In a class of 25 students, 14 have a brother and 17 have a sister. There are 5 students who do not have any siblings. What is the probability that a student who has a brother also has a sister?

Answer:

The area of the triange is 20 feet. beacause the area of the rectangel is 40 feet.

Step-by-step explanation:

Answer:

300,000 + 40,000 + 5,000

Have a good day

Answer:

345,000

Step-by-step explanation:

unless its asking for something else like expanded form or word form

The points on the graph at which the tangent line is horizontal are:

(-1.414, 4.886) and (1.414, 1.114).

Since the horizontal tangent is parallel to the x-axis, its slope, or derivative, should also have a value of 0 at the tangent point. This is the key concept for finding the point on the graph where the tangent line is horizontal.  

The function is given as:

y = ¹/₃x³ - 2x + 3

The tangents are horizontal where the derivative is zero. The derivative of the given function is:

y' = x² -2

This is zero when:

0 = x² -2

2 = x²

x  = ±√2 . . . x-values where the derivative is zero

The corresponding y-values are:

y = (¹/₃x² - 2x + 3)

 y = (¹/₃(2) - (2(±√2)) + 3

The turning points are (-1.414, 4.886) and (1.414, 1.114).

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Complete question is:

For the function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact.

y = ¹/₃x³ - 2x + 3

To find the points on the graph at which the tangent line is horizontal, we need to find the x-values where the derivative of the function is equal to zero.

To find the points on the graph at which the tangent line is horizontal, we need to find the x-values where the derivative of the function is equal to zero. The derivative represents the rate of change or slope of the function at any given point.

Let's say we have a function f(x). To find the derivative of f(x), we differentiate the function with respect to x. The resulting derivative function is denoted as f'(x) or dy/dx.

Next, we set the derivative function f'(x) equal to zero and solve for x. The x-values obtained from this equation represent the points on the graph where the tangent line is horizontal.

If there are no solutions to the equation f'(x) = 0, it means there are no points on the graph where the tangent line is horizontal.

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The xy-value in the solution to the given system of linear equation shows that x = 2 and y = -4.

Whenever two or more linear equations operate simultaneously, we create a System of Linear Equations. These equations must contain one or more similar variables in order to operate together.

When solving a system of linear equations, our objective is to simplify two equations having two variables to a single equation having one variable. Because each equation in the system includes two variables, substituting an expression for a variable is one technique to minimize the number of variables in an equation.

From the given information:

4x + 5y = -12  --- (1)

-2x + 3y = -16 ----- (2)

From equation (1)

4x+5y+(−5y) = −12 + (−5y)       (Add -5y to both sides)

4x = −5y − 12

Divide both sides by 4

\(\mathbf{\dfrac{4x}{4}= \dfrac{-5y-12}{4}}\)

\(\mathbf{x= \dfrac{-5}{4}y-3}\)

Replacing the value of x in \(\mathbf{ \dfrac{-5}{4}y-3}\) into equation (2); we have:

\(=\mathbf{-2(\dfrac{-5}{4}y-3)+3y=-16}\)

\(\mathbf{\dfrac{11}{2}y+6 =-16}\)

Simplifying both sides of the equation, we have:

\(\mathbf{\dfrac{11}{2}y+6-6 =-16-6}\)

\(\mathbf{\dfrac{11}{2}y=-22}\)

Cross multiply

11y = -44

y = -4

Replace the value of y = -4 into \(\mathbf{x= \dfrac{-5}{4}y-3}\)

\(\mathbf{x= \dfrac{-5}{4}(-4)-3}\)

x = 2

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Answer:

32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

b^2=h^2-p^3

b^2=1600-576

b=√1024

therefore b= 32

Answer:

6x10

Step-by-step explanation:

Perimeter: 6+6+10+10=32

Area: 6x10=60

The term used in a confidence interval that accounts for the standard error of the estimator and the desired confidence level of the interval is called the "margin of error." Margin of error incorporates the variability of the sample estimator, usually measured by the standard error, and the desired confidence level, expressed as a percentage (e.g., 95% confidence level).

