Two pieces of equipment were purchased for a total of 2,000. If one piece cost $770 more than the other, find the price of the less expensive piece of equipment. Assume all data are accurate to two significant digits unless greater accuracy is given.

Answer:

40% decrease

Step-by-step explanation:

Answer: coochie man

Step-by-step explanation:

The odds in favor of drawing a 7 are 1 to 12.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

There are four 7s in a deck of 52 cards, so the probability of drawing a 7 is 4/52, which simplifies to 1/13. The odds in favor of drawing a 7 are the ratio of the probability of drawing a 7 to the probability of not drawing a 7, which is:

(1/13) : (12/13

We can simplify this ratio by dividing both terms by the greatest common factor, which is 1:

(1/13) : (12/13) = 1 : 12

Therefore, the odds in favor of drawing a 7 are 1 to 12.

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Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

An equation of this line in slope-intercept form is y = x - 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-1, -2) and a slope of -1, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = -1(x - (-1))  

y + 2 = x + 1

y = x + 1 - 2

y = x - 1

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Complete Question:

Write an equation of a line through point (-1, -2) with a slope of -1.

Answer:

The number of enrollments increased by 5%.

Step-by-step explanation:

Given that:

Number of students at the beginning of the year = 480

Number of students at the end of the year = 504

Change = 504 - 480 = 24

This indicates increase.

Percent of change = \(\frac{Change}{Old\ number\ of\ students}*100\)

Percent of change = \(\frac{24}{480}*100\)

Percent of change = 5%

Hence,

The number of enrollments increased by 5%.

Answer:

50 percent :)

From the graph attached below, the solution to the system of linear inequalities are (1, 4)

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.

In the problem given;

y < - x + 5 ...eq(i)

y ≥ 3x + 1 ...eq(ii)

To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.

From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E

Kindly find attached graph below

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The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

Answer:

175%

Step-by-step explanation:

70 = p * 40

p = 1.75 or 175%

Answer:

Step-by-step explanation:

175%

Answer:

The expected number of defective lava lamps in a week is 3.72.

Step-by-step explanation:

To find the expected number of defective, we multiply each outcome by its probabilities.

The probability of each outcome is:

P(X = 0) = 0.01

P(X = 1) = 0.05

P(X = 2) = 0.15

P(X = 3) = 0.21

P(X = 4) = 0.22

P(X =  5) = 0.3

P(X = 6) = 0.06

Expected number:

Multiplying each outcome by its probability:

E(X) = 0*0.01 + 1*0.05 + 2*0.15 + 3*0.21 + 4*0.22 + 5*0.3 + 6*0.06 = 3.72

The expected number of defective lava lamps in a week is 3.72.

Answer:

cos theta  = adj / hyp is positive (+/+)

Step-by-step explanation:

In this open interval, the hypotenuse (radius) is always positive, whereas the adjacent side is positive and the opposite side negative.

in this interval:

sin theta = opp / hyp is neg (-/+)

cos theta  = adj / hyp is positive (+/+)

tan theta = opp / adj = (-/+) :  negative

The future value (FV) of the loan after 12 months, after the monthly compounding at an interest rate of 5.9%, is about $8977.98.

For one to be able to calculate the future value (FV) of the loan, one need to use the formula for compound interest which is:

FV = PV x (1 + r)ⁿ

Where:

PV = Present value (loan amount)

      = $8,465

r = Monthly interest rate

= 5.9% / 12

= 0.004917

n = Number of compounding periods

 = 12 (months)

Pmt = Monthly payment (unknown)

So by  Using these values, one can calculate the future value (FV) of the loan and thus:

FV = $8,465 x (1 + 0.004917)¹²

=  $8,465 x  1.0606

= $8977.98

So, the future value (FV) of the loan after 12 months, as at the monthly compounding at an interest rate of 5.9%, is about $8977.98.

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Answer:

Option 1

Step-by-step explanation:

\(\frac{2x^2 - 7x-4}{x^2 - 5x+4}=\frac{(x-4)(2x+1)}{(x-4)(x-1)}=\frac{2x+1}{x-1}\)

Answer:

x = 16

m<Y = 34°

Step-by-step explanation:

∆XYZ is an isosceles ∆. An isosceles ∆ has two equal sides, as well as the bases of the isosceles triangle are congruent. In this case, therefore:

<X = <Z

(6x - 23)° = (4x + 9)

Solve for x

6x - 23 = 4x + 9

Collect like terms

6x - 4x = 23 + 9

2x = 32

Divide both sides by 2

x = 16

m<Y = 180° - (m<X + m<Z) (sum of ∆)

m<Y = 180 - ((6x - 23) + (4x + 9))

Plug in the value of x

m<Y = 180 - ((6(16) - 23) + (4(16) + 9))

m<Y = 180 - (73 + 73)

m<Y = 34°

Answer:

Elena scored 22 points.

Step-by-step explanation:

Mai scored 5 points, and Noah scored three times as many. This means Noah scored 15 points and if Tyler scored four points fewer, he scored 11 points. If Elena scored twice as many as Tyler, she scored 22.

Answer:

here are 117,600 ways the runners can finish first, second, and third in the race.

Step-by-step explanation:

The number of ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations. In this case, we are interested in selecting 3 runners from a group of 50.

The number of ways to choose the first-place finisher is 50 because any of the 50 runners can finish first. After one runner is selected for the first place, there are 49 remaining runners.

For the second-place finisher, there are 49 remaining runners to choose from since one runner has already been selected for the first place. Thus, the number of ways to choose the second-place finisher is 49.

Similarly, for the third-place finisher, there are 48 remaining runners to choose from since two runners have already been selected for the first and second places. Hence, the number of ways to choose the third-place finisher is 48.

To determine the total number of ways the runners can finish in first, second, and third places, we multiply the number of choices for each position: 50 * 49 * 48 = 117,600.

Therefore, there are 117,600 ways the runners can finish first, second, and third in the race.

Answer:

12953

Step-by-step explanation:

The equations of the other two sides are AD: y = -3x + 3 and DC: y = 1/2x - 1/2.

What is point-slope form?

The point-slope form is a way to write the equation of a straight line in algebra. It is used when you know the coordinates of a point on the line and the slope of the line. The point-slope form of a linear equation is:

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x1, y1) are the coordinates of a point on the line.

Since AB and BC are two sides of a parallelogram, they are parallel to each other. Thus, we can use the slope formula to find the slopes of these sides.

Slope of AB:

m = (y₂ - y₁)/(x₂ - x₁)

= (6 - 3)/(6 - 0)

= 3/6

= 1/2

Slope of BC:

m = (y₂ - y₁)/(x₂ - x₁)

= (3 - 6)/(7 - 6)

= -3/1

= -3

Now that we know the slopes of AB and BC, we can use the point-slope form to find the equations of the other two sides.

Equation of AD:

We know that AD is parallel to BC and passes through point A. So, we can use the point-slope form with the slope of BC and point A.

y - y₁ = m(x - x₁)

y - 3 = -3(x - 0)

y - 3 = -3x

y = -3x + 3

Equation of DC:

We know that DC is parallel to AB and passes through point C. So, we can use the point-slope form with the slope of AB and point C.

y - y₁ = m(x - x₁)

y - 3 = 1/2(x - 7)

y - 3 = 1/2x - 7/2

y = 1/2x - 1/2

Therefore, the equations of the other two sides are:

AD: y = -3x + 3

DC: y = 1/2x - 1/2

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Answer:

17.18400

Step-by-step explanation:

When rounded to the nearest whole number, it's 17.

Hope this helped :)

When substituting y = 11 into the equation y = 1/2(x) - 25, we find that x = 72, confirming that (23.5, 11) is a valid point of intersection.

Given that x is 23.5, it is required to prove that it is an intersection point for the equation y = 1/2(x) - 25 when y is equal to 11.

