Use the normal approximation to find the indicated probability. the sample size is n, the population proportion of successes is p, and x is the number of successes in the sample.
n = 81, p = 0.5: p(x ≥ 46)
group of answer choices

0.1210

0.1335

0.8790

0.1446

As per the differential equation, the value of k for which the constant function is 1.

The term called differential equation in math is defined as an equation which contains one or more terms and the derivatives of one variable

Here we know that the differential equation is

=> 4t³ dx/dt + 2x - 2 = 0

Here we have also know that x(t) = k is a solution of the differential equation.

Which means the t the value of x' = 0.

Then the value of 4t³ dx/dt = 0.

So, here we have rewritten the equation like the following,

=> 0 + 2x - 2 = 0

Here we know that the value of x = k, then we get the equation like the following,

=> 2k - 2 = 0

=> k = 1

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Answer:  1 1/4

Step-by-step explanation:

the heaviest bunch of grapes weights 1 7/8 pounds

A line plot labeled 0 to 2 with tick marks every one-eighth unit. Above the tick mark at five-eighths is one dark blue dot. Above the tick mark for six-eighths is a column of two light blue dots. Above the tick mark at 1 there is a column of three light blue dots. Above the tick mark at one and four-eighths is a column of two light blue dots. Above the tick mark for one and five-eighths is a column of four light blue dots. Above the tick mark for one and seven-eighths is one light blue dot.

The probability of x taking on a value between 75 to 90 is 0.25.

Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.

The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.

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Answer:

...what's the question you want answered?

Answer:

what is the question?

Step-by-step explanation:

Answer:

f= d/ 1+x

Step-by-step explanation:

Answer:

  f = d/(x+1)

Step-by-step explanation:

Factor out f, then divide by its coefficient.

  \(d=f+fx\\\\d=f(1+x)\\\\\dfrac{d}{1+x}=f\\\\\boxed{f=\dfrac{d}{x+1}}\)

_____

Additional comment

When writing this in plain text, parentheses are needed to perform the same grouping action that the fraction bar performs in a typeset expression:

  f = d/(x+1)

Answer:

1st pic: straight for both boxes

2nd pic: constant for both boxes

3rd pic: exponent (I think)

4th pic: (from left to right, top row then bottom row) linear, non linear, linear, non linear, linear, linear, non linear, non linear

Step-by-step explanation:

Please give brainliest :)

Hope it helps!

As t increases the curve is changing according to the plot points given by the parametric equations.

The coordinates of the points that make up a geometric object, such as a curve or surface, are frequently expressed using parametric equations; in this case, the equations are collectively referred to as a parametric representation or parameterization (alternatively spelled as parametrisation) of the object. It describes a collection of numbers that represent functions with one or more independent variables. The parameters used here are the independent variables. For the representation of the coordinates that make up geometric objects like curves and surfaces, parametric equations are used. Additionally, a curve that is not a function can be drawn using parametric equations.

The equations are

x=1-t²

y=2t-t²,-1≤t≤2

The sketch is in the diagram picture.

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Answer:

Step-by-step explanation:

All the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

To formulate the problem as a linear optimization problem (LO), we can introduce slack variables to represent the signed distances of the points from the plane αTx = β. Let's denote the slack variables as y_i for points in S1 and z_i for points in S2.

1.1 Formulation:

The problem can be formulated as follows:

Minimize: 0 (since it is a feasibility problem)

Subject to:

α1x1 + α2x2 + α3x3 + α4x4 - β ≥ 1 for (x1, x2, x3, x4) in S1

α1x1 + α2x2 + α3x3 + α4x4 - β ≤ -1 for (x1, x2, x3, x4) in S2

α1, α2, α3, α4 are unrestricted

β is unrestricted

y_i ≥ 0 for all points in S1

z_i ≥ 0 for all points in S2

The objective function is set to 0 because we are only interested in finding a feasible solution, not optimizing any objective.

1.2 Finding a feasible solution:

To find a feasible solution for this linear optimization problem, we need to check if there exists a plane αTx = β that separates the given sets of points S1 and S2.

Let's set α = (1, 0, 0, 0) and β = 0. We choose α to have a non-zero value for the first component to satisfy α ≠ (0, 0, 0, 0) as required.