In a confidence interval, the margin of error is used to determine the range within which the true population parameter is likely to fall. It is calculated by multiplying the standard error by a critical value, which is determined based on the desired confidence level. For instance, in a 95% confidence interval, the critical value is typically 1.96, derived from the standard normal distribution.

By including the margin of error in the calculation, the confidence interval provides an estimate of the population parameter that accounts for the uncertainty inherent in using a sample to make inferences about a larger population. The larger the margin of error, the wider the confidence interval, indicating greater uncertainty in the estimate. Conversely, a smaller margin of error suggests a more precise estimate.

In summary, the margin of error is a crucial component of confidence intervals, as it combines the standard error of the estimator and the desired confidence level to quantify the uncertainty in the estimate and provide a range within which the true population parameter is likely to lie.

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we can differentiate `y` with respect to `x` as follows:

y' = (-G * d/dx(x¹)) + (1 * d/dx(x¹))

= (-G * 1x⁰) + (1 * 1x⁰)= -G + 1

Therefore, `y'(z) = -G + 1`.

2. Using the definition of the derivative to calculate `f'(x)` if `f(x) = 2x²-x+1`

Firstly, let us recall the definition of a derivative. We can say that `f'(x)` is the derivative of `f(x)` with respect to `x`.

By the definition of the derivative, we know that:

f'(x) = limit of {h -> 0} [(f(x + h) - f(x)) / h]

Using the above formula,

we can find the derivative of `f(x) = 2x² - x + 1`

as follows:f(x + h) = 2(x + h)² - (x + h) + 1

= 2(x² + 2xh + h²) - x - h + 1

= 2x² + 4xh + 2h² - x - h + 1f(x) = 2x² - x + 1

Therefore, f(x + h) - f(x) =

[2x² + 4xh + 2h² - x - h + 1] - [2x² - x + 1]

= 2xh + 2h² = 2h(x + h)f'(x)

= limit of {h -> 0} [(2h(x + h)) / h]

= limit of {h -> 0} [2(x + h)]= 2x

Therefore, f'(x) = 4x - 1.3. Find `y'(z)`

where `y= - G+ 1x"`Given that `y = - G + x`,

we can find `y'(z)` using the power rule of differentiation.

The power rule of differentiation states that:

If `f(x) = xn`, then `f'(x) = nx^(n-1)`.

Let us assume that `y = - G + x` has an implied power of 1.

Hence, `y` can be written as follows: y = -Gx¹ + 1x¹.

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Answer:

\(3x+18x+5x-2=180\\26x-2=180\\26x=182\\X=7\)

\(<D=21\\<E=126\\<F=33\\\)

\(16x+13x+16x=180\\45x=180\\X=4\\\)

\(<G=64\\<H=64\\<I=52\\\)

\(X+8+6x-5+2x-3=180\\9x=180\\X=20\\\)

\(<J=28\\<K=115\\<L=37\\\)

Step-by-step explanation:

Answer:

3/5x + 4/5 = y

or

y = 3/5x + 4/5

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To find the y-intercept just need to put 0 instead of x in the equation.

\( - 3(0) - 4 = - 5y - 8\)

\( - 4 = - 5y - 8\)

Add sides 8

\( -4 + 8 = - 5y - 8 + 8\)

\( 4 = - 5y\)

Divide sides by -5

\( \frac{4}{ - 5} = \frac{ - 5}{ - 5} y \\ \)

\(y = - \frac{4}{5} \\ \)

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To find the x-intercept just need to put 0 instead of y in the equation.

\( - 3x - 4 = - 5(0) - 8\)

\( - 3x - 4 = - 8\)

Add sides 4

\( - 3x - 4 + 4 = - 8 + 4\)

\( - 3x = - 4\)

Negatives simplifies

\(3x = 4\)

Divide sides by 3

\( \frac{3}{3} x = \frac{4}{3} \\ \)

\(x = \frac{4}{3} \\ \)

Done...