The equation is given as y = 1/2(x) - 25

When y = 11, we can substitute the value of y in the equation to obtain 11 = 1/2(x) - 25

This can be simplified as 11 + 25 = 1/2(x)36 = 1/2(x)

On solving, x = 72Thus, when y is equal to 11 and x is equal to 72, the given point of intersection is valid.

Therefore, it can be concluded that x = 23.5 is a point of intersection for the equation y = 1/2(x) - 25 when y is equal to 11.

In summary, when given an equation with two variables, we can find the point of intersection by setting one of the variables to a given value and solving for the other variable. In this case, when y is equal to 11, we can solve for x and obtain the point of intersection as (72,11).

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The average case complexity is a measure of the expected performance of an algorithm when the input is chosen randomly. The average case complexity of binary search is O(log n), where n is the size of the input.

Average case complexity is a measure of the expected running time of an algorithm when it is run on inputs that are drawn randomly from a specified probability distribution. The average case complexity provides a more realistic estimate of the performance of an algorithm in real-world scenarios.

For binary search, the average case complexity can be derived by considering the probability distribution of the search key in the sorted input array. Assuming a uniform distribution of search keys, the probability of finding a key at any position in the array is 1/n, where n is the size of the array.

Let T(n) be the average case time complexity of binary search on an input array of size n. In the best case, the search key is found in the middle of the array in O(1) time. In the worst case, the search key is not present in the array, and the algorithm performs O(log n) comparisons.

In the average case, the probability of finding the key at any position is 1/n, and the number of comparisons required to find the key is proportional to the distance between the key and the middle of the array. Therefore, the average number of comparisons required in the average case is:

1/n * (1 + 2 + ... + n-1) = (n-1)/2n

Thus, the average case time complexity of binary search is O((n-1)/2n) = O(log n), which is the same as the worst-case time complexity.

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A formula is a fact or rule that uses mathematical symbols. It will usually have: an equals sign (=) two or more variables (x, y, etc) that stand in for values we don't know yet.

Example: The formula for finding the volume of a box is:

x = 2y - 7 Formula (relating x and y)

a2 + b2 = c2 Formula (relating a, b and c)

Answer:

115

Step-by-step explanation:

The answer is 115 degrees

Step-by-step explanation:

a. d = m/v

m = d × v

b. m = d × v

= 5.01g/cm × 1.2cm

= 6.012g

hopefully this makes sense

:)

The mass of pyrite sample in grams will be -  6.012 grams

We have a marble whose volume is 1.2 cubic centimeter and density is 5.01 g/cm. A relation - density d of a substance is given by the formula

d = m/v is also provided.

We have to determine its mass.

The solid state of matter has the highest density because the constituent particles are fixed and not allowed to move inside the solid. Moreover, they are bonded very close to each other.

According to the question -

Density - 5.01g/cm

Volume - 1.2cm.

Using the formula mentioned above, we get -

\($\rho = \frac{M}{V}\)

Rearranging the formula, we get -

M = ρV

M = 5.01 x 1.2 = 6.012 grams

Hence, the mass of pyrite sample in grams will be -  6.012 grams

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Answer:

14

Step-by-step explanation:

Since sine and cosine are cofunctions of each other:

\(\sin (\theta)= \cos (90-\theta)\)

and vice versa. Therefore:

\(18+x=90-58 \\\\18+x=32 \\\\x=32-18=14\)

Hope this helps!

Answer:

72

Step-by-step explanation:

0 < x < 1

Multiply the inequality by 100

0 < 100x < 100

0 < 72 < 100

The p-value of 4.91541E-15 (or 4.91541 x 10^-15) is considerably beneath the conventional significance level of 0.05 employed in statistical hypothesis testing.

In hypothesis testing, the p-value symbolizes the probability of detecting the test statistic (or an even larger value) under the null hypothesis. A p-value of 0.05 or below often appears statistically relevant, suggesting powerful evidence contrary to the null hypothesis.

Therefore, a p-value of 4.91541E-15 being far less than 0.05 implies very compelling evidence against the null hypothesis.

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