if something costs 14.50 and I give 15 pound how much do I get back​

Answer:

x = 50° , y = 40°

Step-by-step explanation:

x and 40° form a right angle and sum to 90° , that is

x + 40° = 90° ( subtract 40° from both sides )

x = 50°

x and y form a right angle and sum to 90° , then

x + y = 90°

50° + y = 90° ( subtract 50° from both sides )

y = 40°

The solution to the equation is (a) -2.

To solve the equation log(3x) = log(2) + log(x - 1), we can use the properties of logarithms.

According to the logarithmic property log(a) + log(b) = log(ab), we can rewrite the equation as:

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

Since the logarithm function is one-to-one, we can equate the expressions inside the logarithms:

3x = 2(x - 1)

Expanding the equation:

3x = 2x - 2

Bringing all terms to one side:

3x - 2x = -2

x = -2

Therefore, the solution to the equation is x = -2.

The correct answer is (a) -2.

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According to the given percentages, 18% of the students at the orientation are male arts majors.

The statement correctly calculates that 60% of the students at the orientation are men and 30% are arts majors.

To determine the percentage of students who are male arts majors, we multiply these two percentages together: 60% x 30% = 18%. Therefore, 18% of the students at the orientation are male arts majors.

This calculation follows the principles of probability, where the intersection of two events (being a male and being an arts major) is determined by multiplying the probabilities of each event occurring individually.

In this case, it results in 18% of the students meeting both criteria.


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Question - Sixty percent of the students at an orientation are men and 30% of the students at the orientation are arts majors. Therefore, 60% X 30% = 18% of the students at the orientation are male arts majors.

Answer:

*** "and" means multiply

2/9

Step-by-step explanation:

*** "and" means multiply

spinning a vowel is 1/3

not spinning a 1 is 2/3

1/3 times 2/3 is 2/9

Aman can write -17 as the sum of two numbers, -8.5 and -8.5, so that when one of the numbers (-8.5) is added to 9, it will equal 0.

To write -17 as the sum of two numbers so that one of the numbers, when added to 9, will equal 0, Aman needs to think of a number that, when added to 9, will equal 17.

Step 1: Aman needs to find the absolute value of -17, which is 17.

Step 2: Aman needs to divide 17 by 2, which gives 8.5.

Step 3: Aman needs to think of the two numbers that add up to -17 and have a difference of 8.5. One number would be -8.5 and the other number would be -8.5 - 8.5, which equals -17.

Step 4: Aman can substitute these numbers into the blanks.

-17 + 9 = -8.5 + (-8.5) + 9
-17 + 9 = -8.5 + (-8.5) + 9
-17 + 9 = -8.5 + 0

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The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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The Laplace transform of the output angular velocity \(\Omega(s)\) is given by:

\[\Omega(s) = \frac{10}{s + 6} \times V(s)\]

The Laplace transform of the output angular velocity \(\Omega(s)\) is given by:

\[\Omega(s) = \frac{10}{s + 6} \times V(s)\]

Given the transfer function for the DC motor system:

\[G_v(s) = \frac{\Omega(s)}{V(s)} = \frac{10}{s + 6}\]

where \(V(s)\) and \(\Omega(s)\) are the Laplace transforms of the input voltage and angular velocity, respectively.

To obtain the output Laplace transform from the input Laplace transform, we multiply the input Laplace transform by the transfer function.

Thus, to obtain the Laplace transform of the angular velocity \(\Omega(s)\) from the Laplace transform of the input voltage \(V(s)\), we multiply the Laplace transform of the input voltage \(V(s)\) by the transfer function:

\[\frac{\Omega(s)}{V(s)} \times V(s) = \frac{10}{s + 6} \times V(s)\]

Hence, the Laplace transform of the output angular velocity \(\Omega(s)\) is given by:

\[\Omega(s) = \frac{10}{s + 6} \times V(s)\]

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The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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The cost of a carpet of the same quality, measuring 5m by 3m is $129.

We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.

In this question, it is given that a carpet measuring 4m × 2.5m costs $86. That means the 10m² area of carpet costs $86 if we divide 10 by both the cost and area of the carpet we will find that, 1 m² area of carpet will cost $8.6. So the cost of a carpet of 5m × 3m will be the area of the carpet multiplied by the cost of the carpet per 1 m² i.e, 15m² of carpet will cost $8.6 × 15 which is equal to $129.

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Answer:

Jeremy's acceleration is about \(1\,\frac{m}{s^2}\)  at t =10 s

His average speed is about 44.5 m/s in this section of his jump approximating with points on the curve (under-estimate)

His average speed is about 46 m/s if using the tangent line (over estimate)

Step-by-step explanation:

Jeremy's acceleration can be estimated by the curve's derivative at that point. That is the slope of the tangent line to the velocity curve at x = 10 sec. Please see attached image where the tangent line is drawn in orange, and the points to use to calculate its slope are drawn in green.

These points are : (6, 42) and (14,50) which using the slope formula give:

\(slope=\frac{y_2-y_1}{x_2-x_1}= \frac{50-42}{14-6}=\frac{8}{8} \frac{m}{s^2} = 1\,\frac{m}{s^2}\)

So his acceleration at that point is about \(1\,\frac{m}{s^2}\)

Now, using about the same interval of x-values (from 6 to 14), the corresponding speeds are approximately: 40 (for time 6 seconds) and 49 (for time 14 seconds (look for the red dots on the attached image). Since  the average velocity is given by the integral of the function between those points divided by the length of the interval where it is calculated:

\(v_{average}=\frac{area}{interval\,\,length}\)

and we don't have the actual velocity function to estimate the integral, we can approximate this area by that of a trapezoid that connects the red dots with the bottom of the horizontal axis (see red trapezoid in the image). Clearly from the image, this approximation would give us an under-estimate of the actual average speed.

The area of this trapezoid is: approximately:

\(Trapezoid\,\, area=(49+40)\,8/2=356\)

Then the average velocity estimated from it is:

\(v_{average}=\frac{356}{8} \frac{m}{s} =44.5\,\frac{m}{s}\)

If the area is approximated instead with the trapezoid form by the green points we used to calculate the acceleration (this would give us an over-estimate):

\(Trapezoid\,\, area=(50+42)\,8/2=368\)

Then the average velocity estimated from it is:

\(v_{average}=\frac{368}{8} \frac{m}{s} =46\,\frac{m}{s}\)

while his actual instantaneous velocity seems to be about 46 m/s from the graph

Answer:

a) 1.0

b) s=45

Step-by-step explanation:

The measure of angle JKN is 177 - x.

To find angle JKN, we need to use the given information that angle NKL is equal to 7x-9 and angle JKM is equal to x+3.

Since angle JKM and angle JKN are adjacent angles, we know that the sum of their measures is 180 degrees.

So, we can set up an equation: (angle JKM) + (angle JKN) = 180

Substituting the given values, we have: (x+3) + (angle JKN) = 180

Now we can solve for angle JKN by isolating it on one side of the equation.

First, we combine like terms: x + 3 + (angle JKN) = 180

Next, we simplify: angle JKN = 180 - x - 3

Finally, we simplify further: angle JKN = 177 - x

Therefore, the measure of angle JKN is 177 - x.

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Answer:

 10x+7y = -8

Step-by-step explanation:

Standard form is Ax + By + C = 0 or Ax + By = C.

The first step is everything is multipled by 7, witch gives you 7y=-10x-8.

To solve that, 10x to both sides must be added, to get 10x+7y-8

Explanation:

First we multiply everything by 7 to clear out the denominators.

We get to 7y = -10x - 8

Then add 10x to both sides to arrive at 10x+7y = -8

Standard form is Ax+By = C where A,B,C are integers

In this case we have: A = 10, B = 7, C = -8

Some math textbooks insist that A > 0.

Answer:

4/23

Step-by-step explanation:

Probability of choosing a red marble = # of red marbles / total # of marbles

We are told that there are 4 red marbles and 19 blue marbles

So the # of red marbles = 4

And the total # of marbles = 4 + 19

4 + 19 = 23

So there are a total of 23 marbles

Recall that probability of choosing a red marble is equal to # of red marbles / total # of marbles

Hence, the probability of choosing a red marble is 4/23

Note: 4/23 is already in it's simplest form so no simplifying has to be done.

Answer:

14/33

Step-by-step explanation:

There are 14 red marbles and 19 blue marbles, meaning that there are 33 marbles in all:

14 + 19 = 33

You are randomly choosing a red marble out of the total amount of marbles. 14/33

Note that you cannot simplify the fraction anymore, and so 14/33 is your answer.

~

Answer:

18

Step-by-step explanation:

Take the original price and multiply by the percent

45*60%

45*.60

27  - this is the amount of the reduction

Subtract this amount from the original price to get the new amount

45-27

18 - this the new price

Answer:

range = 51

Step-by-step explanation:

Range = biggest - smallest

62 - 11 = 51

The greatest common divisor of 6, 14, and 21 is 1, and it can be written as 6(0) 14(0) 21(1).

To find the greatest common divisor (GCD) of 6, 14, and 21 and write it in the form 6r 14s 21t, we can use the Euclidean algorithm.

Step 1: Find the GCD of 6 and 14.
- Divide 14 by 6: 14 ÷ 6 = 2 remainder 2
- Replace 14 with 6 and 6 with 2: Now we have 6 and 2.
- Divide 6 by 2: 6 ÷ 2 = 3 remainder 0
- Since the remainder is 0, the GCD of 6 and 14 is 2.

Step 2: Find the GCD of the result from step 1 (2) and 21.
- Divide 21 by 2: 21 ÷ 2 = 10 remainder 1
- Replace 21 with 2 and 2 with 1: Now we have 2 and 1.
- Divide 2 by 1: 2 ÷ 1 = 2 remainder 0
- Since the remainder is 0, the GCD of 2 and 21 is 1.

Therefore, the GCD of 6, 14, and 21 is 1. In the given form 6r 14s 21t, r would be 0, s would be 0, and t would be 1.

So, the GCD of 6, 14, and 21 is 1, and it can be written as 6(0) 14(0) 21(1).

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Two triangles are congruent if all pairs of corresponding sides and angles are congruent. Using transformations, such as rotation, we can verify if two triangles are congruent.

In the given diagram, we know that JM¯¯¯¯¯¯¯¯≅PR¯¯¯¯¯¯¯¯, MK¯¯¯¯¯¯¯¯¯¯≅RQ¯¯¯¯¯¯¯¯, and KJ¯¯¯¯¯¯¯¯≅QP¯¯¯¯¯¯¯¯. To complete the sentences correctly, we need to drag the following tiles:

Using transformations, such as a rotation, it can be verified that △JKM is congruent to △PQR if all pairs of corresponding angles are congruent. In any pair of triangles, if it is known that all pairs of corresponding sides are congruent, then the triangles are congruent.

Using transformations, specifically rotations, we can verify whether two triangles are congruent or not. If all the pairs of corresponding angles are congruent, then the two triangles are said to be congruent.

In a congruent pair of triangles, each side, as well as each angle, matches the corresponding angle or side of the other triangle.

When all the pairs of corresponding sides are congruent in a pair of triangles, then we can conclude that they are congruent.

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The value of sin(π/6) is 0.50.

Trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given the triangle DEF

and ∠E = π/6

converting the radian to the degree,

for conversion put π = 180°

π/6 = 180/6

π/6 = 30°

to find sin(π/6)

sin(π/6) = sin30 = 1/2

sin(π/6) = 0.50

Hence value for the condition is 0.50.

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Answer:

D. a shift to the right

Step-by-step explanation:

As my teacher use to say, you run the opposite way of your crazy ex. So, if the number is negative, it moves to the right. If it's positive, it moves to the left. If it's a power, it goes up or down.

// have a great day //

Answer:

D, shift to the right

Step- by-step explanation:

When equations or functions have numbers that are subtracting it's shifted to the right

When they are adding they are shifted to the left

Hope this helps!

The parameters' values would be known if we had access to data that covered the entire population, so no statistical inference would be necessary is True.

As per the question given,  

True. If we had access to data that included the entire population, we would have the complete information about the population parameters, and no statistical inference would be needed. However, in practice, it is often not possible or feasible to obtain data on the entire population, and statistical inference is required based on samples from the population.

All citizens present in, or temporarily absent from, a country, as well as foreigners permanently resident in a country, are characterised as population. This statistic depicts the average number of people who reside in a certain location. The yearly changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.

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The internal rate of return (IRR) is a financial metric used to evaluate the profitability of an investment project. It is the discount rate that makes the net present value (NPV) of the project equal to zero. In other words, it is the rate at which the present value of the cash inflows equals the present value of the cash outflows.

To determine whether Nadia should accept the investment in the new factory, we need to compare the IRR of the project with the required rate of return, which is 14.25 percent in this case.

If the IRR is greater than or equal to the required rate of return, then Nadia should accept the investment. This means that the project is expected to generate a return that is at least as high as the required rate of return.

If the IRR is less than the required rate of return, then Nadia should reject the investment. This suggests that the project is not expected to generate a return that is high enough to meet the required rate of return.

So, to determine whether Nadia should accept the investment, we need to calculate the IRR of the project and compare it with the required rate of return. If the IRR is greater than or equal to 14.25 percent, then Nadia should accept the investment. If the IRR is less than 14.25 percent, then Nadia should reject the investment.

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Bending moment curve equation below point A will be:

M = 15x - 3x² for 0 ≤ x ≤ b

Determination of shear and bending moment curves.

For the beam and loading shown, we can do the following:

Equation of shear curve (above point A):V = RA - w.x

For x = a,V = RA - w.a

For x = b,V = RA - w.b

Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b

Equation of shear curve (below point A):

V = RA - w.x

For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a

The shear curve equation becomes;

V = 15k for 0 ≤ x ≤ a

V = 15 - 6a for a ≤ x ≤ b

Equation of bending moment curve (above point A):

M = RAx - ½w.x²For 0 ≤ x ≤ a,

M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,

M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²

The bending moment curve equation above point A becomes:

M = 15x - 3x² for 0 ≤ x ≤ a

M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b

Equation of bending moment curve (below point A):

M = RAx - ½w.x²For 0 ≤ x ≤ b,

M = 15x - ½(6x²) = 15x - 3x²

The bending moment curve equation below point A becomes;

M = 15x - 3x² for 0 ≤ x ≤ b

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A truth table is a table used in logic to systematically represent the possible truth values of a logical expression.

To construct truth tables for the provided statement forms, we need to consider all possible combinations of truth values for the individual propositional variables involved.

Let's go through each statement form and build the respective truth tables:

(a) p∧∼q:

p q ∼q p∧∼q

T T     F     F

T F   T     T

F T   F     F

F F   T     F

(b) ∼(p∧q)∨(p∨q):

p q p∧q ∼(p∧q) p∨q ∼(p∧q)∨(p∨q)

T T   T       F    T            T

T F   F       T    T            T

F T   F       T    T              T

F F   F       T    F             T

(c) p∧(q∧r):

p q r q∧r p∧(q∧r)

T T T   T     T

T T F   F     F

T F T   F        F

T F F   F     F

F T T   T     F

F T F   F     F

F F T   F     F

F F F   F     F

(d) p∧(∼q∨r):

p q r ∼q ∼q∨r p∧(∼q∨r)

T T T   F      T               T

T T F   F      F               F

T F T   T      T               T

T F F   T      T               T

F T T   F      T               F

F T F   F      F               F

F F T   T      T               F

F F F   T      T               F

These truth tables display all the possible combinations of truth values for the propositional variables p, q, and r, and the resulting truth values for each statement form based on the logical operations involved.

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Answer:

The solution to the system is (-2 1/3, -2 2/3)

Step-by-step explanation:

Answer:

.15¢

Step-by-step explanation:

1.20$ total divided by 8 and its .15¢

Answer:

1/4 or 0.25 of a lemon is being used per cup

Step-by-step explanation:

Answer:

its A.

Step-by-step explanation:

Answer:

a

Step-by-step explanation: