in the binomial model, the difference between the up and down factors best represents the: volatility of the underlying. moneyness of an option. pseudo probability.

Answer:

D) \(x^{2} =8y\)

Step-by-step explanation:

Because the receiver of the parabolic dish antenna is 2 feet above the vertex, the parabola must be vertical. Therefore, we will use the equation \((x-h)^2=4p(y-k)\) where \((h,k)\) is the vertex of the parabola and \((h,k+p)\) is the focus point. Since we are given that the receiver is 2 feet above the vertex which is located at the focus point and the vertex is \((0,0)\) at the origin, then the focus point is \((0,0+p)\) where \(p=2\). Therefore, the equation that models a cross section of the dish is \(x^{2} = 8y\).

Answer:

The three hondred grams

Answer:

(-7,22)

Step-by-step explanation:

X=-7 and y=22

Answer:

? = 30°

Step-by-step explanation:

All angles in a triangle add up to 180°

? + 130° + 20° = 180°

? = 180° - 130° - 20°

? = 30°

Answer:

The rule for divisibility by 9 works because numbers are written in base 10.

Step-by-step explanation:

Answer:

"statement 1: The number of boys at the school is \(\frac{4}5\) of the number of girls." is true.

Step-by-step explanation:

Given:

Ratio of Number of boys to the number of girls = 4 : 5

Total number of students = 270

To find:

Number of boys in terms of number of girls = ?

Solution:

As per given statement,

Let, Number of boys = \(4x\)

Let, Number of girls = \(5x\)

Total number of students = Number of boys + Number of girls = 270

\(\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}\)

Therefore, number of boys = 4 \(\times\) 30 = 120

And, number of girls = 5 \(\times\) 30 = 150

As per Statement 1:

Finding \(\frac{4}5\) of the number of girls:

\(\dfrac{4}{5}\times 150 = 4 \times 30 = 120\) = Number of boys.

Finding \(\frac{4}9\) of the total number of students:

\(\frac{4}{9}\times 270= 4 \times 30 = 120\) = Number of boys.

Number of boys is equal to \(\frac{4}9\) of total number of students.

So, "statement 1: The number of boys at the school is \(\frac{4}5\) of the number of girls." is true.

Given:

The expression is

\(0.3+0.6ab+0.5b\)

To find:

The terms and the coefficients.

Solution:

In an expression, the variables, constants and product of variable and constant separated by positive sign "+" are called terms.

We have,

\(0.3+0.6ab+0.5b\)

Here, the terms are 0.3, 0.6ab and 0.5b. The coefficients of variables are 0.6 and 0.5 respectively and 0.3 is a constant.

Answer:

Step-by-step explanation:

-2y = -3x + 12

2y = 3x - 12

y = 3/2x - 6

y - 2 = 3/2(x + 8)

y - 2 = 3/2x + 12

y = 3/2x + 14

The equation of a line that passes through the point (-8,2) and is parallel to the line 3x-2y=12 is 2y - 3x = 28

The equation of a line in point-slope form is expressed as;

\((y-y_1)=m(x-x_1)\)

m is the slope of the line

(x1, y1) is the point on the line = (-8, 2)

Given the line 3x - 2y =12

-2y = -3x + 12

y = 3/2 x - 6

The slope of the line is 3/2

Get the required equation:

\(y - 2=3/2(x-(-8))\\2(y-2)=3(x+8)\\2y-4 =3x+24\\2y-3x = 28\)

Hence the equation of a line that passes through the point (-8,2) and is parallel to the line 3x-2y=12 is 2y - 3x = 28

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Answer:

Are you sure that is the correct problem because your going to get a crazy answer to that

Step-by-step explanation:

Answer:

Step-by-step explanation:

15y + 9 = 15y - 20

0 ≠ -29

no solution

The cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value.

From the question , we are given that the laptop costs $350 more than the desktop, therefore,

let x represent the cost of the laptop thus, x-350 will be the cost of the desktop .

The total finance charge of $388 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as;

388 = 0.08(x) + 0.075(x - 350)

252 = 0.08x + 0.075x - 26.25

278.75 = 0.155x

x = 278.75/0.155

x = 1798

Recall that the cost of desktop = x -350

therefore:

1,798- 350 = 1448

The cost of laptop = $1798

The cost of desktop = $1448

Thus, the cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

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The point (12, 5) on the graph indicates that the bucket has been filled with 5 units of water after 12 units of time.

What is graph?

In mathematics, a graph is a visual representation of a set of data or mathematical relationships between variables.

The coordinates (12, 5) on the graph indicate that after 12 units of time, the amount of water in the bucket is 5 units.

This means that the bucket is being filled at a steady rate, and the rate at which the water is being added to the bucket is consistent over time.

The horizontal axis, usually the x-axis, represents time while the vertical axis, usually the y-axis, represents the amount of water in the bucket.

The graph provides a visual representation of the relationship between the amount of water in the bucket and time, which can be used to make predictions about the amount of water in the bucket at different points in time.

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The lower bound of the 90% confidence interval for the true average menstrual cycle length is 27.4.

a) Calculation for the lower bound of 90% confidence interval: The formula for calculating the confidence interval is, :

Lower Limit = X - Zα/2 × (σ/√n) Where, X = sample mean Zα/2 = 1.645σ = sample standard deviation= sample size Putting the given values into the formula, Lower Limit = 28.86 - 1.645 × (4.24/√50)≈ 27.4

The upper bound of the 90% confidence interval for the true average menstrual cycle length is 30.3.

b) Calculation for the upper bound of 90% confidence interval: The formula for calculating the confidence interval is,:

Upper Limit = X + Zα/2 × (σ/√n) Where ,X = sample mean Zα/2 = 1.645σ = sample standard deviation = sample size Putting the given values into the formula, Upper Limit = 28.86 + 1.645 × (4.24/√50)≈ 30.3

The confidence interval is (27.4, 30.3) and the hypothesized value is 29.5.

c) Hypothesis testing:According to the hypothesis, women's menstrual cycles are typically the same length as a lunar month - 29.5 days. So, we can check if the interval from (a,b) supports this hypothesis or not by comparing the hypothesized value with the confidence interval.

As we see that the hypothesized value is within the interval, we can say that the interval from (a,b) supports the hypothesis. Therefore, the answer is Yes.

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The volume of the solid obtained by rotating the region bounded by the curve y = x^2 and the x-axis between x = 7 and x = 9 about the x-axis is 2080π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = x^2 and the x-axis between x = 7 and x = 9 about the x-axis, we can use the method of cylindrical shells.

The formula for the volume of a solid obtained by rotating a curve y = f(x) between x = a and x = b about the x-axis is given by:

V = ∫[a, b] 2πx * f(x) dx

In this case, we have f(x) = x^2 and a = 7, b = 9. Substituting these values into the formula, we get:

V = ∫[7, 9] 2πx * x^2 dx

V = 2π ∫[7, 9] x^3 dx

To find the antiderivative of x^3, we can use the power rule of integration, which states that the antiderivative of x^n is (1/(n+1)) * x^(n+1). Applying this rule, we have:

V = 2π * (1/4) * x^4 | [7, 9]

V = 2π * (1/4) * (9^4 - 7^4)

V = 2π * (1/4) * (6561 - 2401) = 2π * (1/4) * 4160 = π * 2080

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Answer:

x= 3

Step-by-step explanation:

x on triangle 1 is 5 times less than 15

x on triangle 2 is 3 times bigger than 10

Hope this helps!

Answer:

x = 5

Step-by-step explanation:

The small triangle has been dilated by 2 making it twice as big as before.

The side that measures 10 would be dilated by 0.5 to find x which is half a big.

10 x 0.5 = 5

Now check your work. On one side it asks 6x. So, 6 x 5 = 30. Since 30 is twice as much as 15. The rule applies that x = 5.

5 x 2 = 10

6 x 5 = 30

15 x 2 = 30

Answer:

81.64 cubic inches.

