In a toy factory, 500 toys are made per minute. How many toys will be made in an hour??

Answer:

In a right triangle, one of the angles measures 90 degrees, and the other two angles are acute angles that add up to 90 degrees. Let's call the measures of the two acute angles x and y.

We know that x and y differ by 22 degrees. So we can set up an equation:

x - y = 22

We also know that x + y = 90, since the two acute angles add up to 90 degrees.

Now we can solve this system of equations for x and y. One way to do this is to add the two equations together, which eliminates y:

x - y + x + y = 22 + 90

2x = 112

x = 56

Now we can substitute x = 56 into one of the equations to find y:

x + y = 90

56 + y = 90

y = 34

Therefore, the measures of the two acute angles of the right triangle are 56 degrees and 34 degrees.

Answer: D) -20.99

Step-by-step explanation:

-4.97-2.36+-5.19-8.47 = -20.99

Answer: What grade are you in? Because I had to do this for my 8th or 9th grade year as a homeschooler.... I never had help...I had the same brand laptop and my studies were done on T4L......

Step-by-step explanation:

x2 +3x--3x+5 I think give me a few minutes to check myself

Answer:Independent = Her practice time. Dependent= Her lap time.

Step-by-step explanation: The more she practices the faster she can swim.

Your longitude in DMS is 135 degree. So the option D is correct.

This is because there are 12 hours left in the local time ( i.e. 12 hours noontime or mid-day).

As UT (or GMT) time is 9 p.m., there are 9 hours between GMT time and local time.

9 hours = 9 × 60 minutes = 540 minutes

Now, we know that:

Every four minutes, the Earth turns one degree.

Thus, 1-degree longitude difference = 4 minutes

Or, 4 minutes of time difference = 1 degree of longitude

Or, 1 minute of time difference = 1/4 degree of longitude

Or, 540 minutes of time difference = (1/4) × 540 degrees of longitude

540 minutes of time difference = 135 degrees of longitude

Also, we can infer that the current location is in the Western hemisphere because we know that it is 9 hours behind GMT (or UT) time.

Hence, the longitude of the current location = 135⁰

So the option 4 is correct.

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The complete question is:

Your chronometer is set for Greenwich Mean Time (GMT or Universal Tim, UT). High noon at your present location is 9 pm UT. What is your longitude in DMS (not decimal degrees)?

1. 30° 18'W

2. 30° 16'W

3. 30° 17'W

4. none of the above

The perimeter of the rectangular bedroom is 116 feet.

We know that the distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √(  (x₂ - x₁)² + (y₂ - y₁)²)

Here the corners of the room are at: (21, 18), (21, −7), (−12, −7) and (−12, 18)

Let's find the distances between these points:

d₁ = √(  (21- 21)² + (18 + 7)²) = 25

d₂ = √(  (21 + 12)² + (-7 + 7)²) = 33

d₃ = √(  (-12 + 12)² + (-7 - 18)²) = 25

d₄ =  = √(  (-12 - 21)² + (-7 + 7)²) = 33

The perimeter is the sum of these distances so we will get:

d₁ + d₂ + d₃ + d₄ = 25 + 33 + 25 + 33 = 116

The correct option is the first one.

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The average rate of change of f(x) from x = -3 to x = 6 is 7.

What is meant by average?

The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.

To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.

For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:

[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]

The value of the function at [tex]x = 6[/tex] is:

[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]

The difference in the function values is:

[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]

The difference in the input values is:

6 - (-3) = 9

Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:

average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]

So, the average rate of change of f(x) from x = -3 to x = 6 is 7.

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There are 243 ways to distribute five unlabeled balls into three labeled boxes.

Since the balls are unlabeled, we only need to consider the number of balls in each box, rather than which specific ball goes where.

We can use a combination approach to solve this problem. Let's think about distributing the balls one at a time. For the first ball, there are three boxes to choose from. For the second ball, there are also three boxes to choose from. We can continue this process until all five balls have been distributed.

So, for each ball, there are three choices of which box to put it in. Therefore, the total number of ways to distribute the five balls into the three labeled boxes is

3 x 3 x 3 x 3 x 3 = 3^5 = 243

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The function f(x) = x² - 7 is an example of a function that is neither even nor odd, as it does not exhibit either type of symmetry.

To determine whether a function is even, odd, or neither, we need to examine its algebraic form and look for a particular type of symmetry.

