Last year at a certain high school, there were 140 boys on the honor roll and 68 girls on the honor roll. This year, the number of boys on the honor roll increased by 5% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

The equation that represents a circle in the plane is (d) x² + y² = 25.

A circle in the plane is defined as the set of all points that are equidistant from a fixed center point. The general equation for a circle with center (h, k) and radius r is given by (x - h)² + (y - k)² = r². In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius.

In the equation x² + y² = 25, we can see that the coefficients of both x² and y² are 1, indicating that they are both squared terms. The constant term on the right side of the equation is 25, which represents the square of the radius. Therefore, this equation represents a circle with center at the origin (0, 0) and radius 5.

Let's examine the other equations to see why they do not represent circles:

(a) y = x²: This equation represents a parabola, not a circle. It is a quadratic equation in which y is expressed as a function of x.

(b) x - 2y = 0: This equation represents a line, not a circle. It is a linear equation in which x and y are related by a constant ratio.

(c) y² = 16: This equation represents a parabola, not a circle. It is a quadratic equation in which y² is equal to a constant.

Therefore, the equation x² + y² = 25 represents a circle in the plane.

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Answer:

6,75sugar

Step-by-step explanation:

2,25

2,25

2 25

=6,75

Answer:

35

Step-by-step explanation:

just do 2x11+13 lol.....

Liam’s profits after six years will be \($46,637.44\).

The formula to calculate the amount of profits after six years is given by:

Final Profits = Initial Profits x (1 + Appreciation Rate)^Years

In this case, Liam's profits after six years can be calculated as:

Final Profits = \($43,200 x (1 + 1.2%)^6\)

Final Profits = \($43,200 x 1.07722\)

Final Profits = \($46,637.44\)

Therefore, Liam’s profits after six years will be \($46,637.44\).

The formula used to calculate the profits after six years is useful for predicting the amount of profits Liam will earn in the future given a certain appreciation rate. This can help Liam make more informed decisions about his business and plan for the future.

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Answer:

y = 1

Step-by-step explanation:

Slope = 0 since it is a horizontal line.

y = mx + b is your slope intercept form.

m = slope

b = y-intercept

find b. in other words, when x = 0. We see that when x = 0, y = 1. Therefore, your b = 1.

put together your equation

y = mx + b

y = 0x + 1

therefore, y = 1 is your equation for the line on the graph

Step-by-step explanation:

that a picture of what you need. Go through it and get back to me.

The dimensions of the region bounded by the curve, y² = x, the lines,  x = 1 and x = 4, and the x-axis exists the dimensions ABCD

Thus area of ABCD = \(\int_1^4 \mathrm{ydx} \\\)

\(& =\int_1^4 \sqrt{\mathrm{x}} \mathrm{dx} \\\)

\($& =\left[\frac{\mathrm{x}^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^4 \\\)

\($& =\frac{2}{3}\left[(4)^{\frac{3}{2}}-(1)^{\frac{3}{2}}\right]\)

simplifying,

\($& =\frac{2}{3}[8-1] \\\)

Then we get,

\($& =\frac{14}{3} \text { units }\)

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The length of each side of the sign will be 14.81-inch approx.

It is assumed that an Octagon sign is created by cutting out triangles from a square's corners, and that the stop sign's overall length is 36 inches. Since we are aware that squares have right angles on all four sides, we can use Pythagoras' theorem to solve for the side of the sign in the image below.

           \(s^{2} =x^{2} +x^{2} \\s^{2}=2x^{2} ...................Eq.1\)

Also, it is a square. So, the measurement of length from side to side

            \(2x+s=36....................Eq.2\)

solving Eq.1 we get,

\(s=\sqrt{2} x\)...putting this value in Eq.2,

            \(s=36-2x\\\\\sqrt{2} x=36-2x\\\\x=\frac{36}{2+\sqrt{2} }\)

Putting this value of x in Eq.1,

          s = 14.8

Hence, The length of each side of the sign will be 14.81-inch approx.

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Answer:

D

Step-by-step explanation:

The graph fourth represents the exponential decay option fourth is correct.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a graph shown in the picture.

As we know from the definition of exponential decay, a quantity falls slowly at first before rapidly decreasing.

From the graph given, graph fourth represents the exponential decay.

Thus, the graph fourth represents the exponential decay option fourth is correct.

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Answer:

6.JMK=90-28

=62

STR=180-118

=62

(PROVEN)

Answer:

Step-by-step explanation:

B

Answer:

Step-by-step explanation:

Using pairs of points from the  table to get the equation:

The slope:

y-intercept:

So the equation is:

Answer:

Y=12x

Step-by-step explanation:

Y=12x

Step by step explanation

a) The probability that a new SME is successful can be calculated by considering the proportion of successful SMEs started by graduates and non-graduates.

For SMEs started by graduates, the probability of success is 70%, so the probability of a new SME being successful and started by a graduate is 55% (proportion of SMEs started by graduates) multiplied by 70% (probability of success for SMEs started by graduates), which equals 0.55 * 0.70 = 0.385.

For SMEs started by non-graduates, the probability of success is 10%, so the probability of a new SME being successful and started by a non-graduate is 45% (proportion of SMEs started by non-graduates) multiplied by 10% (probability of success for SMEs started by non-graduates), which equals 0.45 * 0.10 = 0.045.

To get the overall probability of success for a new SME, we sum the probabilities from both categories:

Overall probability of success = Probability of success for SMEs started by graduates + Probability of success for SMEs started by non-graduates

Overall probability of success = 0.385 + 0.045 = 0.43.

b) The probability that a new SME is successful and not started by a graduate can be calculated by considering the proportion of successful SMEs started by non-graduates.

The probability of a new SME being successful and not started by a graduate is 45% (proportion of SMEs started by non-graduates) multiplied by 10% (probability of success for SMEs started by non-graduates), which equals 0.45 * 0.10 = 0.045.

c) If it is known that a new SME is successful, the probability that it was not started by a graduate can be calculated using Bayes' theorem. Let's denote the event "successful SME" as S and the event "not started by a graduate" as NG.

The probability of a new SME being successful and not started by a graduate has already been calculated in part b) as 0.045. The probability of a new SME being successful can be calculated in part a) as 0.43.

Using Bayes' theorem, the probability that a successful SME was not started by a graduate is given by:

P(NG|S) = (P(S|NG) * P(NG)) / P(S)

P(NG|S) = (0.045 * 0.45) / 0.43 = 0.047.

Therefore, if it is known that a new SME is successful, the probability that it was not started by a graduate is 0.047.

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False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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The difference between the three variances, Var(x), Var(y), and Var(x + y), can be determined analytically in the context of the bus ridership example.

In the given context, let's consider two variables: x represents the ridership on line l2, and y represents the ridership on line l1. The statement mentions that intuitively, l1 and l2 are not independent, meaning they are related in some way.

To determine the difference between the variances, we need to calculate the variances of x, y, and the sum of x and y, which is x + y.

Var(x): This represents the variance of the ridership on line l2. It quantifies the spread or variability in the data points of x. To calculate Var(x) analytically, you can use the formula: Var(x) = E[(x - μx)^2], where E represents the expectation (mean) operator and μx represents the mean of x.

Var(y): This represents the variance of the ridership on line l1. Similar to Var(x), it quantifies the spread or variability in the data points of y. Var(y) can be calculated using the same formula as Var(x): Var(y) = E[(y - μy)^2], where μy represents the mean of y.

Var(x + y): This represents the variance of the sum of ridership on both lines l1 and l2. It measures the combined variability of the two variables. To calculate Var(x + y), you can use the formula: Var(x + y) = E[(x + y - μ(x + y))^2], where μ(x + y) represents the mean of the sum of x and y.

By analytically calculating the three variances, Var(x), Var(y), and Var(x + y), you can compare them to understand their differences and the relationship between the ridership on line l1 and line l2.

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The smallest value within the class is the lower class limit, and the largest value within the class is the upper class limit.

A class limit is a set of boundary values in the form of a range that describes the lowest and highest data values that a class can contain. The lower class limit refers to the smallest data value in a class, whereas the upper class limit refers to the largest data value in a class. The width of a class is determined by the difference between the upper and lower class limits. Here are a few examples to give you a better understanding of how this works:

Class:              5-9 5 9

Lower Limit:    10-14 10 14

Upper Limit:    15-19 15 19

This shows class limits for three different classes.

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Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

We have,

To find the mean and variance of the return series, we can substitute the given model into the equation and calculate:

Mean of rt:

E(rt) = E(0.02 + 0.5rt-2 + et)

= 0.02 + 0.5E(rt-2) + E(et)

= 0.02 + 0.5 * 0 + 0

= 0.02

The variance of rt:

Var(rt) = Var(0.02 + 0.5rt-2 + et)

= Var(et) (since the term 0.5rt-2 does not contribute to the variance)

= 0.02

The mean of the return series rt is 0.02, and the variance is 0.02.

