A student has 30 minutes to complete an exam. There are 9 multiple choice questions worth 3 points each. There are also 3 short answer questions worth 5 points each. It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question. How many multiple choice questions and short answer questions should the student answer to maximize his score in the time remaining (Use x = multiple choice; y = short answer.)State the Objective Function (S for score) in the linear programming problem givenA. S = 5x + 3y B. S = 3x + 5y C. S = 2x + 6y D. S = 6y + 2x

The city with a doubling time of 83 years and an initial population of 88200 years will reach a population of 705600 habitants in 249 years.

In this question we have a city whose population is doubled every 83 years. Hence, we can model the growth of the city with an exponential model of the form:

\(y = 88200 \cdot 2^{\frac{t}{83} }\)     (1)

Where:

If we know that t = 249, then the population of the city after 249 years is:

\(y = 88200 \cdot 2^{249/83}\)

y = 705600

The city with a doubling time of 83 years and an initial population of 88200 years will reach a population of 705600 habitants in 249 years.

To learn more on exponential functions: https://brainly.com/question/11487261

#SPJ1

Simplify the expression

Removing all the parentheses, taking special care to change the signs of the last three terms:

Now collect like terms:

The number of hours that Javier spends on cardio and weightlifting will be one hour.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Every Saturday, Javier works out for two hours. His workout consists of two components. Javier works out with cardio and weights.

If he spends the same amount of time on both parts.

Let x be the number of hours spent on weightlifting. Then the equation is given as,

x + x = 2

2x = 2

x = 1 hour

The number of hours that Javier spends on cardio and weightlifting will be one hour.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

The conclusion of the symbolised argument is that N implies (O and P). This can be proven using conditional proof and the eighteen rules of inference, or using the rule of conjunctive simplification.

The symbolic argument's conclusion is that N implies (O and P). This can be demonstrated using conditional proof and the eighteen inference rules.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (3-6 Conditional Proof)

8. N ⊃ (O•P) (2,7 Disjunctive Syllogism)

This leads us to the conclusion that N implies (O and P).

Without the use of conditional proof, the identical result can be reached. The conjunctive simplification rule can be used to do this.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (Conjunctive Simplification)

Therefore, we have derived the conclusion that N implies (O and P).

Complete Question:

Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.

1. N ⊃ O

2. N ⊃ P / N ⊃ (O • P)

To learn more about simplification visit:

https://brainly.com/question/30231919

#SPJ4

Answer:

That would be A!

Step-by-step explanation:

Please tell me if i made a mistake or misunderstood!

The particle is at rest when its velocity vector is zero. To find the values of t for which the particle is at rest, we need to determine when both the x-component and the y-component of the velocity vector are equal to zero.

The values of t that satisfy this condition are t = -1, 0, and 2. Therefore, the particle is at rest at these three values of t.

To determine when the particle is at rest, we need to find the values of t for which both the x- and y-components of the velocity vector are zero. The velocity vector is obtained by taking the derivatives of x and y with respect to t.

The x-component of the velocity is given by dx/dt = 3t^2 - 6t, and the y-component of the velocity is given by dy/dt = 6t^2 - 6t - 12.

Setting dx/dt = 0, we get 3t^2 - 6t = 0, which can be factored as 3t(t - 2) = 0. This gives us t = 0 and t = 2 as solutions.

Setting dy/dt = 0, we get 6t^2 - 6t - 12 = 0, which can be simplified as t^2 - t - 2 = 0. This can be factored as (t - 2)(t + 1) = 0, giving us t = -1 and t = 2 as solutions.

Therefore, the particle is at rest when t = -1, 0, and 2. Hence, the correct answer is option B) -1, 0, and 2 only.

To learn more about derivatives click here:

brainly.com/question/25324584

#SPJ11

If firm issues​ commercial paper with $1000000 face-value and pays EAR of​ 7.4%, then amount the firm will receive is $981500.

To calculate the amount the firm receives from issuing the three-month commercial paper, we need to determine the total interest earned over the three-month period.

The Effective Annual Rate (EAR) of 7.4% indicates the annualized interest rate. Since the commercial paper has 3-month term, we adjust the EAR to account for the shorter period.

To find the quarterly interest rate, we divide the EAR by the number of compounding periods in a year. In this case, since it is a 3-month period, there are 4-compounding periods in a year (quarterly compounding).

Quarterly interest rate = (EAR)/(number of compounding periods)

= 7.4%/4

= 1.85%,

Now, we calculate interest earned on "face-value" of $1,000,000 over 3-months,

Interest earned = (face value) × (quarterly interest rate)

= $1,000,000 × 1.85% = $18,500,

So, amount firm receives from issuing 3-month commercial paper is the face value minus the interest earned:

Amount received = (face value) - (interest earned)

= $1,000,000 - $18,500

= $981,500.

Therefore, the amount that firms receives is $981500.

Learn more about EAR here

https://brainly.com/question/32531122

#SPJ4

The expression for G will be written as G = (-10x² + 100x + 44 ) / x.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is G = -10× + 100 + 44/×. The expression for G will be calculated as:-

G = -10× + 100 + 44/×

Take LCM of x and solve,

G = -10× + 100 + 44/×

G = (-10x² + 100x + 44 ) / x.

To know more about an expression follow

https://brainly.com/question/26236351

#SPJ1

Answer:

equation A,C and E are true if w=100

a. A car travels 97.5 miles in 1.5 hours.

b. A car takes 2 hours to travel 130 miles.

c. Mai's equation matches the story because it is algebraic form of the formula of speed.

In this question, we have been given a car is going 65 miles per hour down the highway.

Part a.

A car is going 65 miles per hour.

This means, in 1 hour car traveled 65 miles.

Let car travels 'm' miles in 1.5 hours.

So, m = 1.5 × 65

m = 97.5 miles

Thus, a car travels 97.5 miles in 1.5 hours

Part b.

Suppose that it will take t hours to travel 130 miles.

We have been given 1 hour = 65 miles

So, we get an equation,

t = 130 / 65

t = 2 hours

This means, a car takes 2 hours to travel 130 miles.

Part c.

Mai wrote the equation y = 65x, with x representing the time traveled, in hours, and y representing the distance traveled, in miles.

We know that the formula of speed.

speed = distance / time

⇒ distance = speed × time

here, speed = 65 miles per hour

⇒ distance = 65 × time

Assuming distance = y  and time = x

y = 65x

This means,  Mai's equation matches the story.

Therefore, a. A car travels 97.5 miles in 1.5 hours.

b. A car takes 2 hours to travel 130 miles.

c. Mai's equation matches the story because it is algebraic form of the formula of speed.

Learn more about speed here:

https://brainly.com/question/2004627

#SPJ1

Answer:

1) \(m\)∠JKL = 145°

2) \(m\)∠IHG = 164°

3) \(m\)∠NME = 50°

4) \(m\)∠TUV = 178°

I hope this helps! (✿◠‿◠)

The equation used to obtain the probability of a number less than 4 on the spinner is given as follows:

P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability is calculated as follows:

P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.

The problem asks for the probability of spinning a number less than 4 on the spinner.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

Answer and Explanation: The conditions when the net force and the net torque are zero are called static equilibrium.

Using male subjects only in a study would have an impact on the power of the test. Specifically, it would decrease the power of the test and limit the scope of inference to males only, which is a drawback of this change.

This would also make it harder to reject the null hypothesis when it is false. To increase the power of the test and allow for a broader scope of inference, it would be beneficial to include a diverse sample of subjects that represents the population being studied.

1. True. The lack of female subjects in the study reduces the diversity of the sample, which can lead to decreased power of the test. This means that it may be more difficult to detect a significant difference if one exists.

4. True. Using male subjects only would increase the power of the test, as there is less variability in the sample.

5. True. The use of male subjects only limits the scope of inference to males, reducing the generalizability of the findings.

To learn more about male subjects please click on below link.

https://brainly.com/question/29570947

#SPJ4

Suppose that researchers had used 628 male subjects but no female subjects in the study.

How would this affect the power of the test? What is a drawback of this change? Select all true statements.

1. Using male infants only would decrease the power of the A drawback is that this limits the scope of inference to males only.

2. Test by eliminating a source of variability.

3. Using male infants only would make it harder to reject the null hypothesis when it is false.

4. Using male infants only would make it easier to reject the null hypothesis when it is false.

5. Using male infants only would increase the power of the A drawback is that this also limits the scope of inference

6. Test by eliminating a source of variability.

7. To females only.

Answer:

She kicked it up

Step-by-step explanation:

How is this math?

I believe your answer is B.) She kicked it up. Think about it, if she kicks it straight up, it goes up ten feet, and then it comes back down (Revered direction) to her.

Answer:

Approximately 45%.

Step-by-step explanation:

We know that Steve's team played in total 33 games. Out of the 33, they won 15 of them.

So, as a fraction of the total won over the total games, we can write:

\(\displaystyle\frac{15}{33}\)

So, by dividing, the percent the team won is:

\(\displaystyle\frac{15}{33}=0.\overline{45}=0.454545...\approx0.45=45\%\)

The team won approximately 45% of its games.

After considering the given data we conclude that the value derived after performing integration by applying cylindrical coordinates is -1029π / 3

The solid E is the region between the cylinders x² + y² = 1 and x² + y² = 49, above the xy-plane, and below the plane z = y/7. We can apply cylindrical coordinates to evaluate this integral.
The limits of integration for r are 1 and 7. The limits of integration for theta are 0 and 2π. The limits of integration for z are 0 and r/7.

Hence , we have

\(\int \int \int E (x- y) dV = \int0^2\pi \int1^7 \int 0^{(r/7)} (r cos\theta - r sin\theta) r dz dr d\theta\)

\(= \int 0^2\pi \int1^7 \int0^{(r/7)} (r^2 cos\theta - r^2 sin\theta) dz dr d\theta\)

\(= \int0^2\pi \int1^7 (r^3 cos\theta/3 - r^3 sin\theta/3) dr d\theta\)
\(= (1/3) * \int0^2\pi [cos\theta * (7^4 - 1) / 4 - sin\theta * (7^4 - 1) / 4] d\theta\)
\(= (1/3) * [(7^4 - 1) / 4 * \int0^2\pi cos\theta d\theta - (7^4 - 1) / 4 * \int0^2\pi sin\theta d\theta]\)
\(= (1/3) * [(7^4 - 1) / 4 * 0 - (7^4 - 1) / 4 * 0]\)
\(= \frac{-1029\pi}{3}\)

Integration is considered one of the two fundamental system of calculus, the other being differentiation. It is a way of computing an integral. It is projected as a method to evaluate problems in mathematics and physics, for instance as finding the area under a curve or determining displacement from velocity.
To learn more about Integration
https://brainly.com/question/27419605
#SPJ4

The values of θ that satisfy the given condition 0° ≤ θ < 360° and are rounded to the nearest tenth are:
1st Quadrant: θ = 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, 80°, 90°
2nd Quadrant: θ = 90°, 100°, 110°, 120°, 130°, 140°, 150°, 160°, 170°, 180°
3rd Quadrant: θ = 180°, 190°, 200°, 210°, 220°, 230°, 240°, 250°, 260°, 270°
4th Quadrant: θ = 270°, 280°, 290°, 300°, 310°, 320°, 330°, 340°, 350°, 360°

To solve for all values of θ such that 0° ≤ θ < 360°, we will use the given range and round all values to the nearest tenth. To find all the values of θ within the given range, we need to consider the entire unit circle (360°).
To begin, let's list the quadrants and their corresponding angles within the unit circle:

1st Quadrant: 0° ≤ θ < 90°
2nd Quadrant: 90° ≤ θ < 180°
3rd Quadrant: 180° ≤ θ < 270°
4th Quadrant: 270° ≤ θ < 360°

Within each quadrant, we can use the reference angles (angle between the terminal side and the x-axis) to find the values of θ. Using the reference angles, we can determine the following values for θ within each quadrant:

1st Quadrant: θ = 0° to 90°
2nd Quadrant: θ = 90° to 180°
3rd Quadrant: θ = 180° to 270°
4th Quadrant: θ = 270° to 360°

Learn more about Quadrants here: https://brainly.com/question/28587485

#SPJ11

Answer:

90 obtuse

Step-by-step explanation:

Answer:

-4 I think

Step-by-step explanation:

The nearest whole number after rounding is, 14

Rounding a number to the nearest tenth means finding the nearest multiple of 0.1.

To do this, you need to look at the digit in the hundredths place (the second digit after the decimal point) of the number you want to round.

If that digit is 5 or greater, you round the number up by adding 0.1 to the nearest whole number.

If that digit is 4 or less, you round the number down by leaving the nearest whole number unchanged.

For example, rounding 3.456 to the nearest tenth gives 3.5, while rounding 3.444 to the nearest tenth gives 3.4.

Given that,

The decimal number  13.5,

after using rules of rounding,

it can be rounded as 14

Hence, the nearest whole number is 14

To know more about Rounding check:

https://brainly.com/question/29878750

#SPJ9

Answer:

\(Cost \ total= \$ 1755\)

Step-by-step explanation:

Find the total cost of a rectangular shaped carpet, given the carpets length,  width, and the cost of carpet per square foot. Using the formula for the area of a rectangle.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Area of a Rectangle:}}\\\\A=l \times w\end{array}\right}\)

Where...

Given:

\(l=15 \ ft\\w=9 \ ft\\ 1 \ ft^2= \$ 13\)

Find:

\(Cost \ total = \ ?? \\)

(1) - Calculating the total area of the carpet, which is a rectangle

\(A=l \times w\\\\\Longrightarrow A=15 \ ft \times 9 \ ft\\\\\therefore \boxed{A=135 \ ft^2}\)

(2) Calculate the total cost of the carpet by multiplying the total area of the carpet by the cost of one square foot of carpet

\(Cost \ total=135 \ ft^2 \times \$ 13\\\\\therefore \boxed{\boxed{Cost \ total= \$ 1755}}\)

Thus, the total cost of the carpet is found.

The value of ∫4-1f(x)dx is 8.4.

We are given two definite integrals:

∫5-1f(x)dx = 12

∫5-4f(x)dx = 3.6

We want to find the value of ∫4-1f(x)dx.

We can use the property of definite integrals that states:

∫a-bf(x)dx = ∫a-cf(x)dx + ∫c-bf(x)dx

We can split the interval [4, 1] into two intervals: [4, 5] and [5, 1]. Therefore, we have:

∫4-1f(x)dx = ∫4-5f(x)dx + ∫5-1f(x)dx

Since we know that ∫5-1f(x)dx is given as 12, we can substitute this value into the equation:

∫4-1f(x)dx = ∫4-5f(x)dx + 12

Now, let's focus on the integral ∫5-4f(x)dx. It is given as 3.6. Therefore, we can rewrite it as:

∫5-4f(x)dx = ∫5-1f(x)dx - ∫4-5f(x)dx

Plugging in the values we know:

3.6 = 12 - ∫4-5f(x)dx

We can solve for ∫4-5f(x)dx by subtracting 3.6 from 12:

∫4-5f(x)dx = 12 - 3.6 = 8.4

Substituting this back into the equation for ∫4-1f(x)dx:

∫4-1f(x)dx = ∫4-5f(x)dx + 12 = 8.4 + 12 = 20.4

Therefore, the value of ∫4-1f(x)dx is 20.4.

Know more about the definite integrals click here:

https://brainly.com/question/30760284

#SPJ11

The function \(z(x, y) = \cos(x) \cos(e^{-y^2})\) has infinitely many local maxima, infinitely many local minima, and infinitely many saddle points.

To determine the local extrema and saddle points of the function \(z(x, y) = \cos(x) \cos(e^{-y^2})\), we need to analyze its partial derivatives with respect to \(x\) and \(y\).

Taking the partial derivative of \(z\) with respect to \(x\), we get:

\(\frac{\partial z}{\partial x} = -\sin(x) \cos(e^{-y^2})\)

Taking the partial derivative of \(z\) with respect to \(y\), we get:

\(\frac{\partial z}{\partial y} = 2y \sin(x) \sin(e^{-y^2}) \cdot e^{-y^2}\)

To find the critical points, we need to solve the equations \(\frac{\partial z}{\partial x} = 0\) and \(\frac{\partial z}{\partial y} = 0\). However, since both \(\sin(x)\) and \(\cos(e^{-y^2})\) oscillate between -1 and 1, and \(\sin(e^{-y^2})\) oscillates between -1 and 1, there is no combination of \(x\) and \(y\) that simultaneously satisfies both equations.

Therefore, there are no critical points, and as a result, there are no local maxima, local minima, or saddle points for the function \(z(x, y) = \cos(x) \cos(e^{-y^2})\).

Learn more about derivatives here:

https://brainly.com/question/31828911

#SPJ11

Answer:

im not sure (dont take this down plz) but i think it is 2175 bc i dont belive there are not more then two or three ways to get that #

Answer:

585/4 or 146.25

Step-by-step explanation:

10 x 6 1/2 x 2 1/4

10 x 13/2 x 9/4

5 x 13 x 9/4

65 x 9/4

585/4 = 146.25

The height of the pyramid is 16 feet.

What is Pythagoras Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can use the Pythagorean theorem to find the height of the pyramid.

The slant height of the pyramid is the hypotenuse of a right triangle whose legs are the height of the pyramid and half the length of the base of the pyramid. Since the base is a square, half the length of the base is 12 feet.

Using the Pythagorean theorem:

height² + 12² = 20²

height² = 20² - 12²

height² = 256

height = 16 feet

Therefore, the height of the pyramid is 16 feet.

To know more about Pythagoras theorem visit:

https://brainly.com/question/343682

#SPJ4

Answer:

Rectangular pyramid : Faces, Vertices, Edges = 5 , 5 , 8 respectively

Step-by-step explanation:

Rectangular pyramid is a 3D shape, with base as rectangle & triangle face corresponding to each side of base (on the top)

Faces = 5 { 1 rectangular base face , 4 triangular faces above}

Vertices = 5 { 4 vertices of rectangle, 1 vertice on top - where triangles' tips intersect}

Edges = 8 {4 edges of rectangle at base , 4 edges of triangles above}

Answer:

b. 5, 5, 8

Step-by-step explanation:

i did the assignment and this was the correct answer <3