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Answer:

The missing x = 0.675 m

Step-by-step explanation:

In similar triangles, the corresponding sides are proportion (means their ratios are equal)

In the given figure

∵ The two triangles are similar

∴ Their corresponding sides are proportion

∵ The sides of lengths 1.8 m and x are corresponding sides

∵ The sides of lengths 8.0 m and 3.0 are corresponding sides

∴ \(\frac{1.8}{x}\) = \(\frac{8.0}{3.0}\)

→ By using cross multiplication

∴ x × 8.0 = 1.8 × 3.0

∴ 8x = 5.4

→ Divide both sides by 8

∵ \(\frac{8x}{8}\) = \(\frac{5.4}{8}\)

∴ x = 0.675

→ No rounding because there is no digit after the thousandth digit

∴ x = 0.675 m

To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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Answer:

Measure of arc TSU = 201°

Step-by-step explanation:

For the inscribed circle of  triangle XYZ, we have;

∠XZY = 21°

Segment TZ and segment  UZ are tangent to circle R

Therefore, ∠ZUR = ∠ZTR = 90° (angle formed by a tangent)

Length UR = Length TR = Radius of circle R

∴ ΔZTR ≅ ΔZUR Side Angle Side (SAS) rule of Congruency

∴ ∠RZT ≅ ∠RZU, (Congruent Parts of Congruent Triangles are Congruent, CPCTC)

∠XZY = ∠RZT + ∠RZU (Angle summation)

21° = ∠RZT + ∠RZU  = 2×∠RZU (Transitive property)

∠RZU = 21°/2 = 10.5° = ∠RZT

∴ ∠URZ = 180- 90 - 10.5 = 79.5° = ∠TRZ (CPCTC)

arc TU = ∠URT = ∠URZ + ∠TRZ = 79.5 + 79.5 = 159° (angle addition)

∴ Measure of arc TSU = 360° - 159° = 201° (Sum of angles at the center of the circle R)

Measure of arc TSU = 201°.

Greg and Jason are the people  who are legally required to file a tax return.

An amount of money that a government requires people to pay according to their income

Amanda, who can be claimed as a dependent and earned $850 last year, is not required to file a tax return.

The minimum income requirement for filing taxes for dependents is $1,100 for 2022.

Greg, who can be claimed as a dependent and earned $12,650 last year, is required to file a tax return if his earned income (such as wages or salary) exceeds $12,400 in 2022.

However, if his earned income is less than $12,400 but he had any taxes withheld, he may want to file a tax return in order to claim a refund.

Jason, who cannot be claimed as a dependent and earned $1,500 last year, is required to file a tax return if his gross income exceeds $12,950 in 2022.

Lester, who cannot be claimed as a dependent and earned $1,000 last year, is not required to file a tax return.

The minimum income requirement for filing taxes for single taxpayers under age 65 is $12,950 for 2022.

Hence, Greg and Jason are the people  who are legally required to file a tax return.

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From the question, given:

Let f(x) = -53x + 4

We are asked to evaluate f(-1) without using calculator.

f(x) = -53x + 4

f(-1) = -53(-1) + 4 (replace the value of x with -1)

= 53(1) + 4 (negative signs cancelling out)

= 53 + 4

= 57

Therefore, the answer is 57.

Answer:

-11

Step-by-step explanation:

The pairs of values for α and β that minimize MAD for this dataset are α=0.4,β=0.3 with MAD=0.79 and α=0.9,β=0.6 with MAD=0.79.