Step-by-step explanation:

Volume of a cylinder is given by the expression \(V=\pi r^2h = \pi \times2^2\times6 = 24\pi \approx 81.64 in^3\)

Answer:

Step-by-step explanation:

Let x be the variable.

One fourth times the difference of ten and x is 2/3

1/4 (10 - x) = 2/3

10 - x = 3/2

-x = 3/2 - 10

x = -3/2 + 10

x = 13/2

The answer is:

\(\rm{\dfrac{1}{4}(10-d)=\dfrac{2}{3}}\)

Work/explanation:

First, the variable is d

Then, the difference of 10 and d is 10 - d.

One-fourth is 1/4.

The equation is : \(\rm{\dfrac{1}{4}(10-d)=\dfrac{2}{3}}\).

Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

They should evaluate the aquifer periodically to ensure the sustainable use of the groundwater.

The community of Limpopo found that the groundwater is a valuable resource and can provide enough water to meet their needs. As the project manager, you need to evaluate the aquifer. In this article, we will discuss the calculations required to find out the discharge from the aquifer and its conclusions.

Calculation 1.1: Discharge from the aquifer can be calculated using the equation;

Q = (2πT × b × H) / ln(R/r)

Where, Q = Discharge from the well

T = Transmissivity of aquifer

b = Thickness of the aquifer

H = Hydraulic head at the well

R = Radius of influence at the well

r = Radius of the well

Given, Transmissivity (T) = 55 m²/day

Thickness of the aquifer (b) = 25 m

Drawdown (h) = 3.5 m

Radius of influence (R) = 250 m

Well radius (r) = 0.4 m

Therefore, we can substitute all the given values in the formula,

Q = (2π × 55 × 25 × 3.5) / ln(250/0.4)

Q = 1227.6 m³/day

Therefore, the discharge from the aquifer is 1227.6 m³/day.

Calculation 1.2: Using the same formula as above,

Q = (2πT × b × H) / ln(R/r)

Given, the radius of the well is increased to 0.5 m

Now, r = 0.5 m

Substituting all the given values,

Q = (2π × 55 × 25 × 3.5) / ln(250/0.5)Q = 2209.7 m³/day

Therefore, the discharge from the aquifer is 2209.7 m³/day with the well diameter of 50 cm.

Calculation 1.3: Using the same formula as above,

Q = (2πT × b × H) / ln(R/r)

Given, the drawdown (h) = 5.5 m

Substituting all the given values,

Q = (2π × 55 × 25 × 5.5) / ln(250/0.4)

Q = 1560.8 m³/day

Therefore, the discharge from the aquifer is 1560.8 m³/day with the increased drawdown of 5.5 m.

Conclusions: From the above calculations, the following conclusions can be made:• The discharge from the aquifer is directly proportional to the well diameter. When the well diameter is increased from 40 cm to 50 cm, the discharge increased from 1227.6 m³/day to 2209.7 m³/day.•

The discharge from the aquifer is inversely proportional to the drawdown. When the drawdown increased from 3.5 m to 5.5 m, the discharge decreased from 1227.6 m³/day to 1560.8 m³/day.

Advise to the Community:

Based on the above conclusions, the community of Limpopo can increase their water supply by increasing the well diameter. However, they need to be cautious while pumping out water from the aquifer as increasing the pumping rate may result in a further decrease in discharge.

Therefore, they should evaluate the aquifer periodically to ensure the sustainable use of the groundwater.

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Answer:

you have it correct sir

Step-by-step explanation:

Answer:

1.33

Step-by-step explanation:

The value of n is 13.3 when the given proportion 8 : 15 = n : 25 is solved, using the cross multiplication method.

The given proportion is:

8 : 15 = n : 25

To solve this proportion, we can use the

cross-multiplication rule which states that the product of the numerator of the first fraction and the denominator of the second fraction must be equal to the product of the denominator of the first fraction and the numerator of the second fraction.

Therefore, we have:

8 × 25 = 15 × n

n = 200/15

n = 13.3 (rounded to the nearest tenth)

Therefore, the value of n is 13.3 when the given proportion is solved.

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The value of n in the proportion 8:15 = n:25 is approximately 13.3.

To solve the proportion 8:15 = n:25, we can use cross-multiplication.
Cross-multiplication involves multiplying the numerator of one ratio by the denominator of the other ratio.
In this case, we have:
8 * 25 = 15 * n
Multiplying, we get:
200 = 15n
To solve for n, we need to isolate it on one side of the equation.
Dividing both sides of the equation by 15:
200 / 15 = n
Simplifying, we get:
n ≈ 13.3

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Answer:

D)  (6.6, 7.4)

Step-by-step explanation:

Begin by finding the margin of error based on the given information.

\(\boxed{\begin{minipage}{7.3cm}\underline{Margin of Error formula}\\\\$\textsf{Margin of Error}= Z \times \dfrac{S}{\sqrt{n}}$\\\\where:\\\phantom{ww} $\bullet$ $Z =$ $Z$ score\\\phantom{ww} $\bullet$ $S =$ Standard Deviation of a population\\\phantom{ww} $\bullet$ $n =$ Sample Size\\\end{minipage}}\)

Given:

The z-score for 95% confidence level is 1.96.

Therefore, to find the margin of error, substitute the values into the formula:

\(\implies \textsf{Margin of Error}= 1.96 \times \dfrac{1.3}{\sqrt{50}}\)

\(\implies \textsf{Margin of Error}=0.360341...\)

To find a reasonable range for the true mean number of hours a teenage spend on their phone, subtract and add the margin of error to the given mean of 7 hours:

\(\begin{aligned}\implies \textsf{Lower bound}&=7-0.360341...\\&=6.63965...\\&=6.6\;\; \sf (1\;d.p.)\end{aligned}\)

\(\begin{aligned}\implies \textsf{Upper bound}&=7+0.360341...\\&=7.360341...\\&=7.4\;\; \sf (1\;d.p.)\end{aligned}\)

Therefore, the reasonable range for the true mean is:

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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a) The cat requires an acceleration of 8.4 m/s² to catch the mouse in 10 seconds.

Let's say that `x = distance`, `v₀ = initial velocity`, `t = time`, `a = acceleration`. For the mouse, the initial velocity `v₀ = 4.2 m/s`. Thus; `distance (mouse) = 4.2t`For the cat, the initial velocity `v₀ = 0.5 m/s`, and the time `t = 10 s`.Thus, `distance (cat) = \(0.5t + (1/2)at²\)`. Since the cat caught the mouse, the distance the cat covered is equal to the distance the mouse covered. `distance (cat) = distance (mouse)`. Therefore;`0.5t + (1/2)at² = 4.2t``(1/2)at² - 4.2t + 0.5t = 0``a/2 * 100 = 420`. Multiplying both sides by 2 yields; `a * 100 = 840`. Dividing both sides by 10² yields; `a = 8.4 m/s²`. Therefore, the cat requires an acceleration of 8.4 m/s² to catch the mouse in 10 seconds.

b) The mouse gets 21 meters from `x = 0` before being caught by the cat.

For the mouse, the initial velocity `v₀ = 4.2 m/s`. Thus; `distance (mouse) = 4.2t` For the cat, the initial velocity `v₀ = 0.5 m/s`, and the time `t = 10 s`. Thus, `distance (cat) = \(0.5t + (1/2)at²\)`. Since the cat caught the mouse, the distance the cat covered is equal to the distance the mouse covered. `distance (cat) = distance (mouse)` Therefore; `\(0.5t + (1/2)at² = 4.2t``(1/2)at² - 4.2t + 0.5t = 0``a/2 * 100 = 420\)` Multiplying both sides by 2 yields; `a * 100 = 840` Dividing both sides by 10² yields; `a = 8.4 m/s²`. To calculate the distance the mouse gets from `x = 0`, we can substitute the value of time into the equation of the mouse; `distance (mouse) = 4.2t``distance (mouse) = 4.2 * 10``distance (mouse) = 42`The distance the mouse gets from `x = 0` before being caught by the cat is `42 - 21 = 21 meters`

c) The velocity of the cat with respect to the mouse at the time it catches the mouse is 4.2 m/s.