Let's apply this concept to the given function, f(x) = x² - 7. To determine whether f(x) is even or odd, we need to evaluate f(-x) and compare it to f(x).

f(-x) = (-x)² - 7 // substitute -x for x

= x² - 7 // simplify

Comparing f(-x) to f(x), we can see that they are not equal:

f(-x) = x² - 7

f(x) = x² - 7

Since f(-x) is not equal to f(x), the function is not even. To determine whether it is odd, we need to evaluate f(-x) + f(x) and see if the result is zero.

f(-x) + f(x) = (x² - 7) + (x² - 7) // substitute -x for x in the second term

= 2x² - 14

Since f(-x) + f(x) is not equal to zero for all values of x, the function is not odd either.

Therefore, we can conclude that the given function, f(x) = x² - 7, is neither even nor odd.

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The length of the reflected line segment is approximately 11.66 units.

The endpoints of the line segment mentioned in the question are (0,5) and (6,5). After the line segment is reflected across the x-axis, the endpoints of the reflected line segment are (0, -5) and (6, -5).To find the length of the reflected line segment, we will use the distance formula.

Using the distance formula:d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (5 - 5)²]d = √[36 + 0]d = √36d = 6 units. So the length of the original line segment is 6 units.Now, let's find the length of the reflected line segment.Using the distance formula :d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (-5 - 5)²]d = √[36 + 100]d = √136d = 11.66 (approx) units. So the length of the reflected line segment is approximately 11.66 units.

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The car was travelling with the speed of 183.5 mph when the brakes were applied.

The pace at which an object travels a certain distance can be described using the speed formula. The distance that a body travels in a certain amount of time is a common way to measure speed. M/s is the SI unit of speed. We will learn more about the speed formula and its uses in this section.

Let's continue and investigate the speed formula in this part in more detail. Speed can be expressed in a variety of ways, including m/s, km/hr, miles/hr, etc. [LT-1] is the dimensional formula for speed. A body's speed may be defined as how quickly it is going. The equation for a given body's speed may be written as,

Speed = Distance ÷ Time

We have the equation,

[tex]s=\frac{\sqrt{d} }{0.04}[/tex]

we have the value of d as 54

putting the value pf d in the equation we get,

[tex]s=\frac{\sqrt{54} }{0.04}[/tex]

s = 7.34/0.04

s = 183.5 mph

So the car was travelling with the speed of 183.5 mph when the brakes were applied.

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Complete question:

The speed that a vehicle was traveling, s, in miles per hour, when the brakes were first applied, can be estimated using the formula

[tex]s=\frac{\sqrt{d} }{0.04}[/tex] where d is the length of the vehicle's skid marks, in feet.

if skid marks on dry concrete are 54 feet long, how fast was the car traveling when the brakes were applied?

If Atharv has 10 nickels and dimes in his pocket, and they have a combined value of 70 cents, then he has 1 nickels and 4 dimes.

Let x be the number of nickels and y be the number of dimes. A nickel is worth 5 cents, and a dime is worth 10 cents. Therefore, we can write two equations:

x + y = 10 (since he has 10 coins in total)

5x + 10y = 70 (since the combined value of the coins is 70 cents)

We can simplify the second equation by dividing both sides by 5:

x + 2y = 14

Now we can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:

x + y = 10x = 10 - y

Now we can substitute this expression for x into the second equation:

x + 2y = 14(10 - y) + 2y = 14

Simplifying, we get:

10 + y = 14

y = 4

Therefore, Atharv has 5 - 4 = 1 nickel and 5 - 1 = 4 dimes.

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The probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.

To solve this problem, we can use the conditional probability formula:

P(A and B) = P(B|A) * P(A)

where:

P(A and B) is the probability that both events A and B occur

P(B|A) is the probability of event B given that event A has already occurred

P(A) is the probability of event A occurring

In this case, we want to find the probability of selecting a blue crayon on the second draw given that the first crayon selected was blue. So we have:

P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)

To find each of these probabilities, we can start by calculating the total number of possible outcomes:

Total number of outcomes = 8 crayons in the box

Next, we need to find the probability of selecting a blue crayon on the first draw:

P(blue on the first draw) = 2/8 = 1/4

After the first blue crayon has been set aside, there are only 7 crayons left in the box, so the probability of selecting a blue crayon on the second draw given that the first crayon was blue is:

P(blue on the second draw | blue on the first draw) = 1/7

Putting it all together:

P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)

= (1/7) * (1/4)

= 1/28

Therefore, the probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.

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Mobile ladder stands with a top step over 10 feet high and 20 inches or more in depth must be equipped with a safety cage or body belt and lanyard to provide protection against a fall.

The cage should be at least 30 inches tall and should be fully enclosed on all four sides. Additionally, the top step should be enclosed and provided with a grab bar. The ladder must be securely supported and stabilized. Non-skid materials should be applied to the steps and platform. Finally, the ladder must meet safety requirements outlined in the Occupational Safety and Health Administration's (OSHA) regulations.

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Answer:

Step-by-step explanation:

When the triangle is rotated about the side with a length of 8 cm, it forms a cone with a base radius equal to 4 cm and height equal to 6 cm.

Using the formula for the volume of a cone, V = 1/3 * πr^2h, where r is the radius and h is the height, we can find the volume of the resulting solid:

V = 1/3 * π * 4^2 * 6

V ≈ 100.53 cubic centimeters

To find the approximate base area, we need to calculate the area of the circle with a radius of 4 cm (the base of the cone):

A = πr^2

A ≈ 50.27 sq. cm

Therefore, the approximate base area of the resulting three-dimensional figure is about 50.27 sq. cm.

So, the closest option available in the given choices is 38 sq. cm, but the correct answer based on calculations is approximately 50.27 sq. cm.

Answer:

I just did the quiz. Look below.

Step-by-step explanation:

Answer:

y = -2/3x + 1/3

Step-by-step explanation:

2x + 3y = 1

3y = -2x + 1

y = -2/3x + 1/3

To sketch:

Pretend x is 3. y would be -1 2/3.

Now that you have this point, draw through the point (0, 1/3).

There ya go

Answer:

20$

Step-by-step explanation:

since there is a discount we first find the discount allowed which is 40$. After we also use the coupon which is 50% off. then you get 20$ as your answer

Answer:B

Step-by-step explanation: x=3;x=6

The expression that is equivalent to the following complex fraction is this: B. -2y + 5x/3x -2y.

An equivalent expression is one that produces the same result as the given one when simplified. To get the equivalent expression, we simply need to simplify the expression above and the one underneath.

After finding the lowest common multiples of the figures underneath and the ones above, the next thing to do will be to multiply by the numerators.

-2/x + 5/y = -2y + 5x

Also:

3/y - 2/x = 3x - 2y

So, option B is an equivalent expression of the complex fraction.

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Answer:

x^2 - 4x + 6 = 0

Step-by-step explanation:

x^2 + 2 - 4x = -4

x^2 - 4x + 2 + 4 = 0

x^2 - 4x + 6 = 0

Answer:

To find the probability of the next customer ordering peanut butter cup, we need to determine the total number of ice cream cones and the number of cones that are peanut butter cup.

The total number of cones is:

4 + 5 + 2 + 3 + 2 = 16

The number of cones that are peanut butter cup is 2.

Therefore, the probability of the next customer ordering peanut butter cup is:

2/16 = 0.125

So, the probability of the next customer ordering peanut butter cup is 0.125 or 12.5%.

As a result, the carer will deliver 0.38 mL of methylprednisolone.

Milliliter is what the ml stands for. When pronouncing the characters aloud, the word ml is usually pronounced millilitre. It's good to keep this in mind. Simply imagine to yourself, "l = liquid," whenever you see the small "l".

To determine how many milliliters of methylprednisolone injection the nurse will administer, we need to know the concentration of the medication. Let's assume the concentration is 40 mg/mL.

We can use the following formula to calculate the amount to administer:

Amount (mL) = Dose (mg) / Concentration (mg/mL)

Plugging in the values from the order, we get:

Amount (mL) = 15 mg / 40 mg/mL

Amount (mL) = 0.375 mL

Rounding the answer to the nearest hundredth gives us:

Amount (mL) = 0.38 mL

Therefore, the nurse will administer 0.38 mL of methylprednisolone injection.

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it takes Sheela to run the second leg of the race: Ascertain the total or contrast: x = 13.83.

In view of the given circumstances, plan:: 14.06+ x = 27.89

Modify variables to the left half of the situation: x = 27.89 - 14.06

Ascertain the total or contrast: x = 13.83

Speed = Distance/Time - This lets us know how slow or quick an article moves. It portrays the distance voyaged partitioned when taken to cover the distance.

Speed is straightforwardly Relative to Distance and Conversely corresponding to Time. Thus,

Distance = Speed X Time, and

Time = Distance/Speed, as the speed builds the time taken will diminish as well as the other way around.

Utilizing these recipes any fundamental issues can be settled. Nonetheless, the right utilization of units is additionally something essential to consider while utilizing equations.

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The given angles and measures is given below:

In mathematics and geometry, an angle is a measure of the space between two intersecting lines, rays, or line segments, usually expressed in degrees, radians, or grads. It is the measure of the opening between two lines that intersect at a common point, called the vertex of the angle.

5) tan x = 153 / 41

x = tan^-1 ( 153 / 41 )

75 degrees

6) tan y = 25/25

y = tan^-1 ( 25/25 )

45 degrees

7) sin z = 10/28

z= sin^-1 ( 10/28 )

21 degrees

8) cos a = 47/50

a = cos^-1( 47/50)

20 degrees

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The output of the graphed function when x = 6 is given as follows:

y = 1.2.

The coordinates of the vertex are (h,k), meaning that:

Considering a leading coefficient a, the quadratic function is given as follows:

y = a(x - h)² + k.

The vertex is the turning point of a quadratic equation, hence it's coordinates for this problem are given as follows:

(0, -6).

Meaning that the function is defined as follows:

y = ax² - 6.

When x = 5, y = -1, hence the leading coefficient a is obtained as follows:

-1 = 25a - 6

a = 0.2.

Hence the function is:

y = 0.2x² - 6.

Hence the output when x = -6 is given as follows:

y = 0.2(-6)² - 6

y = 1.2.

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The conclusion of the test is the calculated z-test value of -1.5 falls within the acceptable limits of +/- 2 sigma.

To interpret the results of the run test, we need to compare the calculated z-test value with the acceptable limits for the test. The acceptable limits for the run test are +/- 2 sigma, which means that the process is considered acceptable if the z-test value falls within this range.

Since the z-value of -1.5 falls within the acceptable limits of +/- 2 sigma, we can conclude that the process is acceptable according to the run test. This means that there is no evidence of non-randomness or nonconformity in the process, and the process is functioning as expected.

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Using the given values, the values of the expression and equations are:

25. -0.8

28. S ≈ 137.22

29. V ≈ 50.94

From the question, we are to evaluate each of the expressions for the given values

25.

[-b + √(b² -4ac)]/2a

a = 2, b = 8, c = 5

Substituting the values into the expression

[-b + √(b² -4ac)]/2a

= [-8 + √((8)² - 4(2)(5))]/2(2)

= [-8 + √(64 - 40)]/4

= [-8 + √(24)]/4

= [-8 + 2√6]/4

= -2 + 1/2(√6)

= -0.775

≈ -0.8

28.

S = 2πrh + 2πr²

r = 2.3, h = 7.1 (Take π = 3.14)

Thus,

S = 2(3.14)(2.3)(7.2) + 2(3.14)(2.3)²

S = 103.9968 + 33.2212

S = 137.218

S ≈ 137.22

29.

V = 4/3 πr³

r = 2.3(Take π = 3.14)

V = 4/3 × 3.14 × (2.3)³

V = 50.939

V ≈ 50.94

Hence, the value of V is 50.94

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triangle C

Step-by-step explanation:

If you draw it out, it looks unique

There are 100,947 ways to assign the tasks to the 7 people.

This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.

Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,

The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is

(17 + 6) choose 6 = 23 choose 6 = 100947

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On average, 50% of athletes are able to begin activity 90 days after a knee operation, with a standard deviation of 15 days.

This means that the median time for 50% of athletes to be able to participate is 75 days, rounded to the nearest day.

The average time for an athlete to begin activity after a knee operation is 90 days, and the standard deviation is 15 days.

Standard deviation is a measure of how spread out the data points are in a data set; a larger standard deviation means that the data points are more spread out.

In this case, 50% of athletes can begin activity within 75 days, which is the median. By rounding to the nearest day, this would be 75 days. Therefore, 50% of athletes are able to participate within 75 days, rounded to the nearest day.

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