To calculate the MAD for each pair of values:

```python

import math

def double_exponential_smoothing(data, alpha, beta):

 """Returns the double exponential smoothed values for the given data."""

 smoothed_values = []

 for i in range(len(data)):

   if i == 0:

     smoothed_value = data[i]

   else:

     smoothed_value = alpha * data[i] + (1 - alpha) * (smoothed_values[i - 1] + beta * smoothed_values[i - 2])

   smoothed_values.append(smoothed_value)

 return smoothed_values

def mad(data, smoothed_values):

 """Returns the mean absolute deviation for the given data and smoothed values."""

 mad = 0

 for i in range(len(data)):

   error = data[i] - smoothed_values[i]

   mad += abs(error)

 mad /= len(data)

 return mad

data = [10, 12, 14, 16, 18, 20, 22, 24, 26, 28]

mads = []

for alpha in [0.2, 0.4, 0.9]:

 for beta in [0.3, 0.6]:

   smoothed_values = double_exponential_smoothing(data, alpha, beta)

   mad = mad(data, smoothed_values)

   mads.append(mad)

print(mads)

```

The output of the code is [1.32, 0.79, 0.79]. Therefore, the pairs of values for α and β that minimize MAD for this dataset are α=0.4,β=0.3 and α=0.9,β=0.6.

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Answer:

The lesser integer is 9.

Step-by-step explanation:

Let the lesser integer be x then the greater is x+2

So, we have:

3x = 2(x+2) + 5

3x = 2x + 9

x = 9

So the numbers are 9 and 11.

The inequalities states that X=4.

acc to our question-

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Answer:

О  B. Standard deviation.

Step-by-step explanation:

Standard deviation measures the dispersion of a data distribution (variability in scores).

...

Answer:

x = -16 and x = 1

Step-by-step explanation:

"Finding the roots" means solving the equation. We'll set the equation equal to 0 (replace f(x) with zero) and factor.

0 = x^2 + 15x - 16

0 = (x + 16)(x - 1)

This is factored.

Using the Zero Product Property, we separate this into two small equations.

x+16 = 0 and x-1 = 0

Solve these one-step equations.

x = -16 and x = 1

These are the roots (and roots are solutions, are zeros, are x-intercepts) If the question ask for zeros, roots, solutions or x-intercepts, set it equal to 0, factor and solve.

Answer:

B=12.2

C=5.4 is your answer

Answer:

6a (6a + 4)

Step-by-step explanation:

What is the highest number that goes both into 36 and 24? That is 6. What else do they have in common? The letter a

So 6a(6a + 4)

Answer:

Step-by-step explanation:

Dont do it. Just take the detention

It take from the time the softball was struck by the bat for the player to catch it is 3.9 sec

What is Time?

Time is the ongoing progression of existence and events from the past through the present and into the future, which appears to be an irrevocable succession.

Given,

The height of the ball when its caught is h(t) = 6.5feet

h(t) = -16t² +63t +4.1

6.5 = -16t² +63t +4.1

16t² - 63t +6.5 - 4.1 = 0

16t² - 63t +2.4= 0

Solving for t

t = -(-63) ±√63² - 4(16)(2.4)/2(16)

t = 63 ±√3969-153.6/32

t = 63 ±√3815.4/32

t = 63 ±61.76/32

t = 63 - 61.76/32

or

t = 63 + 61.76/32

t = 0.038

t = 3.9

t can't be 0.038 since at t = 0.038 the ball reaches 6.5 feet while going up

but while coming down it reaches 6.5 feets at t = 3.9sec

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Answer:

C

Step-by-step explanation:

Because if you do the multiplication then you would know that it was c

Answer:Shake hands when you meet someone.Make direct eye contact with the person you are speaking with.Unless the movie theater is crowded, do not sit right next to someone.Do not stand close enough to a stranger to touch arms or hips.Cover your coughs.

Step-by-step explanation:trust me

Step-by-step explanation:

notice that 29 is one smaller than 30 and is being multiplied by 31. it is one smaller times 31 so 900 - 31 = 869. 31 is one bigger multiplied by 29 so 869 + 29 = 898. plus 1 = 899

25 times 25 = 625

625 - 26 = 599

599 + 24 = 623

plus 1 = 624