An aircraft factory manufactures airplane engines. The unit C(the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made , then the unit cost is given by the function C (x) = 0.9x^2-306x+34,590. What is the minimum unit cost?

9514 1404 393

Answer:

  a = 3

Step-by-step explanation:

Evaluating the given function at the point, we have ...

  f(-1) = a(-1)^2 +1 = 4

  a +1 = 4

  a = 3

The value of 'a' is 3.

Answer:

$48

Step-by-step explanation:

you would first need to find what the cost of 1 book is so

16 divided by 4 is 4

so 1 book is $4

then you would need multiply the cost of one book by 12

so 4 times 12 is 48

so the cost would be $48

Answer:

192

Step-by-step explanation:

times

The distance between M and H is given as follows:

x = 21.3.

Similar triangles are triangles that share these two features presented as follows:

The proportional relationship between the side lengths is given as follows:

x/18 = 24/16

Applying cross multiplication, the distance between M and H is obtained as follows:

16x = 24(18)

x = 24 x 18/16

x = 27.

The diagram is given by the image presented at the end of the answer.

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Answer:

0.343, 0.424, 0.443

Step-by-step explanation:

The graph of the new function would be less steep than the original one but would not be shifted up or down or left or right.

Thus, the correct option is: It would be less steep.

In mathematics, a graph is a visual representation of a set of objects where some pairs of the objects are connected by links. The objects, which are usually represented by points, are called vertices or nodes, and the links, which are usually represented by lines or arcs, are called edges.

The original function y = 5x + 1 has a slope of 5, which means that for every 1 unit increase in x, y increases by 5 units.

The new function y = 2x + 1 has a slope of 2, which is less steep than the slope of the original function.

However, the y-intercept of both functions is the same, which is 1.Therefore, the graph of the new function would be less steep than the original one but would not be shifted up or down or left or right.

Thus, the correct option is: It would be less steep.

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The value of the standardized test statistic: -2.14

Explain hypothesis test.

A hypothesis test is a statistical procedure used to test a hypothesis about a population parameter. It involves comparing a sample statistic to a hypothesized value of the population parameter, using a test statistic and a pre-determined level of significance.

A. The value of the standardized test statistic: -2.14
B. The p-value is 0.0335 with explanation. This value is obtained by finding the probability of getting a t-statistic of -2.14 or less from the Student's t-distribution with 12 degrees of freedom (6 observations from each group). This p-value is less than the significance level of 0.05, so there is evidence to conclude that those who exercise regularly have lower resting heart rates.

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Answer:

3%

Step-by-step explanation:

They made 97+3 total jars, 3 out of 100 is 3 percent.

Answer:

0.02 × 100 = 2

Step-by-step explanation:

move the decimal 2 steps backward according to the numbers of zeros behind the multiplier(100).

0.02 × 100 = 2

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The length of side x is approximately 24.87, rounded to the nearest hundredth.

how can we find side of the triangle?

To find the length of side x, we can use the sine function, which relates the opposite side to an angle to the hypotenuse:

sin(11°) = opposite side/hypotenuse

Rearranging this equation, we get:

opposite side = sin(11°) * hypotenuse

We know that the hypotenuse has a length of 130, so we can substitute that in:

opposite = sin(11°) * 130

Using a calculator, we can evaluate sin(11°) to be approximately 0.1919, so we can substitute that in as well:

opposite = 0.1919 * 130

Simplifying this expression, we get:

opposite ≈ 24.87

Therefore, the length of side x is approximately 24.87, rounded to the nearest hundredth.

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The vertices of triangle image are L'(1, -4), M'(6, 4) and N'(7, -2).

Given that, triangle LMIN with vertices L(2, -8), M(12, 8) and N(14,-4).

Here, scale factor k=1/2

Now, by applying scale factor to the vertices, we get

L(2, -8)→1/2 (2, -8)→L'(1, -4)

M(12, 8)→1/2 (12, 8)→M'(6, 4)

N(14,-4)→1/2 (14, -4)→N'(7, -2)

Therefore, the vertices of triangle image are L'(1, -4), M'(6, 4) and N'(7, -2).

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"Your question is incomplete, probably the complete question/missing part is:"

Triangle LMIN with vertices L(2, -8), M(12, 8), and N(14,-4): k = ½.

The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles

The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles.

Always true. The opposite angles of an isosceles trapezoid are supplementary because the diagonals of an isosceles trapezoid bisect each other. Therefore, the angles formed by the intersection of the diagonals are supplementary, since the sum of two supplementary angles is 180 degrees.

The opposite angles of an isosceles trapezoid are always supplementary due to the diagonals of the trapezoid bisecting each other and forming supplementary angles.

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Based on the information given, we know that the two triangles have two pairs of congruent angles. This is sufficient to prove that the two triangles are congruent using the AAS (Angle-Angle-Side) postulate. Therefore, the method I would use to prove the two triangles congruent is **AAS**.

Answer:

7

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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The number of groups of 7/4 that are in 1 is 4/7.

The value of 3 ÷ 7/4 is 5 1/4.

In order to determine the number of groups of 7/4 that are in 1, divide 7/4 by 1.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

1 ÷ 7/4

= 1 x 4/7 = 4/7

3 ÷ 4/7

3 x 7/4 = 21/4 = 5 1/4

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Answer:

4/4 groups and 12/7

Step-by-step explanation:

\(1. \: 3 \times \frac{4}{7} \\ 2. \: \frac{3 \times 4}{7} \\ 3. \: \frac{12}{7} \)

Answer:

18475

Step-by-step explanation:

given sequence is in A.P.

sum of n terms of an A.P. is =

\( \frac{n}{2} \times (2a + (n - 1) \times d)\)

here n = 50

a = 3

d= 15

ans is 18,475

Answer:

1/12

Step-by-step explanation:

To find experimental probability you have to solve the Number of times an event occurs / Total number of trials. So since the 5 only appears once and there are 12 numbers, it would be 1/12. Did this help?

The experimental probability of rolling 5 will be 0.18.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

The table is given below:

Number      Total

    1                12

   2                16

   3                21

   4                23

   5                18

   6                10

The experimental probability of rolling a 5 is calculated as,

P = 18 / (12 + 16 + 21 + 23 + 18 + 10)

P = 18 / 100

P = 0.18

Thus, the probability is 0.18.

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Answer:

50% of 20 is 10

20 is 50% of 40

sorry, missed the actual question.

the second model fits the problem.

Answer:

2( 4+4) = 16

Step-by-step explanation:

The gcf of 16+32 is 16

The expression that gives the area of the rectangular flag is presented as follows:

5x + 7.5.

The area of a rectangle of length l and width w is obtained by the multiplication of these dimensions, as follows:

A = l x w.

The flag in this problem is composed by three rectangles, as follows:

The total area is obtained by the sum of the areas of each part of the flag, hence:

Area = 2x + 2 x 1.5 + 3(x + 1.5)

Area = 2x + 3 + 3x + 4.5

Area = 5x + 7.5.

The area of each part was obtained by the multiplication of the dimensions, which is the standard procedure to obtain the area of a rectangle.

The flag is given by the image at the end of the answer.

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Answer:

Step-by-step explanation:

The deck is divided into 4 different kinds of cards

Each kind of card has a 2

So there are 4 twos in a standard deck of cards.

Answer:

Answer:

a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12

c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.

d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.

Step-by-step explanation:

Let the event that a student does homework regularly be H.

The event that a student passes the course be P.

- 60% of her students do homework regularly

P(H) = 60% = 0.60

- 95% of the students who do their homework regularly generally pass the course

P(P|H) = 95% = 0.95

- She also knows that 85% of her students pass the course.

P(P) = 85% = 0.85

a) The probability that a student will do homework regularly and also pass the course = P(H n P)

The conditional probability of A occurring given that B has occurred, P(A|B), is given as

P(A|B) = P(A n B) ÷ P(B)

And we can write that

P(A n B) = P(A|B) × P(B)

Hence,

P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')

From Sets Theory,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

P(H n P) = 0.57 (from (a))

Note also that

P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)

0.60 = P(H n P') + 0.57

P(H n P') = 0.60 - 0.57

Also

P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)

0.85 = P(H' n P) + 0.57

P(H' n P) = 0.85 - 0.57 = 0.28

So,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

Becomes

0.03 + 0.28 + 0.57 + P(H' n P') = 1

P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12

c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.

Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,

P(A n B) = 0.

But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.

Hence, the two events aren't mutually exclusive.

d. Are the events "pass the course" and "do homework regularly" independent? Explain

Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when

P(A|B) = P(A)

P(B|A) = P(B)

P(A n B) = P(A) × P(B)

To check if the events pass the course and do homework regularly are mutually exclusive now.

P(P|H) = 0.95

P(P) = 0.85

P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671

P(H) = 0.60

P(H n P) = P(P n H)

P(P|H) = 0.95 ≠ 0.85 = P(P)

P(H|P) = 0.671 ≠ 0.60 = P(H)

P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)

None of the conditions is satisfied, hence, we can conclude that the two events are not independent.

Hope this Helps!!!

Part A: The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5

Part B: The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

Part C: the length of each of the five pieces of wood cut by Warren is 3.8 feet.

It is made up of two mathematical objects, with an equals sign (=) between them. Equations are used to represent relationships between unknown variables and can be solved to find their values.

Part A:

The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5, where x is the length of each piece of wood.

Part B:

The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

This equation can be used to calculate how much wood Warren has cut off from the original 4.5 feet of wood, which is the length of each of the five pieces of wood.

Part C:

Solving the equation from Part A:

x + 0.7 = 4.5

Subtract 0.7 from both sides:

x + 0.7 - 0.7 = 4.5 - 0.7

x = 3.8

Therefore, the length of each of the five pieces of wood cut by Warren is 3.8 feet.

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To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

Answer:

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

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

Answer:

- 1 1/3

Step-by-step explanation:

To solve this, simply divide 4 by -3. 4/-3 = -1 1/3, so that's your answer.

a. Constant speed, C =  0. 19 miles/minutes

b. The fraction representing her constant speed is  1/x miles/minutes

c. The time it takes her to drive exactly 1 mile is 5. 38 minutes

The formula for calculating constant speed is expressed as;

Constant speed = total distance covered/ total time taken

From the information given, we have that;

Now, substitute the values into the formula

Constant speed = 1. 3 / 7

Divide the values

Constant speed = 0. 19 miles/minutes

When distance 1 mile, time taken = x minutes

Constant speed = 1/x miles/minutes

If 1. 3 miles = 7 minutes

Then, 1 mile = x

cross multiply

x = 7/1. 3

x = 5. 38 minutes

Hence, the constant speed is 0. 19 miles/minutes

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The transformations to the parent function are given as follows:

The parent function for this problem is given as follows:

y = 1/x.

The transformed function for this problem is given as follows:

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

Hence the  transformations to the parent function are given as follows:

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Answer:

A, there is a 50% chance of getting heads than tails.

Step-by-step explanation:

B would have a 12% chance of that.

C would have a 43% chance since it kind of still in the winter zone but near summer...