For S1:

(1, 2, 1, -1) - 0 = 3 ≥ 1, feasible

(3, 1, -3, 0) - 0 = 4 ≥ 1, feasible

(2, -1, -2, 1) - 0 = 0 ≥ 1, not feasible

(7, -2, -2, -2) - 0 = 3 ≥ 1, feasible

For S2:

(1, -2, 3, 2) - 0 = 4 ≥ 1, feasible

(-2, π, 2, 0) - 0 = -2 ≤ -1, feasible

(4, 1, 2, -π) - 0 = 5 ≥ 1, feasible

(1, 1, 1, 1) - 0 = 4 ≥ 1, feasible

Since all the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.

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Answer:

its c, 25e11

Step-by-step explanation:

Answer:

2(2x+15)

Step-by-step explanation:

x+(x+30)+2x=

=3x+(x+30)=

=3x+x+30=

=4x+30=

=2(2x+15)

Answer:

D

Step-by-step explanation:

4C1*5C1*6C1*8C1

=960

Answer:

12 1/3 years

Step-by-step explanation:

Let

x = his son's age

Grandpa Burk's age = 52 + x

In five years Grandpa Burk will be four Times as old as his grandson is now.

his son's age = 4(x + 5)

Grandpa Burk's age = 52 + x + 5

= x + 57

4(x + 5) = x + 57

4x + 20 = x + 57

4x - x = 57 - 20

3x = 37

x = 37 / 3

= 12 1/3 years

His son's age will be 12 1/3 years

We find that it takes approximately 47 months to recover the initial investment.

To calculate the time it takes to recover the initial investment on a monthly basis, we need to consider the savings in fuel costs and the cost of funds over time.

First, let's calculate the monthly savings in fuel costs by subtracting the average natural gas cost from the fuel oil cost:

Savings in fuel costs = Fuel oil cost - Natural gas cost

= $145 - $60

= $85

Next, let's calculate the present value of the savings in fuel costs over the recovery period. Since the savings occur monthly, we can use the formula for the present value of an annuity:

Present value of savings = Savings in fuel costs * (1 - (1 + interest rate)^(-n)) / interest rate

Where:

Savings in fuel costs is $85 per month

Interest rate is 9% per year, which is 0.75% per month

n is the number of months it takes to recover the initial investment

Now, let's calculate the present value of the savings using the given values:

Present value of savings = $85 * (1 - (1 + 0.0075)^(-n)) / 0.0075

Next, let's calculate the present value of the initial investment using the formula for present value:

Present value of initial investment = Initial investment / (1 + interest rate)^n

Where:

Initial investment is $2500

Interest rate is 9% per year, which is 0.75% per month

n is the number of months it takes to recover the initial investment

Now, let's calculate the present value of the initial investment using the given values:

Present value of initial investment = $2500 / (1 + 0.0075)^n

To recover the initial investment, the present value of savings must equal the present value of the initial investment:

$85 * (1 - (1 + 0.0075)^(-n)) / 0.0075 = $2500 / (1 + 0.0075)^n

To solve for n, we can rearrange the equation and solve for n using trial and error or by using numerical methods.

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The mean class size at Mountain View School is 4.4 and at Seaside School is 4.2.

The median class size is 5 for both schools.

The range for Mountain View School is 12 and for Seaside School is 8.

The IQR for Mountain View School is 6 and for Seaside School is 3.

To find the measures of center, we can calculate the mean and median for both schools.

Mountain View School:

Mean = (2+1+0+5+8+6+9+8+2+0+1+0+6)/15

Mean = 4.4

Median = 5

Seaside School:

Mean = (0+1+2+5+6+8+8+7+6+5+5+4+4+3+1+0)/15

Mean = 4.2

Median = 5

Part B:

To find the measures of variability, we can calculate the range and interquartile range (IQR) for both schools.

Mountain View School:

Range = largest value - smallest value = 12 - 0

Range = 12

IQR = Q3 - Q1 = 8 - 2 = 6

Seaside School:

Range = largest value - smallest value = 8 - 0

Range = 8

IQR = Q3 - Q1 = 7 - 4 = 3

Part C:

If we are interested in a smaller class size, Seaside School would be the better choice. The median class size is the same at both schools, but Seaside School has a smaller mean, which suggests that on average, class sizes are smaller.

Additionally, the range and IQR are both smaller for Seaside School, indicating less variability in class size.