For the mouse, the initial velocity `v₀ = 4.2 m/s`. Thus; `distance (mouse) = 4.2t` For the cat, the initial velocity `v₀ = 0.5 m/s`, and the time `t = 10 s`. Thus, `distance (cat) = 0.5t + (1/2)at²`Since the cat caught the mouse, the distance the cat covered is equal to the distance the mouse covered. `distance (cat) = distance (mouse)` Therefore; `\(0.5t + (1/2)at² = 4.2t``(1/2)at² - 4.2t + 0.5t = 0``a/2 * 100 = 420\)`. Multiplying both sides by 2 yields; `a * 100 = 840` Dividing both sides by 10² yields; `a = 8.4 m/s²`At the time the cat catches the mouse, the velocity of the cat with respect to the mouse is the difference between the velocity of the cat and the velocity of the mouse; `velocity (cat - mouse) = velocity (cat) - velocity (mouse)`The velocity of the cat at the time it catches the mouse is; `velocity (cat) = v₀ + at ``velocity (cat) = 0.5 + 8.4 * 10``velocity (cat) = 84.5`The velocity of the mouse is; `velocity (mouse) = 4.2 m/s`. Therefore; `velocity (cat - mouse) = 84.5 - 4.2``velocity (cat - mouse) = 80.3 m/s`. Hence, the velocity of the cat with respect to the mouse at the time it catches the mouse is `4.2 m/s`.

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Answer:

Rate of change = 2 & Initial value = -1

Answer:

121 ÷ (3 × 3 + 2) = 11

Step-by-step explanation:

121 ÷ (3 × 3 + 2) = 11

121 ÷ (9 + 2) = 11

121 ÷ 11 = 11

11 = 11

If Faith bounces backwards at 0.5m/s in an isolated system, then

(a) Grace's post-collision speed is 2 m/s,

(b) the percent kinetic energy loss in collision is 70%.

Part (a) : The weight of faith(m₁) = 50Kg,

The weight of Grace (m₂) = 62 Kg,

The weight of bumper cars is (m) = 36 Kg,

The speed at which Faith is cruising the car is (u₁) = 3.6 m/s,

The speed at which Grace is cruising the car is (u₂) = 1.6 m/s,

The speed of Faith after thee Collison is (v₁) = 0.5 m/s.

So, By using the momentum conservation,

We get,

⇒ (m₁ + m)×u₁ - u₂(m₂+ m) = -(m₁ + m)v₁ + (m₂+ m)v₂,

⇒ (50 + 36)×3.6 - 1.6(62 + 36) = -(50 + 36)0.5 + (62 + 36)v₂,

On simplifying further,

We get,

⇒ v₂ = 1.998 m/s ≈ 2m/s

So, Speed of Grace after the collision is 2m/s.

Part(b) : The initial Kinetic Energy will be = (1/2)×(m + m₁)×(u₁)² + (1/2)×(m + m₂)×(u₂)²

⇒ (1/2)×86×(3.6)² + (1/2)×98×(1.6)² = 682.72 J,

The final Kinetic Energy will be = (1/2)×(m + m₁)×(v₁)² + (1/2)×(m + m₂)×(v₂)²,

⇒ (1/2)×86×(0.5)² + (1/2)×98×(2)² = 206.75 J,

So, the percent loss in Kinetic energy will be = (682.72 - 206.75)/682.72 × 100,

⇒ 0.6972 × 100 = 69.72% ≈ 70%.

Therefore, percent loss in kinetic energy after collision is 70%.

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Answer:

W= -6

Step-by-step explanation:

-4w = -5 + 29

-4w = 24

Divide both sides by -4

=

W = -6

Answer:

you change w to the other side then proceed as you normally would