One house key weighs 1/2
ounce.
Which model represents the total weight in ounces of 5 house keys?

Answer: .67

Step-by-step explanation:

got it right on acellus

Answer:

8.98 * 10^6 is the scientific notation

Step-by-step explanation:

The expression [tex]x^{2}[/tex] + 6x + 5 can be completed by transforming it into the form a(x - h)^2 + k.

To complete the square, we want to rewrite the quadratic expression x^2 + 6x + 5 in a perfect square trinomial form. We can achieve this by adding and subtracting a constant term inside the parentheses.

Starting with the given expression: x^2 + 6x + 5

To complete the square, we need to take half of the coefficient of x and square it. Half of 6 is 3, and squaring 3 gives us 9. So, we add and subtract 9 inside the parentheses:

x^2 + 6x + 5 = (x^2 + 6x + 9 - 9) + 5

Now, we can group the first three terms as a perfect square trinomial and simplify:

(x^2 + 6x + 9 - 9) + 5 = (x + 3)^2 - 9 + 5

Simplifying further, we have:

(x + 3)^2 - 4

Therefore, the expression x^2 + 6x + 5 can be written in the form a(x - h)^2 + k as (x + 3)^2 - 4.

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Answer:

12^3

Step-by-step explanation:

Answer:

12 ^3

Step-by-step explanation:

Answer:  

588245.  

Step-by-step explanation:  

nth term = an = a1 r^(n-1)   where a1 = the first term  

a3 = 35 = a1  7^(3 - 1)  

35 = a1* 49  

a1 = 35/49 = 5/7  

So the 8th term = (5/7)* (7)^7

= 588245

Answer:

Let X be the random variable representing the amount of beer poured by the filling machine. Since X follows a normal distribution with mean μ = 12.10 and standard deviation σ = 0.05, we can use the standard normal distribution to find the probability that a bottle contains between 12.00 and 12.06 ounces.

First, we need to standardize the values 12.00 and 12.06 by subtracting the mean and dividing by the standard deviation:

z1 = (12.00 - 12.10) / 0.05 = -2 z2 = (12.06 - 12.10) / 0.05 = -0.8

Now we can use a standard normal distribution table to find the probability that a standard normal random variable Z is between -2 and -0.8:

P(-2 < Z < -0.8) = P(Z < -0.8) - P(Z < -2) ≈ 0.2119 - 0.0228 ≈ 0.1891

So, the probability that a bottle contains between 12.00 and 12.06 ounces of beer is approximately 0.1891.

Step-by-step explanation:

Step-by-step explanation:

54, 54, 72

[tex]180 - 2 \times 54 = \\ = 180 - 108 = \\ = 72[/tex]

Answer:

17÷z = quotient

Step-by-step explanation:

quotient = ÷

Answer:

The unbrella is 13.5 feet tall.

Step-by-step explanation:

35 / 28 = 1.25

1.25x = 16 7/8

x = (16 7/8) / 1.25

x = 13.5 ft

The partial derivatives are as follows :

(a) fx = 1 / (x + 2y^2 + 3z^3)

(b) fz = 3z^2 / (x + 2y^2 + 3z^3)

(c) d^2f/dzdx = -3z^2 / (x + 2y^2 + 3z^3)^2

To find the partial derivatives of the function f(x, y, z) = ln(x + 2y^2 + 3z^3), we differentiate with respect to each variable while treating the other variables as constants.

(a) Partial derivative with respect to x (fx):

To find fx, we differentiate the function f(x, y, z) with respect to x while treating y and z as constants. The derivative of ln(u) with respect to u is 1/u, so we have:

fx = d/dx ln(x + 2y^2 + 3z^3) = 1 / (x + 2y^2 + 3z^3)

(b) Partial derivative with respect to z (fz):

To find fz, we differentiate the function f(x, y, z) with respect to z while treating x and y as constants. Again, applying the derivative of ln(u), we get:

fz = d/dz ln(x + 2y^2 + 3z^3) = 3z^2 / (x + 2y^2 + 3z^3)

(c) Second partial derivative with respect to z and x (d^2f/dzdx):

To find d^2f/dzdx, we differentiate fz with respect to x while treating y and z as constants. We differentiate fx with respect to z while treating x and y as constants, and then take the derivative of the result with respect to z. It can be written as:

d^2f/dzdx = d/dx (d/dz ln(x + 2y^2 + 3z^3)) = d/dx (3z^2 / (x + 2y^2 + 3z^3))

= -3z^2 / (x + 2y^2 + 3z^3)^2

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The dimensions of the rectangle are length = 62.75 inches and width = 20.25 inches.

