Rene is three times as old as his sister Rosy. In 5 years, he will be twice as old as his sister Rosy. What is Rene’s present age?

The equation of the line in slope-intercept form is y = -2x + 1/4

A line is the shortest distance between two points. The standard equation of a line is expressed as y = mx + b

where:

m is the slope

b is the intercept

Using the coordinate points (0, 1/4) and (-1, 2 1/4)

Determine the slope

Slope = (2 1/4 - 1/4)/-1
Slope = 8/-4
slope = -2

Since the y-intercept is the point where x = 0, hence the y-intercept is 1/4

Determine the equation

y = -2x + 1/4

Hence the equation of the line in slope-intercept form is y = -2x + 1/4

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The time the plane arrives at the London airport from the airport in Manchester, found using the kinematic equation for speed, and the conversion of the units from hours to minutes is 11:40 a.m.

The kinematic equations describe the motion of an object that moves with constant acceleration.

Distance from the London airport to the Manchester airport, D = 200 miles

The average speed of the plane, v = 120 mph

Time the plane leaves Manchester airport = 10 a.m.

The kinematic equation that can be used to find the time of flight is presented as follows;

\(Speed, \, v = \dfrac{Distance, \, D }{Time, \, t}\)

Therefore;

\(t = \dfrac{D}{v}\)

The time of flight is therefore;

\(t = \dfrac{200}{120} = \dfrac{5}{3} = 1\dfrac{2}{3}\)

The time of flight is \(1\frac{2}{3}\) hours or 5/3 hours which in minutes is therefore:

\(t = \dfrac{5}{3} \, hr \times 60 \, min/hr= 100 \, min\)

The time of arrival is 10 a.m. + 1 hour 40 minutes = 11:40 a.m.

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Answer:

18

X + 12 = 30

-12. -12. Subtract 12

X = 18. Answer

Answer:

42

Step-by-step explanation:

Answer and Step-by-step explanation:

I think this is the correct answer (in picture):

This is because you can either get Heads or Tails, so once you flip it once, you just flip it again and you will get either heads or tails.

#teamtrees #PAW (Plant And Water)

The value of γ is greater than 1 for any v > 0, greater than 10 for v > 0.995c, and greater than 100 for v > 0.99995c.

To determine for what speed (in terms of c) the value of γ is greater than 1, 10, and 100, we'll use the formula for the Lorentz factor (γ):
γ = 1 / √(1 - v²/c²)
where v is the speed and
c is the speed of light.

(a) For γ > 1:
Since γ is always greater than 1 for any speed v greater than 0, we can say that γ is appreciably greater than 1 for any v > 0.

(b) For γ > 10:
We need to solve the equation 10 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 100 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/100 = 99/100.
So, v/c = √(99/100), which implies v > 0.995c for γ > 10.

(c) For γ > 100:
Similar to (b), solve the equation 100 = 1 / √(1 - v²/c²) for v/c:
Squaring both sides, we get 10000 = 1 / (1 - v²/c²).
Now, solve for v²/c²: v²/c² = 1 - 1/10000 = 9999/10000.
So, v/c = √(9999/10000), which implies v > 0.99995c for γ > 100.

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What is a slope in math?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

To find the correct answer, we need to look at the formula for a straight line: y=mx+b where m= the slope of the line and b= the y intercept. We know from the problem that the slope must be equal to -4, leaving us with y= -4x +b. From here you can substitute the given point in the equation and solve for b.

-3= -4(4) +b

-3= -16+b

+16  +16

13= b

This tells us that b=13, now we simply substitute that into the formula.

The solution to your question is y=-4x+13

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The statement refers to anorexia nervosa and not bulimia nervosa. Therefore, the statement is FALSE.

Bulimia nervosa can be described as an eating disorder whereby an individual eats a lot of food without control and afterwards try to purge themselves to get rid of extra calories.

On the other hand, a similar eating disorder that is characterized with fear of being overfat but also follows with abnormal excessive weight loss is called anorexia nervosa.

Therefore, the statement refers to anorexia nervosa and not bulimia nervosa. Therefore, the statement is FALSE.

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Answer:

4°=1

g g g g g g g g g g

Step-by-step explanation:

the probability that none of the four non-overlapping one-half hour intervals contains any call is approximately 0.00000614.

(a) The probability of having more than three calls in one-half hour can be calculated using the exponential distribution. Since the mean of the exponential distribution is 10 minutes, the rate parameter (λ) can be calculated as λ = 1/mean = 1/10 = 0.1 calls per minute.

To find the probability of having more than three calls in one-half hour (30 minutes), we need to calculate the cumulative distribution function (CDF) of the exponential distribution up to three calls and subtract it from 1.

P(X > 3) = 1 - P(X ≤ 3)

        = 1 - (1 - e^(-λt))   [where t is the time duration in minutes]

        = 1 - (1 - e^(-0.1 * 30))

        = 1 - (1 - e^(-3))

        = 1 - (1 - 0.049787)

        = 0.049787

Therefore, the probability of having more than three calls in one-half hour is approximately 0.0498 or 4.98%.

(b) The probability of having no calls within one-half hour can be calculated using the exponential distribution as well.

P(X = 0) = e^(-λt)   [where t is the time duration in minutes]

        = e^(-0.1 * 30)

        = e^(-3)

        ≈ 0.049787

Therefore, the probability of having no calls within one-half hour is approximately 0.0498 or 4.98%.

(c) To determine x such that the probability of having no calls within x hours is 0.01, we need to solve the exponential distribution equation.

0.01 = e^(-0.1 * x * 60)

Taking the natural logarithm of both sides, we get:

ln(0.01) = -0.1 * x * 60

x = ln(0.01) / (-0.1 * 60)

  ≈ 230.26

Therefore, x is approximately 230.26 hours.

(d) The probability of having no calls within a two-hour interval can be calculated using the exponential distribution.

P(X = 0) = e^(-λt)   [where t is the time duration in minutes]

        = e^(-0.1 * 120)

        = e^(-12)

        ≈ 6.14e-06

Therefore, the probability of having no calls within a two-hour interval is approximately 6.14e-06 or 0.00000614.

(e) If four non-overlapping one-half hour intervals are selected, the probability that none of these intervals contains any call can be calculated by multiplying the individual probabilities of no calls in each interval.

P(no calls in one interval) = e^(-0.1 * 30)

                          ≈ 0.0498

P(no calls in all four intervals) = (0.0498)^4

                               ≈ 6.14e-06

Therefore, the probability that none of the four intervals contains any call is approximately 6.14e-06 or 0.00000614.

Conclusion: In this scenario with exponentially distributed call intervals, we calculated probabilities for different cases. The probability of having more than three calls in one-half hour is approximately 4.98%, while the probability of having no calls within one-half hour is also approximately 4.98%. We found that x is approximately 230.26 hours for a 0.01 probability of having no calls within x hours. The probability of having no calls within a two-hour interval is approximately 0

.00000614. Lastly, the probability that none of the four non-overlapping one-half hour intervals contains any call is approximately 0.00000614.

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The relationship between the number of address lines A on a decoder and its number of output lines Q is :

Q = 2^A

A multiplexer has 4 address lines, 1 output bit.

Binary Decoders are another type of digital logic device that has inputs of 2-bit, 3-bit or 4-bit codes depending upon the number of data input lines, so a decoder that has a set of two or more bits will be defined as having an n-bit code, and therefore it will be possible to represent 2n possible values. Thus, a decoder generally decodes a binary value into a non-binary one by setting exactly one of its n outputs to logic “1”.

The relationship between the number of address lines A on a decoder and its number of output lines Q is :

Q = 2^A

The number of select lines for a multiplexer is determined by the number of input lines, where the select lines are equal to the base-2 logarithm of the number of input lines. For example, a 16-input multiplexer requires four select lines because 2^4 = 16.

If a multiplexer has 4 address lines, 1 output bit.

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Answer:

\(\frac{2}{k+2}\)

Step-by-step explanation:

Given the expression:

\(\frac{4k+2}{k^2-4} * \frac{k-2}{2k+1}\)

We are to find the product as shown:

\(= \frac{4k+2}{k^2-4} * \frac{k-2}{2k+1}\\\\= \frac{2(2k+1)}{k^2-2^2} * \frac{k-2}{2k+1}\\\\= \frac{2(2k+1)}{(k-2)(k+2)} * \frac{k-2}{2k+1}\\\\= \frac{2}{k+2} * 1\\\\= \frac{2}{k+2}\)

Hence the required function is \(\frac{2}{k+2}\)

d. StartFraction 2 Over k + 2 EndFraction

aka

d. 2/k+2

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer: He has 4 apples left.

Step-by-step explanation:

5-1=4

(hope this helps)

Answer:4

Step-by-step explanation: James had 5 apples which later he gave one to aliya so 5-1 is 4

Answer: $1.33.

Step-by-step explanation:

Earnings per share = (Net income - Preferred dividends) / Common shares outstanding

Preferred dividends = 10,000 shares * 50 * 10%

= $50,000

Earnings per share = (150,000 - 50,000) / 75,000

= $1.33

Answer:

Step-by-step explanation:

t = 158                         Corresponding angles

t + s = 180                   They are supplementary angles

158 + s = 180               Subtract 158 from both sides

s = 180 - 158

s = 22

As a note, all angles in this situation are either 158 or 22.

Answer:

The answer is "Option C".

Step-by-step explanation:

Please find the correct question in the attached file.

\(\to 1 \frac{2}{5} = \frac{7}{5} \\\\let \\ \to \frac{7}{5} =1.4\\\\\to \frac{2}{5}= 0.4\\\\\to 1.4- 0.4\\\\ \to 1\\\)

Its outcome is 1.4 if we subtract from 0.4. However, a fraction of less than 2/5 may be deducted. This means that the outcome still exceeds 1, that's why choice C is correct.

Answer:

C

Step-by-step explanation:

The probability of rain tomorrow is the same regardless of whether it has rained in the past two days or not. Therefore, we cannot use the given information to make a prediction about the weather tomorrow.

In example 4.4, we are given a situation where it has not rained in the past two days. The question asks for the probability of rain tomorrow. This type of question falls under the category of conditional probability. In conditional probability, we find the probability of an event given that another event has already occurred.
To solve this problem, we can use Bayes' theorem. Bayes' theorem states that the probability of an event A given that event B has occurred is equal to the probability of event B given that event A has occurred multiplied by the probability of event A divided by the probability of event B.
Let us define the events in this problem as follows:
A = It will rain tomorrow
B = It has not rained in the past two days
Using the given information, we know that P(B) = 0.75 (since there are four possible outcomes: rain yesterday, rain day before yesterday, rain both days, no rain both days, and we are given that the latter has occurred). We need to find P(A|B).
To find P(A|B), we need to find P(B|A), which is the probability that it has not rained in the past two days given that it will rain tomorrow. Since we do not have any information about the relationship between these two events, we can assume that they are independent.
Therefore, P(B|A) = P(B) = 0.75
Now, we can use Bayes' theorem to find P(A|B):
P(A|B) = P(B|A) * P(A) / P(B)
P(A|B) = 0.75 * P(A) / 0.75
P(A|B) = P(A)
This means that the probability of rain tomorrow is the same regardless of whether it has rained in the past two days or not. Therefore, we cannot use the given information to make a prediction about the weather tomorrow.

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The required values are :

\(\qquad \sf  \dashrightarrow \:x = 4\)

and

\(\qquad \sf  \dashrightarrow \:y = 1\)

Check the attachment for solution ~

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Answer:

B. 4.09 cm²

Step-by-step explanation:

Let point O be the center of the circle.

As the center of the circle is the midpoint of the diameter, place point O midway between P and R.

Therefore, line segments OP and OQ are the radii of the circle.

As the radius (r) of a circle is half its diameter, r = OP = OQ = 5 cm.

As OP = OQ, triangle POQ is an isosceles triangle, where its apex angle is the central angle θ.

To calculate the shaded area, we need to subtract the area of the isosceles triangle POQ from the area of the sector of the circle POQ.

To do this, we first need to find the measure of angle θ by using the chord length formula:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Chord length formula}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the central angle.\\\end{minipage}}\)

Given the radius is 5 cm and the chord length PQ is 6 cm.

\(\begin{aligned}\textsf{Chord length}&=2r\sin\left(\dfrac{\theta}{2}\right)\\\\\implies 6&=2(5)\sin \left(\dfrac{\theta}{2}\right)\\\\6&=10\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{3}{5}&=\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{\theta}{2}&=\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=2\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=73.73979529...^{\circ}\end{aligned}\)

Therefore, the measure of angle θ is 73.73979529...°.

Next, we need to find the area of the sector POQ.

To do this, use the formula for the area of a sector.

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Substitute θ = 73.73979529...° and r = 5 into the formula:

\(\begin{aligned}\textsf{Area of section $POQ$}&=\left(\dfrac{73.73979529...^{\circ}}{360^{\circ}}\right) \pi (5)^2\\\\&=0.20483... \cdot 25\pi\\\\&=16.0875277...\; \sf cm^2\end{aligned}\)

Therefore, the area of sector POQ is 16.0875277... cm².

Now we need to find the area of the isosceles triangle POQ.

To do this, we can use the area of an isosceles triangle formula.

\(\boxed{\begin{minipage}{6.7 cm}\underline{Area of an isosceles triangle}\\\\$A=\dfrac{1}{2}b\sqrt{a^2-\dfrac{b^2}{4}}$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the leg (congruent sides). \\ \phantom{ww}$\bullet$ $b$ is the base (side opposite the apex).\\\end{minipage}}\)

The base of triangle POQ is the chord, so b = 6 cm.

The legs are the radii of the circle, so a = 5 cm.

Substitute these values into the formula:

\(\begin{aligned}\textsf{Area of $\triangle POQ$}&=\dfrac{1}{2}(6)\sqrt{5^2-\dfrac{6^2}{4}}\\\\ &=3\sqrt{25-9}\\\\&=3\sqrt{16}\\\\&=3\cdot 4\\\\&=12\; \sf cm^2\end{aligned}\)

So the area of the isosceles triangle POQ is 12 cm².

Finally, to calculate the shaded area, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Area of sector $POQ$}-\textsf{Area of $\triangle POQ$}\\\\&=16.0875277...-12\\\\&=4.0875277...\\\\&=4.09\; \sf cm^2\end{aligned}\)

Therefore, the area of the shaded region is 4.09 cm².

Y = 8000/1000= 8

Y= 8*20

Y= 160

Answer:

-1

Step-by-step explanation:

the line crosses y at -1

Answer:

Explanation:

According to the factor theorem, if we set x+1 to zero, the substitute the x value into the polynomial, if we get a value of zero, then x+1 is a factor of the polynomial, otherwise, it is not

We start by setting x+1 to zero:

Substitute -1 into the polynomial:

This shows that (x+1) is a factor of the polynomial

Let x be the height, we know that the base is six times as long, this means that the base can be express as:

Now, thas we know the height and the base we plug them in the equation for the area and solve for x:

Now, that we know the value of x we can calculate the length of the base (which is the longer side of the playground):

Therefore, the length of the longer side is 173.88 ft

Answer:

325

Step-by-step explanation:

k = -7

d=4

5(-7k + 4d)

5(-7(-7) + 4(4))

5(49 + 16)

325

please give brainliest I need it to level up

Complete question :

Stacy has a spinner (1 - 4) and a number cube (1 - 6) after spinning and rolling the number cube she will add two number what is the probability that the sum of the numbers from the spinner and number cube will be 3 or 4

Answer:

5 /24

Step-by-step explanation:

The sample space for the sun of the outcome of the spinner and rolled number cube ;

Sample space = total possible outcomes = 6 * 4 = 24

Required outcome = sum equals 3 or 4 = 5

P(obtaining a sum of 3 or 4) = required outcome / Total possible outcomes

P(obtaining a sum of 3 or 4) = 5 /24

This refers to the total amount of money that the federal government owes to creditors, including individuals, businesses, and foreign governments. It is primarily the result of unpaid budget deficits, which occur when the government spends more money than it collects in revenue. The federal debt can increase over time due to interest charges on the outstanding debt, as well as additional deficits in future years. Rising interest rates, periods of structural unemployment, and competitive devaluations of currency can all have an impact on the economy and government finances, but they do not directly contribute to the federal debt.

The Federal Reserve can change the discount rate, which is the interest rate at which banks can borrow from the Fed, to influence the borrowing behavior of banks. If the Fed lowers the discount rate, it becomes cheaper for banks to borrow money, which can lead to increased lending activity and economic growth. Conversely, if the Fed raises the discount rate, it becomes more expensive for banks to borrow money, which can decrease lending activity and slow down economic growth.

 A marginal tax on sellers of a good will increase the costs of production, leading to a decrease in supply. This means that sellers will produce and offer less of the good at any given price, which will shift the supply curve to the left.

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Answer:

c

Step-by-step explanation:

The solution is,  (c)  Yes, because angle 3 and angle 6 are congruent.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

given that,

Angles 3 and 6 are "alternate interior" angles. When those angles are congruent, as these are, then the lines crossed by the transversal are parallel.

we have,

We expect angles 5 and 6 to be supplementary because they are a linear pair.

That fact says nothing about the relationship of line d to line c.

Hence, The solution is,  (c)  Yes, because angle 3 and angle 6 are congruent.

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Group theory is a branch of mathematics that studies the properties and structures of groups. It provides a framework for understanding symmetry, transformations, and patterns in various mathematical and scientific disciplines.

Group theory is a mathematical concept that explores the properties of groups. In mathematics, a group is a set of elements combined with an operation that satisfies specific conditions.

These conditions include closure (the operation performed on two elements of the group results in another element of the group), associativity (the order in which operations are performed does not affect the outcome), identity (there exists an element that does not change other elements when combined with them), and inverse (every element has an inverse element that, when combined, yields the identity element).

Groups have applications in many areas, including abstract algebra, geometry, physics, and computer science. In the context of linear algebra, group theory is particularly relevant.

The study of matrices and their operations involves understanding groups and their properties. For example, matrix multiplication exhibits the closure and associativity properties of groups. By applying group theory, we can analyze the behavior of matrices and identify patterns and symmetries.

Moreover, group theory connects to other mathematical concepts such as fields and rings. Fields are mathematical structures that include operations of addition, subtraction, multiplication, and division, while rings involve operations of addition and multiplication.

By studying the relationships between groups, fields, and rings, we can deepen our understanding of algebraic structures and their applications.

To illustrate the usefulness of group theory, consider the example of dihedral groups. Dihedral groups are a specific type of group that represents symmetries of regular polygons.

By applying group theory to dihedral groups, we can analyze the rotational and reflective symmetries of polygons, which have implications in geometry, crystallography, and other areas.

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