hours of use per year = X × 100.The number of kilowatt hours expended annually Y is equal to the product of the power consumed and hours of use per year.

Therefore, we haveY = PX × 100 = (P/100) XThe expected value of Y is given byE(Y) = E(PX) / 100where E(PX) is the expected value of PX.So, we have to calculate E(PX).The expected value of PX is given bye(PX) = ∫ xf(x) dx (0 to 1) + ∫ xf(x) dx (1 to 2) (as given)Now, substituting the given function in the above formula we getE(PX) = ∫ x² dx (0 to 1) + ∫ 2x - x² dx (1 to 2)E(PX) = [x³/3] (0 to 1) + [(x² - x³/3)] (1 to 2)E(PX) = 2/3 + 4/3 = 2

The expected value of PX is 2.Therefore,E(Y) = E(PX) / 100= 2 / 100= 0.02The mean of the random variable Y, where Y is equal to the number of kilowatt hours expended annually is 0.02. Therefore, the correct option is (D) 0.02.

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Precession is a phenomenon that refers to the gradual and continuous change in the orientation of the Earth's rotational axis over long periods of time.

This shift in the orientation of the axis of rotation results in changes in the position of the celestial pole with respect to the stars, which causes a shift in the apparent position of stars over time. The precession of the Earth's axis is caused by the gravitational forces of the Sun, Moon, and other planets in the solar system.
Precession is characterized by changes in the magnitude of the angle of tilt, which causes changes in the rate of the Earth's spin. As the axis of rotation moves, it causes the length of the day to change over time. Additionally, deviations in the circularity of the orbit also affect the precession of the Earth's axis.
Precession is a significant phenomenon in astronomy and has been observed for thousands of years. It has important implications for studies of astronomy, geology, and climate change. For instance, precession affects the timing of the seasons and has a significant impact on the Earth's climate. It also affects the orientation of the Earth's magnetic field, which has important implications for navigation and communication systems.
In conclusion, precession is the gradual change in the orientation of the Earth's rotational axis, caused by the gravitational forces of the Sun, Moon, and other planets. It results in changes in the magnitude of the angle of tilt, changes in the rate of Earth's spin, and deviations in the circularity of the orbit. Precession has significant implications for various fields of study, including astronomy, geology, and climate change.

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The probability of getting two red counters is 27.77%, the probability of getting two blue counters is 20.38%, and the probability of getting one of each color is 51.38%.

Given that Tina has two bags of counters, Bag A and Bag B, and there are 5 red counters and 3 blue counters in bag A, while there are 4 red counters and 5 blue counters in bag B, to determine, if Tina takes at random a counter from each bag, the probability of obtaining each counter, the following calculation must be made:

Therefore, the probability of getting two red counters is 27.77%, the probability of getting two blue counters is 20.38%, and the probability of getting one of each color is 51.38%.

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Answer:

associative

Step-by-step explanation:

because this picture show what it is

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

We can expect that in a random draw of 4 peas from this cross, the number of yellow peas is likely to fall within the range of 2 to 4, with a typical range of 2.134 to 3.866.

The ratio of 3 yellow to 1 green suggests that the cross is between two heterozygous pea plants, each carrying one dominant (yellow) and one recessive (green) allele. This type of cross is called a monohybrid cross.

We can use the binomial distribution to calculate the probability of obtaining a certain number of yellow pea plants in a sample of four. Let p be the probability of obtaining a yellow pea plant, and q be the probability of obtaining a green pea plant, where p + q = 1. Since the ratio is 3 yellow to 1 green, we have p = 3/4 and q = 1/4.

The probability of obtaining exactly k yellow pea plants out of n trials is given by the binomial probability formula:

P(k) = (n choose k) * p^k * q^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n without regard to order. It can be calculated as:

(n choose k) = n! / (k! * (n-k)!)

where n! is the factorial of n.

To find the typical range of the number of yellow peas drawn from a random draw of 4 peas expressed as the 1st SD window, we need to calculate the mean and standard deviation of the binomial distribution. The mean is given by:

μ = n * p

and the standard deviation is given by:

σ = sqrt(n * p * q)

where sqrt represents the square root function.

Substituting n = 4, p = 3/4, and q = 1/4, we have:

μ = 4 * 3/4 = 3

and

σ = sqrt(4 * 3/4 * 1/4) = sqrt(3/4) = 0.866

The typical range of the number of yellow peas drawn from a random draw of 4 peas expressed as the 1st SD window is given by:

[μ - σ, μ + σ] = [3 - 0.866, 3 + 0.866] = [2.134, 3.866]

Therefore, we can expect that in a random draw of 4 peas from this cross, the number of yellow peas is likely to fall within the range of 2 to 4, with a typical range of 2.134 to 3.866.

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Answer:

A and B i hope

Step-by-step explanation:

A and B

I took the test

By using the concept of interest, we can calculate the year in which the tuition will reach $10,000 as 2027

Interest is the extra money you pay for borrowing money or for an investment, and it accumulates over time.

In this case, the interest rate is 3%, so the total tuition increases by 3% each year. To calculate the year in which tuition will reach $10,000, we will need to use the following formula:

Interest = (principal × rate × time) / 100.

The principal is $8,000, the rate is 3%, and the time is the number of years it takes for the tuition to reach $10,000. Thus, the equation becomes:

Interest = (8000 × 0.03 × time) / 100.

We can solve for time by multiplying both sides of the equation by 100 and dividing by 240. This gives us the following result:

Time = ($10,000 - $8,000) / (0.03 × $8,000) = 4.17 years.

Therefore, the tuition will reach $10,000 in

(2023 + 4.17) = 2027

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Answer: [45]

Step-by-step explanation:

Had this same question

The 33rd term of the arithmetic progression whose first term and common difference are -11 and 7 respectively is 213.

It is given that the first term is -11 and the common difference is 7.

So, the first term (a) = -11

Common difference (d) = 7

The general term of an Arithmetic Progression is given by

\(T_{n} = a + (n-1)d\)

Putting the given parameters in the general equation of the Arithmetic progression, we get :

\(T_{n} = -11 + (n-1)7\)

We need to evaluate the 33rd term of the Arithmetic progression.

So, n = 33

Putting n = 33 in the above equation, we get

\(T_{33} = -11 + (33-1)7 = -11 + 32*7 = -11 + 224 = 213\)

Thus, the 33rd term of the arithmetic progression whose first term and common difference are -11 and 7 respectively is 213.

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Answer: p-12 would find how many points Jason scored

Step-by-step explanation

Answer:

$50

Step-by-step explanation:

5= 26+4=30

6=30+4=34

7=34+4=38

8=38+4=42

9=42+4=46

10=46+4=50

Rose would be saving 50 dollars after 10 months. At first Rose only had $10 in 0 months and $14 in the next month and again.This means that every month it adds up to another $4. If you want to find the total or 10 months keep on add 5 4 times which is 20. Then add 30 from the 0-5 months and which gives you $50. So Rose would be saving up 50 bucks in 10 months.

Answer:

x=-400

x=-95

Step-by-step explanation:

They are negative because a negative times a negative is a positive.

The function \(z(x, y) = \cos(x) \cos(e^{-y^2})\) has infinitely many local maxima, infinitely many local minima, and infinitely many saddle points.

To determine the local extrema and saddle points of the function \(z(x, y) = \cos(x) \cos(e^{-y^2})\), we need to analyze its partial derivatives with respect to \(x\) and \(y\).

Taking the partial derivative of \(z\) with respect to \(x\), we get:

\(\frac{\partial z}{\partial x} = -\sin(x) \cos(e^{-y^2})\)

Taking the partial derivative of \(z\) with respect to \(y\), we get:

\(\frac{\partial z}{\partial y} = 2y \sin(x) \sin(e^{-y^2}) \cdot e^{-y^2}\)

To find the critical points, we need to solve the equations \(\frac{\partial z}{\partial x} = 0\) and \(\frac{\partial z}{\partial y} = 0\). However, since both \(\sin(x)\) and \(\cos(e^{-y^2})\) oscillate between -1 and 1, and \(\sin(e^{-y^2})\) oscillates between -1 and 1, there is no combination of \(x\) and \(y\) that simultaneously satisfies both equations.

Therefore, there are no critical points, and as a result, there are no local maxima, local minima, or saddle points for the function \(z(x, y) = \cos(x) \cos(e^{-y^2})\).

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The pressure inside the container is 81.625 pascals

From the question, we are to determine the pressure applied inside the container

From the Pressure equation, we have that

P = F/A

Where P is the pressure

F is the force

and A is the area

From the given information,

F = 1306 N

A = 16 m²

P = 1306/16

P = 81.625 pascals

Hence, the pressure inside the container is 81.625 pascals

Here is the complete question:

In the pressure equation, P represents the pressure on the object in pascals (Pa), F represents the force applied on the object in newtons (N), and A represents the area, in square meters, of the object over which the pressure is applied. What is the pressure applied inside a container having an inner area of 16 square meters over which a force of 1,306 newtons is applied?

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The distance between your house and school is 4.1 miles.

According to the given question.

Point c represents your house.

Point d represents post office which is directly west to the point c i.e from house.

And point e represents school which is west of the post office.

Also, it is given that the distance between house and post office, cd is 1.7 miles.

And the distance between the post office and school,de is 2.4 miles.

Now, if we see the attached figure we can say that

cd + de = ce

⇒ 1.7miles  + 2.4miles  = 4.1 miles

Hence, the distance between your house and school is 4.1 miles.

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Answer:

Slope = -4

Step-by-step explanation:

Given:

Rate of change (Slope) formula:

\(\text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1} }\)

Where:

Substitute the coordinates of the given points in the formula to determine the slope of the line (Rate of change).

\(\implies \text{Slope} = \dfrac{(-18) - (-10)}{8 - 6 }\)

Finally, let's simplify the fraction on the right hand side as needed.

\(\implies\text{Slope} = \dfrac{(-18) + 10}{8 - 6 }\)

\(\implies \text{Slope} = \dfrac{-8}{2 } = -4\)

Therefore, the slope of a line that passes through (6 , -10 ) and (8, -18) is -4.

Answer:

7/8 x 1/3 is 7/24

Step-by-step explanation:

Multiple: 7/8 * 1/3 = 7 · 1/8 · 3 = 7/24

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(7, 24) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven eighths multiplied by one third is seven twenty-fourths.  

Answer:

46%

Step-by-step explanation:

divide 12 by 26

12÷26= 0.46153846153

then move the decimal two places to the right to get your percentage

so Mrs. Childs' got a 46% on her test

Answer:

24

Step-by-step explanation:

Given a quadratic equation in standard form, ax² + bx + c = 0 (a ≠ 0 )

Then the discriminant is

b² - 4ac

Given

2x + 5x² = 1 ( subtract 1 from both sides )

5x² + 2x - 1 = 0 ← in standard form

with a = 5, b = 2, c = - 1 , then

b² - 4ac = 2² - (4 × 5 × - 1) = 4 - (- 20) = 4 + 20 = 24

Answer:

D.24

Step-by-step explanation: hope this helps!! :)

What is the quotient?

StartFraction (negative 3) Superscript 0 Over (negative 3) squared EndFraction

Negative 9

StartFraction 1 Over 9 EndFraction

StartFraction 1 Over 9 EndFraction

9  

Answer:1/9

(-3)^0= 1

Answer:

A = 2k + 8

Step-by-step explanation:

so if Abby read 8 more then twice what Kristen read

she read 2k + 8 books

k = Kristen

A = Abby