1 Jason is pulling a box across the room. He is pulling with a force of 29 newtons and his arm is making a 37 angle with the horizontal, what is the vertical component of the force he is pulling with?
2 One force of magnitude 41 acts on an object. Another force of magnitude 86 acts on the object at a right angle, what is the magnitude of the resultant force on the object?
3 Final grades are often computed using weighted averages. Some college professors use complicated weighted averages. Your college professor tells you he will give a 33%-67% split on grades between tests and homework where whichever average is higher will be the 67%. What will your final grade be if your homework average is 94 and your test average is 80?​

Answer:

66.3

Step-by-step explanation:

Trust

The two equations to set up to solve |2x−3|=11 are 2x − 3 = 11 and 2x − 3 = -11

Hence, option C)2x − 3 = 11 and 2x − 3 = -11 is the correct answer.

Given the equation in the question;

| 2x − 3 | = 11

To solve the equation, we have to remove the absolute value term and this will create the a ± on the right side of the equation.

Note that; |x| = ±x

Hence;

| 2x − 3 | = 11

2x − 3 = ±11

The solution of the equation is the result of both the positive and negative portions of the of the solution.

2x − 3 = 11 and 2x − 3 = -11

Therefore, the two equations to set up to solve |2x−3|=11 are 2x − 3 = 11 and 2x − 3 = -11

Hence, option C)2x − 3 = 11 and 2x − 3 = -11 is the correct answer.

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Answer:6

Step-by-step expla

Answer:

a) 0.5 = 50% probability that an NPN transistor will be selected.

b) 0.3333 = 33.33% probability that it came from the cabinet that contains both types

c) 66.67% probability that it comes from the cabinet that contains only NPN transistors

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

a) What is the probability that an NPN transistor will be selected?

1/3 probability that the first cabinet is chosen. This cabinet has two transistors, both of which are NPN, so 100% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, both of which are PNP, so 0% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, one of which is NPN, so 50% probability of selecting a NPN transistor.

So

\(p = \frac{1}{3}*1 + \frac{1}{3}*0 + \frac{1}{3}*0.5 = \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = 0.5\)

0.5 = 50% probability that an NPN transistor will be selected.

b) Given that the hobbyist selects an NPN transistor, what is the probability that it came from the cabinet that contains both types?

Here we use the conditional probability formula.

Event A: NPN transistor

Event B: From the third cabinet.

50% probability that an NPN transistor will be selected, so \(P(A) = 0.5\).

1/6 probability that it is from the third cabinet and NPN, so \(P(A \cap B) = \frac{1}{6}\)

The desired probability is:

\(P(B|A) = \frac{\frac{1}{6}}{0.5} = 0.3333\)

0.3333 = 33.33% probability that it came from the cabinet that contains both types.

c) Given that an NPN transistor is selected what is the probability that it comes from the cabinet that contains only NPN transistors?

Either it comes from the cabinet with only NPN transistors, or it comes from the cabinet with both types of transistors. The sum of the probabilities of these outcomes is 100%. So

x + 33.33 = 100

x = 66.67

66.67% probability that it comes from the cabinet that contains only NPN transistors

Answer: The usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen.

Step-by-step explanation: To find the usual dose of ibuprofen for a child, we need to follow these steps:

Therefore, the usual dose for an 18-month-old weighing 21 pounds is 48 mg of ibuprofen. Hope this helps, and have a great day! =)

The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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Answer:

Step-by-step explanation:Move the decimal point in the divisor and dividend. ...

Place a decimal point in the quotient (the answer) directly above where the decimal point now appears in the dividend.

Divide as usual, being careful to line up the quotient properly so that the decimal point falls into place.

Answer:

0.11

Step-by-step explanation:

0.44/x=100/25

(0.44/x)*x=(100/25)*x

0.44=4*x

0.44/4=x

0.11=x

From what I see in the problem, the expression is

\((\frac{3^a^2}{3a^-1} )^k\)

To solve, plug in a and k.

\((\frac{3^(5)^2}{3*5^-1} )^-2\)

3*5^2=75

(3*5)^-1 = 1/15

\(75 / \frac{1}{15} = 5\)

5^-2 = 1/25

Answer:

-4.5 -0.5 0.3 0.7 2.3

Step-by-step explanation:

Answer:

Find the area of all of the different shapes (2D)

and then add them up together to find the surface area.

3×2

6×2

6×2

5×3

6×3

1×3

1×4

1×4

4×3

Then you add them up together.

6+12+12+15+18+3+4+4+12=ANS.

Answer:

D+7=K

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

A surveyor is estimating the distance across a river. The actual distance is 284.5 m. The surveyor's estimate is 300 m. Find the absolute error and the percent error of the surveyor's estimate. If necessary, round your answers to the nearest tenth.

(i) Absolute error = 15.5m

(ii) Percent error = 5.5%

Given:

Actual measurement of the distance = 284.5 m

Estimated measurement of the distance by the surveyor = 300 m

(i) The absolute error is the magnitude of the difference between the estimated value measured by the surveyor and the actual value of the distance across the river.

i.e

Absolute error = | estimated value - actual value |

Absolute error = | 300m - 284.5m | = 15.5m

(ii) The percent error (% error) is given by the ratio of the absolute error to the actual value then multiplied by 100%. i.e

% error = \(\frac{absoluteError}{actualValue}\) x 100%

% error = \(\frac{15.5}{284.5}\) x 100%

% error = 0.05448 x 100%

% error = 5.448%

% error = 5.5%  [to the nearest tenth]

Answer: She has 40 shirts in all

Step-by-step explanation: 50% of 40 is 20

The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question

The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

Amounts of weight that male college students gain during their freshman year are normally distributed

mean of μ = 1.1 kg and

Standard deviation of o= 4.6 kg.

Z score=x-μ/o

=25-1.1/4.6

=23.9/4.6

=5.196

Z score=x-μ/o

=25-1.1/0

=0

Z score=25-1.1/3

=23.9/3

=7.966

By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%

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Answer:

A

Step-by-step explanation:

Use Math-way to help.

The standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.

In order to use the formula sigma x = sigma/ to calculate the standard deviation of the sampling distribution of the sample mean, all three conditions must be met. The first condition is that n must be greater than or equal to 30. This is because the larger the sample size, the more likely it is that the population's distribution is approximately normal. The second condition is that the population's distribution is approximately normal. This is because the Central Limit Theorem states that when the sample size is large enough (usually n ≥ 30) the sample means will have an approximately normal distribution. The third condition is that the sample size is less than 10% of the population size. This is because samples that are too large can lead to sample means that are not representative of the population.

To calculate the standard deviation of the sampling distribution of the sample mean, we can use the following formula:

σx = σ/√n

Where σ is the population standard deviation, and n is the sample size. For example, if the population standard deviation is 5, and the sample size is 30, then the standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.

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The number of ways which he can choose 5 courses if more than 3 must be humanities is; 8 ways.

According to the question;

If the condition requires that he chooses more than 3 humanities courses, it follows that;

On this note, the number of ways he can choose the required 5 courses is; 8 ways.

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Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.

The profit function is given by P(x) = -50x + 20,000x - 1,500,000.

To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:

-50x + 20,000x - 1,500,000 > 0.

Combining like terms, we have:

19,950x - 1,500,000 > 0.

Now, let's solve this inequality for x:

19,950x > 1,500,000.

Dividing both sides by 19,950, we get:

x > 1,500,000 / 19,950.

Simplifying the right side, we have:

x > 75.

The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

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Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The interest is 6%, compounded continuously.

After 1 year there is $400.

The continuous compound formula is

Where P is the principal, A is the final amount, i is the interest and t is the time in years.

Replacing all the given information, we have.

Answer:

-2/3

Step-by-step explanation:

Answer:

the debt ratio remains the same

Answer:

5/3

Step-by-step explanation:

(5/6)÷(1/2)

= (5/6) x 2

= 10/6 = 5/3

Hope this helps!

Answer:

the correct answer is 5/3

I'm 100000000000% sure

The mistake is when you try to divide by X - 1, because you can't divide by zero.

Here we start by defining:

X = 1

The second step makes sense, we are adding the same value in both sides:

X + X = X + 1

2X = X + 1

Now subtract 2 in both sides:

2X - 2 = X + 1 - 2

2X - 2 = X - 1

Here is the mistake, you divide both sides by X - 1

But we already defined that X = 1

Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.

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Answer:

The answer is C,(x^2+2)(x+7)

Step-by-step explanation:

x3 + 7x2 − 2x − 14.

We will group the terms.

Make pairs of the terms:

(x3 + 7x2 ) - (2x + 14.)

Now find the common factor of each pair

x^2(x+7)-2(x+7)

(x^2-2)(x+7)

Thus the factors of x3 + 7x2 − 2x − 14. are (x^2-2)(x+7)