Justine paid 35.70 for a lego set that was on sale. The original price of the set was $42.00 what is the percentage discount for the cost of the lego set?

By applying the concept of central and extreme scores, it can be concluded that a score of x = 85 would be considered a central score in population 1, and an extreme score in populations 2 dan 3.

A central score is a score that is near the middle of the distribution, while an extreme score is a score that is far out in the tail of the distribution.

In order to determine whether a score of x = 85 is a central score or an extreme score for each of the following populations, we need to look at the distribution of scores in each population.

Overall, whether a score of x = 85 is considered a central score or an extreme score depends on the distribution of scores in the population. If the scores are evenly distributed and x = 85 is near the middle of the distribution, it would be considered a central score. However, if the scores are clustered around a different value and x = 85 is far out in the tail of the distribution, it would be considered an extreme score.

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A rock that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge is a(n)  ventifact:

A rock refers to the solid portion of the earth crust which contains minerals. There are three types of rocks; The sedimentary rock: They are formed from dead plants, dead animals, sand etc.

The metamorphic rock: They are formed from previously existing rocks. The igneous rock: They are formed from the solidification of the molten magma.

Hence, ventifact are rock  that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge.

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Answer:

x=13

Step-by-step explanation:

The DC current gain (βdc) of the transistor is 73.

The DC current gain (βdc) of a transistor is the ratio of the collector current (IC) to the base current (IB) at DC conditions. Therefore, to determine the βdc of a transistor with IB = 50 µA and IC = 3.65 mA, we simply substitute these values into the equation:

βdc = IC / IB

βdc = 3.65 mA / 50 µA

βdc = 73

Therefore, the DC current gain (βdc) of the transistor is 73.

This result indicates that for every 1 µA of base current, the transistor can allow 73 µA of collector current to flow. A high βdc value indicates that the transistor can provide significant amplification in a circuit. In addition, the βdc value is essential in selecting the appropriate biasing resistors and determining the operating point of the transistor in amplifier circuits.

Thus, by determining the βdc value, we can gain valuable insights into the performance characteristics of a transistor and how it can be used in various circuit designs.

Therefore, The DC current gain (βdc) of the transistor is 73.

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Answer:

112 ft

Step-by-step explanation:

9) Here, we are finding the area of a triangle. The equation for area is:

\(A = \frac{1}{2} *b*h\)

Where A is area, b is the base, and h is height.

\(A = \frac{1}{2} * 16 * 14\)

\(A = 112\)

Answer:

So if he's paid £1500 and he's getting an increase of 3%, we only need to calculate the 3% of 1500 and then add it what he's paid now (£1500)

To calculate the x% of a number, we multiply the number by \(\frac{x}{100}\)%.

So, if we want to calculate the 3%, we need to multiply by \(\frac{3}{100}\)%, by 0.03:

1500 * 0.03 = £45

So now, we know he'll be paid £45 more than the last month, so we sum what he got before (£1500) plus those £45.

1500 + 45 = £1545

Answer:

Answer to x is 3. so it would be x = 3

Answer:

x=3

Step-by-step explanation:

36x+2-2=110-2

36x=108

36x/36=108/36

x=3

Answer:

I think it is true, please let me know if I am wrong:)

The angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

The given values are:

AD = 150 mm

AB = 40 mm

CD = 80 mm

The crank AB rotates at 120 r.p.m. clockwise.

BC and AD are of equal length.

To find:

The angular velocity of link CD when angle BAD = 60°.

From the given data, we have to first find the value of angle BCD.

Angle BCD can be calculated as follows:

AB = 40 mm

BC = AD

= 150 mm

In ΔABC,

By using Cosine rule;

AC² = AB² + BC² - 2 × AB × BC × Cos ∠ABC∴ AC² = (40)² + (150)² - 2 × 40 × 150 × Cos 180°

∴ AC = 160.6 mm

In ΔBCD,

By using Cosine rule;

BD² = BC² + CD² - 2 × BC × CD × Cos ∠BCD

∴ BD² = (150)² + (80)² - 2 × 150 × 80 × Cos ∠BCD

In ΔABD,By using Cosine rule;

BD² = AB² + AD² - 2 × AB × AD × Cos ∠BAD

∴ BD² = (40)² + (150)² - 2 × 40 × 150 × Cos 60°

∴ BD = 184.06 mm

In ΔABD,By using Sine rule;

AB / Sin ∠BAD = BD / Sin ∠ABD

∴ Sin ∠ABD = BD × Sin ∠BAD / AB

∴ ∠ABD = Sin⁻¹ [BD × Sin ∠BAD / AB]

∴ ∠ABD = Sin⁻¹ [184.06 × Sin 60° / 40]

∴ ∠ABD = 87.2°∠ACD = ∠ABD - ∠ACB

∴ ∠ACD = 87.2° - 180°

∴ ∠ACD = - 92.8°∠BCD

= 180° - ∠ACD

∴ ∠BCD = 180° - (- 92.8°)

∴ ∠BCD = 272.8°

As we know that for four-bar mechanism, we have a formula for finding the angular velocity of link CD.

ωCD / Sin ∠BCD = ωAB / Sin ∠BADωCD / Sin 272.8°

= ωAB / Sin 60°

Substituting the values, ωCD / Sin 272.8° = ωAB / Sin 60°ωCD

= ωAB × Sin 272.8° / Sin 60°

But, ωAB = 2 × π × N / 60

= 2 × π × 120 / 60

= 4 × π rad/s

∴ ωCD = 4 × π × Sin 272.8° / Sin 60°ωCD

= 21.16 rad/s

Therefore, the angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

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a) 8780

b) i) 1159   ii) 1990

c) 9611

a) The total number of workers at the beginning is 2340 + 3455 + 675 + 960 + 1350 = 8780 workers.

b)

i) The first two companies laid off 1 worker for every 5 workers, so for the first company (2340 workers) this means 2340/5 = 468 workers lost their job. For the second company (3455 workers) this means 3455/5 = 691 workers lost their job.

In total, 468 + 691 = 1159 workers lost their job.

ii) The other three companies recruited 2 new workers for every 3, so for the third company (675 workers) this means 6752/3 = 450 new workers were recruited. For the fourth company (960 workers) this means 9602/3 = 640 new workers were recruited. For the fifth company (1350 workers) this means 1350×(2/3) = 900 new workers were recruited.

In total, 450 + 640 + 900 = 1990 new workers were recruited.

c) The total number of workers finally is 8780 - 1159 + 1990 = 9611 workers.

The complete question is -

Five companies employed 2340, 3455, 675, 960, and 1350 workers. The first two companies laid off 1 worker for every 5 workers, while the other three recruited 2 new workers for every 3.

a) What was the total number of workers at the beginning?

b) How many people: i) Lost job ii) Got a job?

c) What was the total number of workers finally?

The probability that for a randomly chosen integer n between 1 and 10 inclusive there exist no real solutions to the equation x^2 + 5 = n is 3/10.

we can first find the values of n for which there are real solutions to the equation x^2 + 5 = n. We can do this by rearranging the equation to get x^2 = n - 5 and then seeing that there are real solutions only if n - 5 is non-negative, i.e. n >= 5.

Since we are choosing a random integer between 1 and 10 inclusive, there are 10 possible values for n. Out of these, only 5, 6, 7, 8, 9, and 10 are greater than or equal to 5, which means that there are real solutions to the equation for these values of n. Therefore, there are only 6 possible values of n for which there exist no real solutions to the equation.

Therefore, the probability of choosing one of these 6 values of n is 6/10, which simplifies to 3/5. However, we need to find the probability of choosing one of the values of n for which there exist no real solutions to the equation, which is the complement of the probability of choosing one of the values of n for which there are real solutions. This complement is 1 - 6/10, which simplifies to 2/5.

Therefore, the main answer to the question is that the probability that for a randomly chosen integer n between 1 and 10 inclusive there exist no real solutions to the equation x^2 + 5 = n is 2/5.

The probability that for a randomly chosen integer n between 1 and 10 inclusive there exist no real solutions to the equation x^2 + 5 = n is 2/5. This can be found by first determining the values of n for which there are real solutions to the equation, and then finding the complement of this probability.

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Answer:

4

Step-by-step explanation:

Answer:

Speed = 0.895 feet per minute

Step-by-step explanation:

Distance covered by the sloth = 38 of a foot

                                                   = \(\frac{1}{38}\) foot

Time taken to move this distance = 34 of a minute

                                                        = \(\frac{1}{34}\) minute

Since, formula for the speed is,

Speed = \(\frac{\text{Distance covered}}{\text{Time taken}}\)

           = \(\frac{\frac{1}{38}}{\frac{1}{34}}\)

           = \(\frac{1}{38}\times \frac{34}{1}\)

           = \(\frac{17}{19}\)

           = 0.895 feet per minute

By following below steps, you will be able to determine which triangle represents the image of triangle XYZ after the given transformations.

To determine which triangle represents the image of triangle XYZ after it was reflected across line M and then dilated to form a similar triangle, you should follow these steps:

1. Identify the reflection: Find the image of triangle XYZ after reflecting it across line M. The reflected triangle will have the same shape and size, but its orientation and position will be changed.

2. Identify the dilation: From the reflected triangle, find the image that represents a similar triangle by checking if all corresponding angles are equal and the side lengths are proportional. This triangle will have the same shape as the reflected triangle, but its size may be different due to dilation.

By following these steps, you will be able to determine which triangle represents the image of triangle XYZ after the given transformations.

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Answer: B

Step-by-step explanation:

The equation that represents the graph of y = x² + 2x - 3 moved 3 units to the left is: D. y = (x+3)² + 2(x+3)-3

What is graph equation?

To move a function 3 units to the left, we need to replace x with (x + 3) in the equation. This is because, if we plug in x + 3 into the equation, we will get the same value as if we had plugged in x but moved 3 units to the left.

So, starting with the original equation y = x² + 2x - 3, we replace x with (x + 3):

y = (x + 3)² + 2(x + 3) - 3

Now, we can simplify this equation to get it into standard form:

y = x² + 8x + 18

Therefore, the equation that represents the graph of y = x² + 2x - 3 moved 3 units to the left is:

D. y = (x+3)² + 2(x+3)-3

which simplifies to:

y = x² + 8x + 18.

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Option (C) It means the technician charges a fixed amount of $75 for the repair is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

The graph of the equation is given:

From the graph the equation of the straight line will be:

y = 45x + 75

For the y-intercept plug x = 0

y = $75

The y-intercept represents the technician charging a fixed amount of $75 for the repair.

Thus, option (C) It means the technician charges a fixed amount of $75 for the repair is correct.

The graph is attached is in the picture.

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For any integer a, 14 does not divide (33 - 5) or 21 does not divide (2a + 3).

There exists an integer a such that 14 divides (33 - 5) or 21 divides (2a + 3).

There exist odd integers a and b such that 4 does not divide (3a^2 + b^2).

For all odd integers a and b, 4 does not divide (353^2 + b^2).

To prove or disprove the statement "For any integer a, 14 | (33 - 5) or 21 | (2a + 3)", we can evaluate the expressions for different values of a. Let's try a = 1 and a = 2:

For a = 1:

(33 - 5) = 28 and

(2a + 3) = 5. Neither 14 divides 28 nor 21 divides 5.

For a = 2:

(33 - 5) = 28 and

(2a + 3) = 7. Neither 14 divides 28 nor 21 divides 7.

From these examples, we can see that the statement is false. For any integer a, neither 14 divides (33 - 5) nor 21 divides (2a + 3).

To prove or disprove the statement "There exists an integer a such that 14 | (33 - 5) or 21 | (2a + 3)", we can again evaluate the expressions for different values of a. Let's try a = 4:

For a = 4:

(33 - 5) = 28 and

(2a + 3) = 11. Neither 14 divides 28 nor 21 divides 11.

From this example, we can conclude that the statement is false. There does not exist an integer a such that 14 divides (33 - 5) or 21 divides (2a + 3).

To prove or disprove the statement "There exist odd integers a and b such that 4 | (3a^2 + b^2)", we can try different combinations of odd integers for a and b and check if 4 divides (3a^2 + b^2). Let's try a = 1 and b = 1:

For a = 1 and

b = 1:

(3a^2 + b^2) = (3 * 1^2 + 1^2) = 4. In this case, 4 divides (3a^2 + b^2).

Therefore, we have found an example where 4 divides (3a^2 + b^2) for odd integers a and b. The statement is true.

To prove or disprove the statement "For all odd integers a and b, 4 | (353^2 + b^2)", we can again try different combinations of odd integers for a and b and check if 4 divides (353^2 + b^2). Let's try a = 1 and b = 1:

For a = 1 and

b = 1:

(353^2 + b^2) = (353^2 + 1^2). In this case, 4 does not divide (353^2 + 1^2).

Therefore, we have found a counterexample where 4 does not divide (353^2 + b^2) for odd integers a and b. The statement is false.

For any integer a, 14 does not divide (33 - 5) or 21 does not divide (2a + 3).

There does not exist an integer a such that 14 divides (33 - 5) or 21 divides (2a + 3).

There exist odd integers a and b such that 4 divides (3a^2 + b^2).

For all odd integers a and b, 4 does not divide (353^2 + b^2).

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Multiplication and division of regular numbers are the same as fractions and we will learn them with the multiplication and division of rational numbers worksheet.

To do the multiplication, first find the greatest common divisor of the numerator and the denominator. The factors are then grouped together so that the score equals one. Then multiply by the remaining factors. To divide, first rewrite the division as multiplication by the inverse of the denominator.

Cuemath's interactive math worksheets contain visual simulations to help your child visualize the concepts being taught, "see things as they really are, and reinforce learning from them". The Rational Numbers Multiplication and Division Worksheet follows a step-by-step learning process that helps students better understand concepts, identify errors, and eventually develop strategies for solving future problems.

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The 95% confidence interval for the difference between the two population proportions is (0.1, 0.16).

The parameter being estimated is the difference between two population proportions.

To find the 95% confidence interval for this parameter, we can use the margin of error formula:

where z is the z-score for the desired level of confidence (95% in this case), p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

We know that the difference between the sample proportions (phat1 - phat2) is 0.13, and the margin of error is 3%. Since the sampling distribution is assumed to be symmetric and bell-shaped, we can assume that the standard deviation of the difference between the sample proportions is equal to the standard error, which can be estimated by the margin of error.

Setting up an equation using the margin of error formula, we get:

We don't know the sample sizes or the sample proportions, so we can't solve for the confidence interval directly. However, we can use a conservative estimate for the standard deviation of the difference between the sample proportions:

Using this formula, we get:

This is approximately equal to the margin of error, so we can assume that z ≈ 1.96 (the z-score for 95% confidence) and use the formula:

Therefore, the 95% confidence interval for the difference between the two population proportions is (0.1, 0.16).

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In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

Note that by examining the the image if ∠EDA≅∠HCB, the two lines can never intersect even if they go a longer distance.

The reason why is that there are no parallel lines on it and as such, they cannot intercept.

Hence, In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

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Thus we only take the positive root:x = 27/8 = 3.375Answer: 3.375 feet.

The problem states that a rectangular garden that measures 50 feet wide and 45 feet long is enclosed by a uniform width of x feet paved path. To solve the problem,

we can use the formula of the combined area of the garden and the paved path and equate it to 2646 square feet. The combined area is computed by adding the area of the garden and the area of the paved path.

Garden area:Length of garden = 45 ftWidth of garden = 50 ftArea of garden = Length x Width= 45 x 50= 2250 square feet

Paved path:

If the garden has a uniform width of x feet paved path, then the width of the paved path would be x + 2x + x= 4x. The width is multiplied by 2 because there are two widths surrounding the garden.

Length of paved path = length of garden + 2 (width of paved path)= 45 + 2 (4x)= 8x + 45Width of paved path = width of garden + 2 (width of paved path)= 50 + 2 (4x)= 8x + 50

The area of the paved path is computed by subtracting the area of the garden from the combined area.Area of paved path = Combined area - Garden area2646 square feet

= (8x + 45) (8x + 50) - 2250= 64x² + 760x + 675

We then solve for the value of x by factoring the quadratic equation.2646 square feet = 64x² + 760x + 6752646 - 2646

= 64x² + 760x + 675 - 264664x² + 760x - 1971

= 0(8x - 27) (8x + 73) = 0

The value of x cannot be negative,

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the graph of f(x) = x^3 - 3x^2 - 9x + 5 is concave down on the interval (-∞, 1), concave up on the interval (1, +∞), and has a point of inflection at x = 1.

To determine the intervals on which the graph of a function is concave up or concave down, we need to analyze the second derivative of the function. The concavity of a function can change at points where the second derivative changes sign.

Here's the step-by-step process to find the intervals of concavity and points of inflection:

Find the first derivative of the function, f'(x).

Find the second derivative of the function, f''(x).

Set f''(x) equal to zero and solve for x. The solutions give you the potential points of inflection.

Determine the intervals between the points found in step 3 and evaluate the sign of f''(x) in each interval. If f''(x) > 0, the graph is concave up; if f''(x) < 0, the graph is concave down.

Check the concavity at the points of inflection found in step 3 by evaluating the sign of f''(x) on either side of each point.

Let's go through an example to illustrate this process:

Example: Consider the function f(x) = x^3 - 3x^2 - 9x + 5.

Find the first derivative, f'(x):

f'(x) = 3x^2 - 6x - 9.

Find the second derivative, f''(x):

f''(x) = 6x - 6.

Set f''(x) equal to zero and solve for x:

6x - 6 = 0.

Solving for x, we get x = 1.

Therefore, the potential point of inflection is x = 1.

Determine the intervals and signs of f''(x):

Choose test points in each interval and evaluate f''(x).

Interval 1: (-∞, 1)

Choose x = 0 (test point):

f''(0) = 6(0) - 6 = -6.

Since f''(0) < 0, the graph is concave down in this interval.

Interval 2: (1, +∞)

Choose x = 2 (test point):

f''(2) = 6(2) - 6 = 6.

Since f''(2) > 0, the graph is concave up in this interval.

Check the concavity at the point of inflection:

Evaluate f''(x) on either side of x = 1.

Choose x = 0 (left side of x = 1):

f''(0) = -6.

Since f''(0) < 0, the graph is concave down on the left side of x = 1.

Choose x = 2 (right side of x = 1):

f''(2) = 6.

Since f''(2) > 0, the graph is concave up on the right side of x = 1.

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To study the effect of elevation above sea level on air temperature and air pressure while hiking from Heart Lake (elevation 2,179 feet) to the peak of Mt. Marcy (elevation 5,344 feet) in the Adirondack Mountains, the students should use the following instruments to collect their data:

1. Thermometer: A thermometer is an instrument used to measure air temperature. The students should take temperature readings at various elevations during their hike to determine the relationship between elevation and temperature.

2. Barometer: A barometer is an instrument used to measure air pressure. The students should take air pressure readings at various elevations during their hike to determine the relationship between elevation and air pressure.

By using these two instruments and comparing the data collected at different elevations, the students can study the effect of elevation on air temperature and air pressure.

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Answer:

1a) 25, 1b) 3, 2a) 14, 2b) 4

Step-by-step explanation:

1a)

x/5 + 10 = 15

Subtract 10 from both sides:

x/5 = 15 - 10

x/5 = 5

Multiply both sides by 5:

x = 5 * 5

x = 25

1b)

25x + 26 = 101

Subtract 26 from both sides:

25x = 101 - 26

25x = 75

Divide both sides by 25:

x = 75/25

x = 3

2a)

Four less than a number is 10.

Let's call the number x. This means:

x - 4 = 10

Now add 4 to both sides:

x = 10 + 4

x = 14

2b)

The product of three and a number equals 12.

Let's call the number x. This means:

3 * x = 12

Now divide both sides by 3:

x = 12/3

x = 4

Answer:

Step 3: The measure of angle DAB is 60°. Reason: Since DAE is a right angle, and EAB is 30 degrees, 90 - 30 is 60. (Just find the reason that is related to this statement).

Step 4: The measure of angle ABC is 130°. Reason: Same-side Interior Angles Theorem

Step-by-step explanation:

The common ratio of the corresponding sides of the given triangles

indicate that the triangles are similar.

Reasons:

The given relationship are;

The ratio of each side of ΔAOB to the corresponding side of ΔCOD is constant, therefore;

ΔAOB is similar to ΔCOD by Side-Side-Side similarity postulate

Which gives;

ΔAOB ~ ΔCOD

Therefore, the three angles of ΔAOB are congruent to their corresponding angles of ΔCOD, which gives;

(CASTC); Corresponding Angles of Similar Triangles are Congruent

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The 95%-confidence interval (45.76%, 50.23%) is a confidence interval for the percentage of listeners in the sample who would accept the invitation to enter the competition.

This means that if we were to repeat the same process of randomly selecting 500 listeners and offering them the chance to enter the competition, we would expect the true percentage of listeners who would accept the offer to fall within this interval 95% of the time. It is important to note that this interval only applies to the sample of 500 listeners who were selected for the promotion, and we cannot generalize these results to all listeners of the radio station. However, this information can still be useful for the radio station in terms of understanding the response rate to promotions among a specific group of its listeners.

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Answer:

In order to go from the first point to the second, we need to rise from 4 to 7, i.e. by 3. We also need to run from -4 to -2, i.e. by 2. Therefore the slope is 32 .

Step-by-step explanation: