22. (6 points) The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. a) If a student is randomly selected, what is the probability that the student completes the exam in less than 45 minutes? b) How much time should be given to complete the exam so 80% of the students will complete the exam in the time given?

Answer:

16cm

Step-by-step explanation:

The answer to this question is 16cm

(a) The type of indeterminate form obtained by direct substitution is "0/0" since plugging in 0 for x gives ln(0) which is undefined.

Direct substitution is a method used in mathematics to evaluate a function at a specific value by substituting that value directly into the function expression.

To use direct substitution, you simply replace the variable in the function expression with the given value and compute the result. This method is applicable when the function is defined and continuous at the given value.

(b) We can use L'Hôpital's Rule to evaluate the limit. Taking the derivative of both the numerator and denominator, we get limit evaluates to INFINITY.

The rule states that if the limit of the ratio of two functions, f(x)/g(x), as x approaches a certain value, is of the form 0/0 or ∞/∞, and the derivatives of both functions f'(x) and g'(x) exist and satisfy certain conditions, then the limit of the ratio can be found by taking the derivative of the numerator and the derivative of the denominator separately and then evaluating the resulting ratio.

lim x [In(x)] = lim x [1/x] (by the derivative of ln(x) = 1/x)
x→0+

Now, plugging in 0 for x, we get:

lim x [1/x] = INFINITY
x→0+

Therefore, the limit evaluates to INFINITY.

(c) Using a graphing utility (such as Desmos), we can graph the function y = ln(x) and see that as x approaches 0 from the right, the y-values increase without bound, confirming our result from part .

(b). The graph also shows that ln(x) is undefined for x <= 0.

            |

          5 |       /

            |     /

            |   /  

          2 | /    

            |      

            |      

         -5 |      

            |      

            |      

       -10  |      

            |

            |

       -15  |_______

            -10 -5 0 5 10

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The directional derivative of a function f(x, y) at a point (a, b) in the direction of a unit vector u = ⟨cosθ, sinθ⟩ is given by the dot product of the gradient of f at (a, b) and the unit vector u.

That is, D_uf(a, b) = ∇f(a, b) · u

Here, f(x, y) = xy^3 - x^2, so ∇f(x, y)

= ⟨y^3 - 2x, 3xy^2⟩.

At the point (1, 4), we have ∇f(1, 4) = ⟨60, 192⟩.

The direction indicated by the angle theta = π/3 is u = ⟨cos(π/3), sin(π/3)⟩ = ⟨1/2, √3/2⟩.

Therefore, the directional derivative of f at (1, 4) in the direction of u is:

D_uf(1, 4) = ∇f(1, 4) · u

= ⟨60, 192⟩ · ⟨1/2, √3/2⟩

= 60/2 + 192(√3/2)

= 30 + 96√3

So the directional derivative of f at (1, 4) in the direction of θ = π/3 is 30 + 96√3.

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Answer: A. 83.7

Step-by-step explanation:

Answer:

a) 83.7

Step-by-step explanation:

Q) 18.6 × 4.5 = ?

→ 18.6 × 4.5

→ 83.7

So, option (a) is correct.

Answer:

y=5x-3

Step-by-step explanation:

y-intercept is always at the end

so it is y=mx-3

gradient replaces m

y=5x-3

For a sample size of 150 employees, the mean wage per hour (μx) is expected to be RM14.50, the same as the population mean. The standard deviation of the mean wage (σx) is approximately RM0.122.

The mean wage for a random sample of 150 employees can be considered an estimate of the population mean wage. The mean of the sample, denoted by μx, is expected to be approximately equal to the population mean, which is RM14.50 per hour. Therefore, the mean of x is also RM14.50 per hour.

To calculate the standard deviation of x for a sample size of 150, we use the formula for the standard error of the mean (SE):

SE = σ / √n

Where σ is the population standard deviation and n is the sample size. In this case, the population standard deviation is RM1.50 per hour and the sample size is 150. Plugging these values into the formula, we get:

SE = 1.50 / √150

Calculating this, we find:

SE ≈ 0.122

The standard deviation of x, denoted by σx, is equal to the standard error of the mean. Therefore, σx ≈ 0.122.

In summary, for a sample size of 150 employees, the mean wage per hour (μx) is expected to be RM14.50, the same as the population mean. The standard deviation of the mean wage (σx) is approximately RM0.122. This indicates that the mean wage of the sample is likely to be close to the population mean, with relatively low variability or dispersion among the sample means.

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Based on the text, the primary source of primate endangerment today is habitat destruction.

Habitat destruction is considered the primary source of primate endangerment based on various factors mentioned in the text. Primates, like many other species, heavily rely on their natural habitats for survival, including food, shelter, and breeding. However, human activities such as deforestation, urbanization, and land conversion for agriculture or infrastructure development have significantly reduced and fragmented primate habitats.

Habitat destruction leads to the loss of critical resources and disrupts the ecological balance necessary for primate populations to thrive. As their habitats shrink, primates face increased competition for limited resources, reduced access to food and water sources, and decreased opportunities for successful reproduction and rearing of offspring. This loss of habitat also exposes primates to increased vulnerability to predation, disease transmission, and human-wildlife conflicts.

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Calamitous Clod creates a geometric sequence with common ratio 2 by adding 2 to the second term and 11 to the third term. The first term is 7.

Let the numbers are: a₁, a₂, a₃.

These three numbers form an arithmetic sequence, which means the differences between 2 consecutive terms are the same.

Hence,

a₃ - a₂ = a₂ - a₁

a₃ = 2a₂ - a₁   ..... (equation 1)

Calamitous Clod creates a geometric sequence with common ratio 2 by adding 2 to the second term and 11 to the third term.

Hence, the geometric sequence is:

a₁, a₂ + 2, a₃ + 11.

with common ratio =  2

common ration = (a₃ + 11) / (a₂ + 2) = 2

a₃ + 11 = 2a₂ + 4

a₃ = 2a₂ - 7  ..... (equation 2)

Substitute equation 2 into equation 1

2a₂ - 7  = 2a₂ - a₁

a₁ = 7

Hence,

The first term =  a₁ = 7

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The required height of the sailboat is 24 feet.

Given that,

A sailboat casts a shadow of 4 yards.

Height of buoy = 2 feet

To find the height of the sailboat,

we can set up a proportion,

⇒ (sailboat height) / 4 yards = 2 feet / 1 foot

Now convert 4 yards to feet, since the height of the buoy was given in feet,

⇒ 4 yards = 12 feet

Now put the values and solve for the sailboat height,

⇒ (sailboat height) / 12 feet = 2 feet / 1 foot

⇒ sailboat height = 24 feet

Therefore, the height of the sailboat is 24 feet.

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The gradient is -4/5, so the equation is of the form

\(y=-\frac{4}{5}x+c\)

Substituting in the coordinates (4, -2),

\(-2=-\frac{4}{5}(4)+c \\ \\ c=\frac{6}{5} \\ \\ \therefore y=-\frac{4}{5}x+\frac{6}{5}\)

Answer:

A=120

B=20

C=20

Total area=160 cm2

This is really weird because the numbers dont look proportional to the shape but according to the data it should be correct :/

Answer:

Area of A=120cm²

Area of B=20cm²

Area of C=20cm²

Total area=160cm²

Step-by-step explanation:

For A

\(Length(l)=15cm\\Breadth(b)=8cm\\Now,\\Area=l*b\\Area=15cm*8cm=120cm^{2}\)

For B

\(Length(l)=5cm\\Breadth=12cm -8cm=4cm\\Now,\\Area=l*b\\Area=5cm*4cm\\Area=20cm^{2}\)

Area of C=20cm²

Total Area=160cm²

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

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Answer:

1,900

Step-by-step explanation:

Answer:

1900 is my pick

Step-by-step explanation:

The given circle equation is x² + y² = 4We can obtain y² = 4 - x² by subtracting x² from both sides.If the cross-sections are perpendicular to the x-axis, the plane slices the circle into semicircles, which are circles of radius y with areas of πy²/2.

We use integral calculus to compute the volume of the solid by adding up the volumes of each slice from x = -2 to x = 2. The general formula for a volume of a solid with variable cross sections is:Volume = ∫A(x)dxwhere A(x) is the cross-sectional area at x. For our problem, we have:Volume = ∫A(x)dxwhere A(x) = πy²/2 is the area of the circle that is perpendicular to the x-axis and whose radius is given by y.

Therefore:A(x) = πy²/2 = π(4 - x²)/2 = 2π(2 - x²/2)The volume is obtained by integrating A(x) with respect to x over the range [−2, 2]:Volume = ∫A(x)dx= ∫[−2,2]2π(2−x²/2)dx=2π∫[−2,2](2−x²/2)dx=2π[2x−x³/3] [−2,2]=2π[(2⋅2−2³/3)−(2⋅−2−(−2)³/3)]=2π[(4−8/3)+(4+8/3)]=2π⋅8/3=16π/3 cubic unitsThus, the volume of the solid is 16π/3 cubic units.

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Answer:

i cant read it

can u type so i can help?

Step-by-step explanation:

The DWL falls when the monopolist receives the subsidy because it leads to an increase in output and a decrease in price.

The cost function and demand function of a monopolist can be found in the question. These can be used to derive the marginal revenue and marginal cost.

The optimal level of output and profit can be derived using the marginal revenue and marginal cost equations. After that, you can confirm that the demand is elastic at the optimal output.

After that, you need to calculate the markup and the DWL associated with the monopoly output. Finally, you need to find the new optimal output and determine if the DWL increases or decreases.

Given:Cost Function C(Q) = ¼ Q2 Marginal cost MC(Q) = ½ Q Demand P = 100 – ¼ Q. a.

Sketch the market demand, marginal costs, and marginal revenues.

Market demand:Marginal cost:Marginal revenue: b. What is the monopolist’s optimal level of output and profits?In the monopolistic market, the optimal level of output and profits are given by the condition that Marginal Revenue = Marginal Cost.

Marginal Revenue is the derivative of Total Revenue with respect to Quantity, which can be found by using the demand equation and solving for Q:TR(Q) = P × Q = (100 – ¼ Q)Q = 100Q – ¼ Q2MR(Q) = dTR(Q)/dQ = 100 – ½ QMarginal Cost is given by the question as MC(Q) = ½ Q.

The monopolist's optimal level of output and profits can be found by equating MR and MC:100 – ½ Q = ½ Q => Q = 66.67 units of outputWhen Q = 66.67, the price is given by the demand equation:P = 100 – ¼ Q => P = 83.33.

Therefore, the monopolist's optimal output is 66.67 and optimal profits are (P – MC) × Q = (83.33 – 33.33) × 66.67 = $2,000.

Confirm that demand is elastic at the optimal output.The demand is elastic at the optimal output if the absolute value of the price elasticity of demand is greater than one.

The price elasticity of demand is given by:Ed = (% Change in Quantity Demanded)/(% Change in Price) = (dQ/Q)/(dP/P) × P/QSince MR = P(1 - 1/Ed), MR is greater than MC if Ed is less than 1 and less than MC if Ed is greater than 1. Therefore, the optimal output occurs where Ed is equal to
Substituting the values of P and Q, we get:Ed = (dQ/Q)/(dP/P) × P/Q = -1.47Therefore, demand is elastic at the optimal output.

Calculate the firm’s markup.The markup is given by the formula (P - MC)/P.Substituting the values of P and MC, we get:(83.33 - 33.33)/83.33 = 0.6 = 60% markup .

What is the DWL associated with the monopoly output?DWL (Deadweight Loss) is the difference between the total surplus in a competitive market and the total surplus in a monopoly market.

The formula for DWL is:DWL = (1/2)(Pmon - Pcomp)(Qcomp - Qmon)DWL can be calculated by using the demand equation and finding the quantity demanded at the monopoly price and the competitive price. At the monopoly price of $83.33, the quantity demanded is 66.67.

At the competitive price of $66.67, the quantity demanded is 100. Therefore, DWL can be calculated as follows:DWL = (1/2)(83.33 - 66.67)(100 - 66.67) = $1,111.1 f.

Suppose the government offered a $10 production subsidy to the monopolist. What is their new optimal output?The new optimal output will be where the new marginal cost equals the original marginal revenue.

The subsidy reduces the marginal cost to (1/2) Q - $10.

Therefore, the monopolist's new optimal output can be found by solving for Q:100 - 1/2 Q + 10 = 1/2 Q => Q = 74.07 units of outputWhen Q = 74.07, the price is given by the demand equation:P = 100 - 1/4 Q => P = $81.48 g. Does the DWL fall or rise?The DWL falls when the monopolist receives the subsidy because it leads to an increase in output and a decrease in price.

Therefore, the deadweight loss falls.

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Answer:

exterior angle is equal to the sum of two interior opposite angle

?=53+53=106°

missing exterior angle =106°

The measure of the exterior angle is 106°.

Exterior angles are angles that are parallel to the inner angles of a polygon but lie on the outside of it.

Given that, a triangle has two interior angles 53° and 53° and an exterior angle x,

Since, we know that, sum of opposite two interior angles of a triangle is equal to measure of exterior angle.

Therefore,

53° + 53° = x

x = 106°

Hence, the exterior angle is 106°

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Answer:

x = 13, y = 24.

Step-by-step explanation:

5x - 8 + 63 + 7x - 31 = 180  (interior alternate angles are equal).

12x + 24 = 180

12x = 180 - 24 = 156

x = 156/12

x = 13.

4y + 27 =  63 + 7x - 31       (interior alternate angles are equal).

4y +27 = 32 +7(13)

4y = -27 +32 + 91

4y = `96

y = 96/4

y = 24.

Answer:

x=0 and x=5/2

Step-by-step explanation:

Combine like terms.

-2x=0

x=0/-2

x=0

-4x=-10

x=-10/-4

x=5/2

The exponential equation y = 2500 * 0.76^t models the relationship between the value of a laptop computer (y) and the number of years since it was purchased (t). It shows that each year the value decreases by 24%.

y = 2500 * 0.76^t

Given:

In 2005, a laptop computer was purchased for $2500.

Each year since then, the real value has decreased by 24%.

Let t be the number of years since 2005.

Let y be the value of the laptop computer, in dollars.

We can model this relationship using an exponential function.

Since the real value has decreased by 24% each year, we can use the equation 1 - 0.24 = 0.76 to represent this.

We can then use this to write the exponential function.

y = 2500 * 0.76^t

This equation shows the relationship between y (the value of the laptop computer) and t (the number of years since 2005). The exponential equation y = 2500 * 0.76^t models the relationship between the value of a laptop computer (y) and the number of years since it was purchased (t). It shows that each year the value decreases by 24%.

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Hello, This is the answer.

Please check the attached image.

By Benjemin ☺️

The sample mean is significantly different from 10 at a 0.1 significance level.

The null hypothesis is a statement about the population parameter that we are testing, and the alternative hypothesis is the complement of the null hypothesis. The significance level is the probability of rejecting the null hypothesis when it is true.

In this case, we can use the following null and alternative hypotheses:

Null hypothesis: The population mean is equal to 10.

Alternative hypothesis: The population mean is not equal to 10.

We will use a two-tailed test because the alternative hypothesis is not directional.

We can use the t-test to test the null hypothesis. The t-test statistic is calculated as follows:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

In this case:

\(t = (11 - 10) / (3.2 / \sqrt{10} ) = 1.58\)

We need to find the critical value of t at the 0.1 significance level with 9 degrees of freedom (10 - 1 = 9). We can use a t-table or a statistical software to find this value. The critical value is ±1.833.

Since the calculated t-value of 1.58 is not greater than the critical value of ±1.833, we cannot reject the null hypothesis. We do not have sufficient evidence to conclude that the population mean is different from 10 at the 0.1 significance level.

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Answer:

.37

Step-by-step explanation:

1/3 is represented in decimal form by: .33 with a bar on the second 3

Using the formula A = P(1+r/n)nt, we can solve for t to find how long it takes for an investment to double.  It will take approximately 6.721 years for an investment of $1,900.00 to double if it is invested at 10% compounded annually.

Let P = 1900 (the initial investment), r = 0.1 (the annual interest rate), n = 1 (since it is compounded annually), and A = 2P = 3800 (since we want to find how long it takes for the investment to double).
Plugging these values into the formula, we get: 3800 = 1900(1 + 0.1/1)^(1*t)
Simplifying the right side, we have:  3800 = 1900(1.1)^t
Dividing both sides by 1900, we get:
2 = 1.1^t
Taking the natural logarithm of both sides, we have:
ln(2) = t*ln(1.1)
Solving for t, we have:
t = ln(2) / ln(1.1)
Using a calculator, we get:
t ≈ 6.721 years

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In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.

The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true

. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.

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In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.

This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters

the first false condition since the overall result will definitely be false.

In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing

any further conditions. This is also known as short-circuit evaluation.

In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing

any further conditions. The Nor and Xor operators are less commonly used and have different behavior.

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Answer:

40 students.

Step-by-step explanation:

There are 60 12th graders that voted for Nick and only 20 12th graders that voted for Garett. 60 - 20 = 40.

Hope this helps!

sin(2θ) = 12√30/49.

Explanation:

8) Given that cos e = - 5/13 and π/2 < θ < π, we need to find cos(2θ).

We know that cos(2θ) = 2 cos²(θ) - 1. Therefore, we need to first find cos(θ).

Using the given value of cos e, we can use the identity cos(π - e) = - cos(e) to find cos(θ) as follows:

cos(θ) = cos(π - e) = - cos(e) = -(-5/13) = 5/13

Now, we can substitute this value to find cos(2θ):

cos(2θ) = 2 cos²(θ) - 1 = 2(5/13)² - 1 = 0.647

Therefore, cos(2θ) ≈ 0.647.

9) Given that sin 8 = 2√10/7 and θ < 0, we need to find sin(2θ).

We know that sin(2θ) = 2 sin(θ) cos(θ). Therefore, we need to find sin(θ) and cos(θ).

Since θ < 0, we know that sin(θ) < 0 and cos(θ) > 0.

Using the given value of sin 8, we can use the identity sin(π - 8) = sin(8) to find sin(θ) as follows:

sin(θ) = sin(π - 8) = sin(8) = 2√10/7

Using the fact that sin²(θ) + cos²(θ) = 1, we can find cos(θ) as follows:

cos²(θ) = 1 - sin²(θ) = 1 - (2√10/7)² = 27/49

cos(θ) = √(27/49) = 3√3/7

Now, we can substitute these values to find sin(2θ):

sin(2θ) = 2 sin(θ) cos(θ) = 2(2√10/7)(3√3/7) = 12√30/49

Therefore, sin(2θ) = 12√30/49.

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Developers determine the specifics of how to build a system in the design phase. b

The design phase and its importance:
Define Objectives:

The design phase begins after the completion of the analysis phase, where developers have gathered and evaluated requirements.

The main objective of the design phase is to create a blueprint for the system that addresses all identified requirements.
Create Architectural Design:

During this step, developers establish the overall structure of the system, including its components, their relationships, and the interactions between them.

This architectural design provides a high-level view of the system's organization.
Design System Components:

With the architectural design in place, developers focus on designing individual components or modules of the system. They create detailed specifications, which include the functionality, inputs, outputs, and processes for each component.
Design User Interface:

The user interface design involves creating a user-friendly and efficient way for end-users to interact with the system. This can include designing screen layouts, menus, buttons, and other interface elements.
Validate Design:

The final step in the design phase is to ensure that the proposed design meets all the requirements identified during the analysis phase.

Developers may use various methods, such as reviews and simulations, to validate their design before proceeding to the implementation phase.
The design phase is a crucial part of the system development process, as it defines how the system will be built, ensuring it meets the needs of its users and the project's objectives.

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