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Answer:

3. p ≥ 15

Step-by-step explanation:

When there is an "at least" we can say that the sign relating p and 15 has to have an underline since p can be equal to 15. And, also, it implies that p is greater. When we put this together, we get:

p ≥ 15

9514 1404 393

Answer:

  (b)  a trapezoid

Step-by-step explanation:

A graph of the points reveals one pair of parallel sides: a trapezoid.

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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Answer:

3

Step-by-step explanation:

\(-2(-2)^3 - 3(-2)^2 + 4(-2) + 7\\= -2(-8) - 3(4) - 8 + 7\\= 16 - 12 - 8 + 7\\ = 3\)

Answer:

(x + 7)² = 0

Step-by-step explanation:

Given

x² + 14x + 49 = 0 ( subtract 49 from both sides )

x² + 14x = - 49

To complete the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(7)x + 49 = - 49 + 49

(x + 7)² = 0

Answer:

The number of different committees can be  formed = 55.

Step-by-step explanation:

On solving the provided question, we can say that - here in graph Between the lowest number, which is 0, and the highest value, which is 5, there is a range. The range is therefore -9=y=5.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

There is a range between the minimum value, which is 0, and the greatest value, which is 5. Thus, the range is -9=y=5.

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Answer:

p-6

Step-by-step explanation:

You just balance the equation by putting the variable equations on the first side, and the equation on the other side. Simple!

Answer:

p-6

Step-by-step explanation:

You just balance the equation by putting the variable equations on the first side, and the equation on the other side. Simple!

Answer:

11) 1 3/8

12) 17/18

Step-by-step explanation:

Answer:

skp

Step-by-step explanation:

Answer:

3x - 2y = 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (4, 5) ← 2 points on the line

m = \(\frac{5-2}{4-2}\) = \(\frac{3}{2}\) , then

y = \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, 2 )

2 = \(\frac{3}{2}\) (2) + c = 3 + c ( subtract 3 from both sides )

- 1 = c

y = \(\frac{3}{2}\) x - 1 ← equation in slope- intercept form

multiply through by 2 to clear the fraction

2y = 3x - 2 ( subtract 3x from both sides )

- 3x + 2y = - 2 ( multiply through by - 1 )

3x - 2y = 2  ← in standard form

solution 1:

\(\rightarrow \sf 7 * 3\dfrac{1}{5}\)

\(\rightarrow \sf 7 * \dfrac{16}{5}\)

\(\rightarrow \sf \dfrac{112}{5}\)

\(\rightarrow \sf 22\dfrac{2}{5}\)

solution 2:

\(\rightarrow \sf 5\dfrac{4}{10}*2\)

\(\rightarrow \sf \dfrac{54}{10}*2\)

\(\rightarrow \sf \dfrac{108}{10}\)

\(\rightarrow \sf 10\dfrac{8}{10}\)

The height in feet of the tree is 111.5 ft.

The height of a house is 52 ft.

A tree beside the house is 7.5 ft more than twice as tall.

The height of the tree is as follows:

let

x = height of the house

Therefore,

The height of the house = x = 52 ft

Hence,

height of the tree = 7.5 + 2x

height of the tree = 7.5 + 2(52)

height of the tree = 7.5 + 104

height of the tree = 111.5

height of the tree = 111.5 ft

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The critical value for this test, at the specified significance level, would be approximately 1.96.

To find the critical value for the given test, we need to conduct a hypothesis test to compare the proportions of two populations. The claim is not specified in the question, so we will assume it is a claim about the difference between the two proportions.

The null hypothesis (H₀) would state that there is no difference between the proportions, while the alternative hypothesis (H₁) would claim that there is a significant difference.

Let's denote the sample proportion of the first population as p₁ = 0.933 (93.3%) with a sample size of n₁, and the sample proportion of the second population as p₂ = 0.916 (91.6%) with a sample size of n₂.

To find the critical value, we first calculate the test statistic z using the formula:

z = \((p₁ - p₂) / √[(p₁(1 - p₁) / n₁) + (p₂(1 - p₂) / n₂)]\)

Given that we are not using the continuity correction and are approximating the binomial distribution with a normal distribution, we can use the standard normal distribution to find the critical value.

Using a significance level of α (which is missing in the question), we can look up the critical value in the standard normal distribution table or use a calculator.

For example, if α = 0.05 (5% significance level), we find the critical value zₐ/₂ = 1.96 (rounded to three decimal places).

The critical value for this test, at the specified significance level, would be approximately 1.96.

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