The length of a petal on a certain flower varies from 1.96 cm to 5.76 cm and has a probability density function defined by f(x)= the probabilities that the length of a randomly selected petal will be

Answer:

4) 100 ounces

5:

a) 377.6

b) 7.084

c)1,107.6

d) 680.8

6) 8.9207 percent

Answer:

x = 29

Step-by-step explanation:

Sum of interior angles of a triangle = 180°

⇒ 59 + 3x + x + 5 = 180

⇒ 4x + 64 = 180

⇒ 4x = 116

⇒ x = 29

Answer:

C) 29

Step-by-step explanation:

All triangles add up to 180 degrees,

subtract the known 59 from 180 to get 121.

then combine (3x) and (x + 5) to get 4x + 5

4x + 5 = 121 solve

4x = 116

x = 29

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

C

Step-by-step explanation:

Move 2x to the right side of the equation and it becomes -7y= -2x + 24 and then divide by -7 and then it becomes y = 2/7 x -24/7

Answer:

2x - 7y = 24

2x - 24 = 7y

7y = 2x - 24

y = (2x - 24)/7

= 2/7x - 24/7

The chi-square goodness-of-fit test can provide information on categorical data match an expected distribution and which categories are contributing to any deviation from that distribution.

The chi-square goodness-of-fit test is a statistical test used to determine whether a set of observed categorical data matches an expected distribution. Specifically, the test compares the observed frequencies of each category to the expected frequencies based on a hypothesized distribution, and calculates a chi-square statistic. This statistic measures the degree of difference between the observed and expected frequencies, with larger values indicating greater deviation from the expected distribution. If the chi-square statistic is large enough to reject the null hypothesis (i.e., the observed data do not match the expected distribution), the test can provide information on which categories are contributing the most to the discrepancy. This can help identify which categories are over-represented or under-represented in the observed data, and can inform further investigation into potential causes of the deviation. In summary, the chi-square goodness-of-fit test can provide information on whether observed categorical data match an expected distribution and which categories are contributing to any deviation from that distribution.

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Answer:

see explanation

Step-by-step explanation:

The figure has one pair of parallel sides and is a trapezoid.

Each lower base angle is supplementary to the upper base angle on the same side, thus

15x + 30 + 10x = 180 , that is

25x + 30 = 180 ( subtract 30 from both sides )

25x = 150 ( divide both sides by 25 )

x = 6

Also

3y + 18 + 90 = 180 , that is

3y + 108 = 180 ( subtract 108 from both sides )

3y = 72 ( divide both sides by 3 )

y = 24

-------------------------------------------------------------------

2x, 90 and x lie on a straight line and sum to 180 , thus

2x + 90 + x = 180 , that is

3x + 90 = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

------------

2y and x are alternate angles and congruent , thus

2y = x = 30 ( divide both sides by 2 )

y = 15

Answer:

Step-by-step explanation:

I don't think they are. It sounds like a direct proportion to me. The more rice you buy, the higher the cost.

Cost = k * quantity.

That would be the most general formula.

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer:

Option (A) is the answer.

Answer:

A. 115t + 7,600 ≤ 28,000

Step-by-step explanation:

First, you see that the answer to the question has to show that 115t plus or minus 7,600 has to be less than 28,000 because that is how much the neighborhood group has of money to spend. So, that narrows the answers to a or c. The correct answer would be answer A because you need to add 115t and 7,600 because both of those two numbers are the costs for the improvements of the park. Therefore, the correct answer would be A. 115t + 7,600 ≤ 28,000.

Answer:

D

Step-by-step explanation:

The limit of the function 5x⁴ +8x²/3x⁴ -16x² as x approaches 0 is -1/2.

To evaluate the limit of the function 5x⁴ +8x²/3x⁴ -16x², we can start by factoring the numerator and denominator:

[(x²(5x² + 8))/(x²(3x² - 16))]

Next, we can cancel out the common factor of x²:

[(5x² + 8)/(3x² - 16)]

Now we can plug in x = 0 to get:

(5(0)² + 8)/(3(0)² - 16)

= 8/-16

Simplifying this expression, we get:

lim x → 0 [5x⁴ +8x²/3x⁴ -16x²)] = -1/2

Therefore, the limit is equal to -1/2.

When we try to simplify any function or any equation, we get a simplified term which is often a fraction. The elements of a fraction are constituted by numerator and denominator.

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The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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Answer:

4x+148

Step-by-step explanation:

Let the temperature be x and time taken by cricket to chirp be y

if when it is about 68°F, crickets chirp 124 times a minute, this means;

at x1 = 68, y1 = 124

If it is about 80°F, they chirp 172 times a minute, then;

at x2 = 80, y2 = 172

The standard form of equation in point slope form is expressed as;

y-y0 = m(x-x0)

m is the slope

(x0, y0) is a point on the line.

First we need to get the slope.

m = y2-y1/x2-x1

m = 172-124/80-68

m = 48/12

m =4

Substitute m = 4 and any point into the expression above. Using the coordinate (68, 124)

get the intercept c

124 = 4(68) + c

c = 272-124

c = 148

The required equation is expressed as y = 4x+148 OR y - 124 = 4(x-68)

The exponential distribution is a special case of the gamma distribution with alpha = 1, not 0.

False.

The exponential distribution is a special case of the gamma distribution when the shape parameter (alpha) is equal to 1, not 0.

The probability density function (pdf) of the gamma distribution with shape parameter alpha and rate parameter beta is:

f(x) = (1/((beta^alpha)*gamma(alpha))) * (x^(alpha-1)) * (e^(-x/beta))

When alpha = 1, this reduces to the exponential distribution with rate parameter lambda = 1/beta:

f(x) = lambda * e^(-lambda*x)

So the exponential distribution is a special case of the gamma distribution with alpha = 1, not 0.

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Answer:

8:7

8 to 7

8/7

3 ways yep

The propagated absolute uncertainty in F is ±1.

To calculate F, we can use the given values of A, B, C, x, y, and z in the formula:

F = A·z / ((x-y)·B·C)

To propagate the uncertainties in the given values, we can use the formula:

dF = sqrt((∂F/∂A)·dA)² + ((∂F/∂B)·dB)² + ((∂F/∂x)·dx)² + ((∂F/∂y)·dy)² + ((∂F/∂z)·dz)²

where ∂F/∂A, ∂F/∂B, ∂F/∂x, ∂F/∂y, and ∂F/∂z are the partial derivatives of F with respect to A, B, x, y, and z, respectively, and dA, dB, dx, dy, and dz are the uncertainties in A, B, x, y, and z, respectively.

Taking the partial derivatives and plugging in the given values, we get:

∂F/∂A = z / ((x-y)·B·C)

∂F/∂B = -A·z / ((x-y)²·B·C)

∂F/∂x = A·z / ((x-y)²·B·C)

∂F/∂y = -A·z / ((x-y)²·B·C)

∂F/∂z = A / ((x-y)·B·C)

Substituting the given uncertainties, we get:

dF = sqrt((z/(B·C·(x-y)))²·0 + (-A·z/((x-y)²·B·C)²·0.079)² + (A·z/((x-y)²·B·C)²·0.003)² + (-A·z/((x-y)²·B·C)²·0.003)² + (A/((x-y)·B·C)²·0.002)²)

Simplifying and calculating, we get:

dF = 1

Therefore, the propagated absolute uncertainty in F is ±1.

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Answer:

D) 9.8

Step-by-step explanation:

The geometric mean of two numbers x and y is

\(\sqrt{xy}\)

so \(\sqrt{8*12}\) = \(\sqrt{96}\) \(\approx 9.7979\)

Which, since the 9 in the hundredths place is greater than 5, we can round up to 9.8

Answer:

4.

Step-by-step explanation:

(4- 11\2)..here is the help u need

Answer:

it is a whole number, 30. please give me more details if you want it as a mixed number.

Step-by-step explanation:

31+-1 (31-1)= 30

Answer:

zero

Step-by-step explanation:

=================================================

Work Shown:

P( (A u B u C)' ) = 0.33

P(A u B u C) = 1 - P( (A u B u C)' )

P(A u B u C) = 1 - 0.33

P(A u B u C) = 0.67

--------

P(AuBuC) = P(A)+P(B)+P(C)-P(AnB)-P(AnC)-P(BnC)+P(AnBnC)

0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02

0.67 = P(C) + 0.37

P(C) = 0.67 - 0.37

P(C) = 0.30

For more information, search out "inclusion-exclusion principle". Also feel free to ask me if you have any questions.

a) The forecast is approximately miles. b) the Mean Absolute Deviation (MAD) based on the forecast is approximately miles. c) The forecast for year 6 is approximately miles. d) the last forecast is 3,468 miles.

a) To calculate the forecast for year 6 using a 2-year moving average, we take the average of the mileage for years 5 and 4. This provides us with the forecasted value for year 6.

b) The Mean Absolute Deviation (MAD) for the 2-year moving average forecast is calculated by taking the absolute difference between the actual mileage for year 6 and the forecasted value and then finding the average of these differences.

c) When using a weighted 2-year moving average, we assign weights to the most recent and previous periods. The forecast for year 6 is calculated by multiplying the mileage for year 5 by 0.40 and the mileage for year 4 by 0.60, and summing these weighted values.

The MAD for the weighted 2-year moving average forecast is calculated in the same way as in part b, by taking the absolute difference between the actual mileage for year 6 and the weighted forecasted value and finding the average of these differences.

d) Exponential smoothing involves assigning a weight (α) to the most recent forecasted value and adjusting it with the previous actual value. The forecast for year 6 is calculated by adding α times the difference between the actual mileage for year 5 and the previous forecasted value, to the previous forecasted value.

In this case, with α=0.20 and a forecast of 3,100 miles for year 1, we perform this exponential smoothing calculation iteratively for each year until we reach year 6, resulting in the forecasted value of approximately 3,468 miles.

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It will take 10 days for 1023 students to know the secret.

We can start by using the formula for exponential growth: n = 2^k

where n is the number of students who know the secret and k is the number of days.

On Monday, 1 student knew the secret (Jessica). On Tuesday, 2 students knew the secret. On Wednesday, 2 x 2 = 4 students knew the secret. And so on, each day the number of students who know the secret doubles.

We want to find k when n = 1023, so we can solve for k:

1023 = 2^k

log2 1023 = k

k = 10

So, it takes 10 days for 1023 students to know the secret. Since Monday was the first day, the 10th day is 10 days after Monday, which is a Thursday. Therefore, on Thursday, 1023 students will know the secret.

Therefore, It will take 10 days for 1023 students to know the secret.

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It will take 10 days for 1023 students to know the secret.

We can start by using the formula for exponential growth: n = 2^k

where n is the number of students who know the secret and k is the number of days.

On Monday, 1 student knew the secret (Jessica). On Tuesday, 2 students knew the secret. On Wednesday, 2 x 2 = 4 students knew the secret. And so on, each day the number of students who know the secret doubles.

We want to find k when n = 1023, so we can solve for k:

1023 = 2^k

log2 (1023) = k

k = 10

So, it takes 10 days for 1023 students to know the secret. Since Monday was the first day, the 10th day is 10 days after Monday, which is a Thursday. Therefore, on Thursday, 1023 students will know the secret.

Therefore, It will take 10 days for 1023 students to know the secret.

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The given system of equations do not have a solution since their related line equations have the same slope.

The given system of equations is:

-x + 5y = 3   .......... (1)

2x - 10y = 4   ........(2)

In Equation (1), add both sides by (-5y)

-x + 5y + (-5y) = 3 + (-5y)

-x = -3 - 5y

Multiply by (-1)

x = 3 + 5y

Substitute x = 3 + 5y into equation (2)

2x - 10y = 4

2.(3 + 5y) - 10y = 4

6 + 10y - 10y = 4

6 = 4 (False)

Since the last equation is false, we might suspect that the given system of solution does not have solutions.

We need to check the slope of both equations:

-x + 5y = 3

⇒ 5y = x + 3

⇒ y = 1/5 x + 3/5

2x - 10y = 4

⇒ -10 y = -2x + 4

⇒ y = (2/10) x - 4/10

⇒ y = 1/5 x - 2/5

We can see that both equations have the same slope, i.e. 1/5.

Hence, they do not have solutions since the lines are parallel to each other.

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Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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Answer:

Ryan sold 12 cell phones

Step-by-step explanation:

2000+15x12

The factor that does NOT control the stability of a slope is the angle of repose for intact bedrock. The angle of repose refers to the steepest angle at which a pile of loose material remains stable without sliding. It is mainly applicable to loose materials like soil and granular substances, not intact bedrock.

Bedrock stability depends on factors such as its strength, fracturing, and geological properties, rather than the angle of repose. Factors that control the stability of a slope include whether the slope is rock or soil. Rock slopes tend to be more stable than soil slopes due to the cohesive nature of intact rock.

The amount of water in the soil also affects slope stability, as excessive water can increase pore pressure and reduce the shear strength of the soil, leading to slope failure. Additionally, the orientation of fractures, cleavage, and bedding in the rock can influence slope stability by creating planes of weakness or strength.

To summarize, while the angle of repose is a significant factor in slope stability, it is not applicable to intact bedrock. The stability of a slope is influenced by the type of material (rock or soil), the presence of water, and the orientation of fractures and bedding.

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