The given problem states that the length of a rectangle is two more than triple the width.

If the perimeter is 166 inches, what are the dimensions of the rectangle? Let's solve the problem,

Step 1

Given, The length of the rectangle = l

Width of the rectangle = w

The perimeter of the rectangle = 166 inches

The formula for the perimeter of a rectangle is,

Perimeter = 2(l + w)

So, 166 = 2(l + w)166/2 = l + w83 = l + w ----(1)

Step 2

According to the given problem, The length of a rectangle is two more than triple the width

Therefore,

l = 2 + 3w

Substitute this value in equation (1)

83 = (2 + 3w) + w

83 = 2 + 4w

83 - 2 = 4w

81 = 4w

w = 81/4

w = 20.25 (approx)

Step 3

We have width w = 20.25 inches.

We can find the length l by substituting w in l = 2 + 3w

So,

l = 2 + 3(20.25)

= 2 + 60.75

= 62.75

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Answer:

-1/3x + 5 = y

Step-by-step explanation:

Answer:

x = 5

x = 6

x = 10

Step-by-step explanation:

NOTE: IT HAS TO BE MORE THAN 5 OR EQUAL TO 5

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Answer: 52.7856cm

Step-by-step explanation:

Circumference of a circle = 2πr

Note that radius = Diameter / 2 = 16.8/2 = 8.4cm

Circumference = 2πr

= 2 × 3.142 × 8.4

= 52.7856cm

Therefore, the circumference of the circle is 52.7856cm

Answer:

just did it on edg, 2021

Hence, AB≈CD and BC ≈ DA

What is a parallelogram?

A four sided closed figure with all its sides parallel to its opposite side.

Consider two triangles ΔABD and ΔBCD

∠BCD=∠BCA( opposite angles are always equal)

∠ABD=∠BDC (AD||BC)

∠ADB=∠DBC(AD||BC)

ΔABD ≅ ΔBCD

AB≈CD by CPCTC

BC ≈ DA by CPCTC

Hence, proved

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The z-score to test the hypothesis that the part is coming out longer than usual is approximately 1.61.

Sample mean = x = 12.20 cm

Population mean = μ = 12.05 cm

Standard deviation = σ = 0.350 cm

Sample size = n = 14

A hypothesis is an informed prediction regarding the solution to a scientific topic that is supported by sound reasoning. there is the expected result of the experimentation even if there is not proved in an experiment.

Calculating the z-score -

[tex]z = (x - u) / (\alpha / \sqrt n)[/tex]

Substituting the values -

[tex]z = (12.20 - 12.05) / (0.350 / \sqrt{14)[/tex]

= z = 0.15 / (0.350 / √14)

= 0.093

Substituting the value again into the formula:

z = 0.15 / 0.093

= 1.61

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The correct answer is D to identify the problem.

What is the decision-making process?

The decision-making process is the method by which a judgment or a decision is reached. It involves identifying the problem or decision to be made, analyzing potential courses of action, evaluating alternatives, and selecting the best possible solution.

It's a structured process that assists in making effective decisions, and it can be useful in both personal and professional contexts. What is the first step in the decision-making process?

The first step in the decision-making process is to identify the problem. This entails defining the issue that requires a decision to be made. It's a crucial step because without accurately identifying the issue or problem, it's impossible to make the best decision.

Analyzing the problem and its causes (A), generating alternatives (B), and soliciting and analyzing feedback (C) are all critical components of the decision-making process, but they come after the problem has been identified.

As a result, option D, identifying the problem, is the first step in the decision-making process.

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The solution of the initial-value problem is:

y(t) = C1e^(-4t) + C2e^(4t) + Y(t)

where C1 and C2 are constants determined by the initial conditions, and Y(t) is the particular solution given by the formula provided.

To find the solution of the initial-value problem, we can use the given fundamental set of solutions of the homogeneous equation and the particular solution.

The fundamental set of solutions is y1(t) = e^at, where a = -4 and y2(t) = e^bt, where b = 4.

The particular solution is Y(t) = ds-y1(t) to + y2(t) • y3(t), where y3(t) is another function that satisfies the non-homogeneous equation.

Combining the solutions, the general solution of the non-homogeneous equation is y(t) = C1e^(-4t) + C2e^(4t) + Y(t), where C1 and C2 are constants

To determine the specific solution, we need to use the initial conditions. Given y(0) = 2, y'(0) = 2, and y''(0) = 88, we can substitute these values into the general solution and solve for the constants C1 and C2.

Finally, the solution of the initial-value problem is y(t) = C1e^(-4t) + C2e^(4t) + Y(t), where C1 and C2 are the constants determined from the initial conditions and Y(t) is the particular solution.

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The explicit formula for the beetle population after n weeks can be determined using the given data. The formula is Pn = 4 + (n - 0) * ((67 - 4) / (7 - 0)), where Pn represents the population after n weeks. It will take 28 weeks for the beetle population to reach 256.

The linear growth model assumes that the beetle population increases by a fixed amount each week. To find the explicit formula, we start by calculating the growth rate per week. We know that in 7 weeks, the population increased from 4 to 67. The change in population is 67 - 4 = 63, and the change in weeks is 7 - 0 = 7. Therefore, the growth rate per week is (67 - 4) / (7 - 0) = 9.

Using this growth rate, we can express the population after n weeks using the formula Pn = 4 + (n - 0) * 9. This simplifies to Pn = 4 + 9n. Now, to determine how many weeks it takes for the population to reach 256, we substitute Pn = 256 into the formula. Solving for n, we get 256 = 4 + 9n. By rearranging the equation, we find 9n = 252, and dividing both sides by 9 yields n = 28. Therefore, it will take 28 weeks for the beetle population to reach 256.

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Answer:

Step-by-step explanation:

(-1,-9)

To solve the given differential equation:

y(ln(x) - ln(y)) dx = (x ln(x) - x ln(y) - y) dy

We can start by rearranging the terms:

y ln(x) dx - y ln(y) dx = x ln(x) dy - x ln(y) dy - y dy

Next, we can integrate both sides of the equation:

∫ y ln(x) dx - ∫ y ln(y) dx = ∫ x ln(x) dy - ∫ x ln(y) dy - ∫ y dy

To integrate the left-hand side, we can use integration by parts. Let's denote u = ln(x) and dv = y dx. Then, du = (1/x) dx and v = xy. Applying integration by parts, we have:

∫ y ln(x) dx = xy ln(x) - ∫ (1/x)(xy) dx

= xy ln(x) - ∫ y dx

= xy ln(x) - yx + C1

where C1 is the constant of integration.

Similarly, integrating the other terms:

∫ y ln(y) dx = xy ln(y) - yx + C2

∫ x ln(x) dy = (x^2 ln(x))/2 - ∫ (x^2)(1/x) dy

= (x^2 ln(x))/2 - ∫ x dy

= (x^2 ln(x))/2 - (x^2)/2 + C3

∫ x ln(y) dy = (x^2 ln(y))/2 - ∫ (x^2)(1/y) dy

= (x^2 ln(y))/2 - ∫ (x^2/y) dy

= (x^2 ln(y))/2 - x^2 ln(y) + ∫ x dy

= (x^2 ln(y))/2 - x^2 ln(y) + (x^2)/2 + C4

∫ y dy = (y^2)/2 + C5

Substituting these results back into the original equation:

xy ln(x) - yx + C1 - xy ln(y) + yx - C2 = (x^2 ln(x))/2 - (x^2)/2 + C3 - (x^2 ln(y))/2 + x^2 ln(y) - (x^2)/2 + C4 - (y^2)/2 - C5

Simplifying:

xy ln(x) - xy ln(y) = (x^2 ln(x))/2 - (x^2 ln(y))/2 - (y^2)/2 + C

where C = C1 - C2 + C3 + C4 - C5.

We can further simplify this equation:

xy (ln(x) - ln(y)) = (x^2 ln(x) - x^2 ln(y) - y^2)/2 + C

Finally, dividing both sides by (ln(x) - ln(y)), we get:

xy = (x^2 ln(x) - x^2 ln(y) - y^2)/(2(ln(x) - ln(y))) + C

This is the general solution to the given differential equation.

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The charge on the capacitor at time t is given by Q(t) = 6C - 6C * e^(-t/2)---- Eqn. (1) and the current at time t is given by I(t) = 3A * e^(-t/2) --- Eqn. (2).

R(dQ/dt) + (1/C)Q = E(t)

The general solution of the above equation (when E(t) is a constant E) is:

Q(t) = CE + (Q(0) - CE)e^(-t/RC)

Plugging in the given values:

Q(t) = 0.1F * 60V + (0C - 0.1F * 60V)e^(-t/(20Ω * 0.1F))

Simplify this to get:

Q(t) = 6C - 6C * e^(-t/2)      Eqn. (1)

The current is the derivative of the charge with respect to time:

I(t) = dQ(t)/dt = d/dt [6C - 6C * e^(-t/2)]

Taking the derivative and simplifying gives:

I(t) = 3A * e^(-t/2)     Eqn. (2)

So the charge on the capacitor at time t is given by Eqn. (1) and the current at time t is given by Eqn. (2).

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Answer:

77 meters

Step-by-step explanation:

For a right triangle, the formula for side length is

a^2 + b^2 = c^2 where c is the hypotenuse (opposite the right angle)

36^2 + b^2 = 85^2

1296 + b^2 = 7225

b^2 = 5,929

find the square root of both sides:

b = 77

Please let me know if you have questions.

The equation of the regression line for the relationship between job performance (X) and attitude ratings (Y) is Y = 57.124 + 0.352X.

To find the equation of the regression line, we will use a technique called simple linear regression. This method allows us to model the relationship between two variables using a straight line equation. In our case, the variables are job performance (denoted as Perf) and attitude ratings (denoted as Att).

The equation of a regression line is typically represented as: Y = a + bX

To find the equation of the regression line, we need to calculate the values of 'a' and 'b' using the given data points. Let's go step by step:

Mean of Perf (X): (59 + 63 + 65 + 69 + 58 + 77 + 76 + 69 + 70 + 64) / 10 = 66.0

Mean of Att (Y): (75 + 64 + 81 + 79 + 78 + 84 + 95 + 80 + 91 + 75) / 10 = 80.2

Perf differences:

(59 - 66.0), (63 - 66.0), (65 - 66.0), (69 - 66.0), (58 - 66.0), (77 - 66.0), (76 - 66.0), (69 - 66.0), (70 - 66.0), (64 - 66.0)

Att differences:

(75 - 80.2), (64 - 80.2), (81 - 80.2), (79 - 80.2), (78 - 80.2), (84 - 80.2), (95 - 80.2), (80 - 80.2), (91 - 80.2), (75 - 80.2)

Squared Perf differences:

(-7)², (-3)², (-1)², (3)², (-8)², (11)², (10)², (3)², (4)², (-2)²

Squared Att differences:

(-5.2)², (-16.2)², (0.8)², (-1.2)², (-2.2)², (3.8)², (14.8)², (-0.2)², (10.8)², (-5.2)²

Step 3: Calculate the sum of the squared Perf differences and the sum of the squared Att differences.

Sum of squared Perf differences:

7² + 3² + 1² + 3² + 8² + 11² + 10² + 3² + 4² + 2² = 369

Sum of squared Att differences:

5.2² + 16.2² + 0.8² + 1.2² + 2.2² + 3.8² + 14.8² + 0.2² + 10.8² + 5.2² = 734.72

Sum of Perf differences multiplied by Att differences:

(-7)(-5.2) + (-3)(-16.2) + (-1)(0.8) + (3)(-1.2) + (-8)(-2.2) + (11)(3.8) + (10)(14.8) + (3)(-0.2) + (4)(10.8) + (-2)(-5.2) = 129.8

Calculate the slope (b) using the following formula:

b = sum of Perf differences multiplied by Att differences / sum of squared Perf differences

b = 129.8 / 369 = 0.352

a = Mean of Att (Y) - b * Mean of Perf (X)

a = 80.2 - 0.352 * 66.0 = 57.124

Y = a + bX

Y = 57.124 + 0.352X

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The correct answer is D. 68 inches. The trend line equation y = x + 2 indicates that there is a linear relationship between height and arm span. The coefficient of 1 on x suggests that, on average, for every increase of 1 inch in height, the arm span increases by 1 inch as well.

The intercept of 2 indicates that even at a height of 0 inches, there is a minimum arm span of 2 inches. By substituting the given height value into the equation, we can accurately predict the corresponding arm span

The equation of the trend line given is y = x + 2, where y represents the arm span and x represents the height of the players. We need to predict the arm span for a player who is 66 inches tall.

To make the prediction, we substitute x = 66 into the equation and solve for y:

y = 66 + 2

y = 68

Therefore, the predicted arm span for a player who is 66 inches tall is 68 inches.

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Answer:

A

Step-by-step explanation:

Answer:

the one that is a horizontal straight line on x axis that lies on 2