To compute the lag-1 and lag-2 autocorrelations of rt, we need to determine the correlation between rt and rt-1, and between rt and rt-2:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

Since we are given r100 = -0.01 and r99 = 0.02, we can substitute these values into the equations:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

= Cov(r100, r99) / (σ(r100) * σ(r99))

= Cov(-0.01, 0.02) / (σ(r100) * σ(r99))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

= Cov(r100, r98) / (σ(r100) * σ(r98))

To compute the 1- and 2-step-ahead forecasts of the return series at

t = 100, we use the given model:

1-step ahead forecast:

E(rt+1 | r100, r99) = E(0.02 + 0.5rt-1 + et+1 | r100, r99)

= 0.02 + 0.5r100

2-step ahead forecast:

E(rt+2 | r100, r99) = E(0.02 + 0.5rt | r100, r99)

= 0.02 + 0.5E(rt | r100, r99)

= 0.02 + 0.5(0.02 + 0.5r100)

The associated standard deviation of the forecast errors can be calculated as the square root of the variance of the return series, which is given as 0.02.

Thus,

Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

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Answer:

Step-by-step explanation:

10,000 x 12% = 1,200

10,000 + 1,200 = 11,200

There are 60 months in 5 years

11,200 ÷ 60 = $186.67

None of these responses is correct

Answer:

A 7.85 cm2 should be right

2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

$10,000 was invested in the 4% fund, and $15,000 was invested in the 6% fund. x + y = 25,000 and 0.04x + 0.06y = 1,300 equations model this situation.

(a) To determine the amount of money invested in each fund, we can set up a system of equations based on the given information.

Let's denote the amount invested in the 4% fund as x, and the amount invested in the 6% fund as y.

1. The total amount invested is $25,000:

x + y = 25,000

2. The total interest earned is $1,300, which is the sum of the interest earned from each fund:

0.04x + 0.06y = 1,300

We have the following system of equations:

x + y = 25,000

0.04x + 0.06y = 1,300

To solve this system of equations, you can use various methods such as substitution or elimination. Let's solve it using the elimination method:

Multiply the first equation by 0.04 to make the coefficients of x in both equations equal:

0.04x + 0.04y = 1,000

Subtract the second equation from the modified first equation:

(0.04x + 0.04y) - (0.04x + 0.06y) = 1,000 - 1,300

0.04y - 0.06y = -300

-0.02y = -300

y = (-300) / (-0.02)

y = 15,000

Substitute the value of y back into the first equation to solve for x:

x + 15,000 = 25,000

x = 25,000 - 15,000

x = 10,000

Therefore, $10,000 was invested in the 4% fund, and $15,000 was invested in the 6% fund.

(b) The equations to model this situation are:

x + y = 25,000  (Equation representing the total amount invested)

0.04x + 0.06y = 1,300 (Equation representing the total interest earned)

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Answer:

x = 6 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

6^2+ x^2 = 12^2

36 + x^2 = 144

Subtract 36 from each side

x^2 = 144-36

x^2 =108

Take the square root of each side

sqrt(x^2) = sqrt(108)

x = sqrt(36*3)

x = 6 sqrt(3)

If two events, event A with probability P(A) and event b with probability P(B) are complementary events then the sum of the probability of events A and B will be one.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

When one event happens if and only if the other one doesn't, two occurrences are said to be complimentary. The odds of two complementary events equal one.

P(A) + P'(A) = 1

The chance of events A and B added together will equal one if events A with probability P(A) and event B with probability P(B) are complementary occurrences.

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The uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

To calculate the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ for the given wave packet, we need to find the expectation values of the observables (x^ - ⟨x⟩)^2 and (p^ - ⟨p⟩)^2, respectively.

The wave packet is represented by the function ψ(x) = [2πa^2]^(1/2) exp[-4a^2(x - ⟨x⟩)^2 + iℏpx]. Here, a is a constant, ⟨x⟩ represents the expectation value of x, and p is the momentum operator.

To find ⟨Δx^2⟩, we calculate the expectation value of (x^ - ⟨x⟩)^2 with respect to ψ(x). By integrating (x - ⟨x⟩)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δx^2⟩ = a^2/2.

Similarly, to find ⟨Δp^2⟩, we calculate the expectation value of (p^ - ⟨p⟩)^2 with respect to ψ(x). Since p is the momentum operator, its expectation value is ⟨p⟩ = 0 for the given wave packet. By integrating (p^ - 0)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

Therefore, the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).

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Answer:

D

Step-by-step explanation: