The area of a rectangle is 4 square units. What is the area of a triangle, which is cut off from the rectangle by a line connecting the midpoints by 2 adjacent sides?

Answer:

9.8 carats.

Step-by-step explanation:

5.1 + 0.7 + 1.4 + 2.6

= 9.8

Supplementary angles have a sum of 180°

Therefore, we can add the expressions for Angles A and B and set their sum equal to 180.

( 7x - 15 ) + ( 2x - 3 ) = 180

Now we can combine like terms and use inverse operations to find the value of x:

( 7x - 15 ) + ( 2x - 3 ) = 180

9x - 18 = 180

9x - 18 + 18 = 180 + 18

9x  = 198

9x/9 = 198/9

x = 22

Then Angle A will have a measure of 7x - 15 or 7• 22 -15 = 154 - 15 = 139°

m∠A = 139°

The measure of Angle b will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°

m∠ B = 41°

NOTE:  139 + 41 = 180

Answer:

1/250

Step-by-step explanation:

5^-3 × 2^-1

5^-3 = 1/5^3 = 1/125

2^-1 = 1/2^1 = 1/2

so 5^-3 × 2^-1 means 1/125 × 1/2

= 1/125 × 1/2

= 1/250

Rounded to the nearest whole number, the standard deviation of the data is 29.

The following notations and formulas will be used in these calculations:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

Standard deviation = Variance^0.5

Where:

n = number of values = 4

x = each value

Therefore, we have:

Mean = (65 + 75 + 100 + 130) / 4 = 92.50

Variance = ((65-92.5-)^2 + (75-92.50)^2 + (100-92.50)^2 + (130-92.50)^2) / (4-1) =  2,525 / 3 = 841.666666666667

Standard deviation = Variance^0.50 = 841.666666666667^0.5 = 29.011491975882

Rounding to the nearest whole number, we have:

Standard deviation = 29

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Answer:

The answer is C. 100

Step-by-step explanation:

The probability that at least one of the ten random numbers drawn from a uniform distribution on [0, 4.62] will exceed 4.62 is approximately 0.450.

In a uniform distribution, the probability of a value falling within a specific range is proportional to the length of that range. Since the range of the uniform distribution is [0, 4.62], the probability of drawing a number less than or equal to 4.62 from this distribution is 1.

Therefore, the probability that at least one number will exceed 4.62 is equal to 1 minus the probability that all ten numbers drawn are less than or equal to 4.62. Since the draws are independent, we can calculate this probability as (1 - 1)^10 = 1^10 = 1.

Rounded to three decimal places, the probability that at least one number will exceed 4.62 is approximately 0.450.

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Option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

The distance across a circle through the centre is called the diameter.

Diameter = 2 × radius

In the given figures, option B has a diameter of 20

so radius = diameter /2

=20/2

=10 units

Hence, option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

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L = 1.3245 is  the legnths of the pen's sides .

What is area and perimeter?

Perimeter is the distance around the outside of a shape. Area measures the space inside a shape.

The equation for perimeter is 2L + W = 30 ( I'm assuming that the shed takes up one of the Widths, but you can use the Length if you want, it doesn't matter.)

So W = 30 - 2L.

Area = L x W = L (30 - 2L) = 30L - 2L^2.

This is a quadratic equation, easily graphed as a parabola, with a maximum point at L = 1.3245 .

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Answer:

50

Step-by-step explanation:

since 5 and above is rounded up, 4 and below is rounded down

Answer: Range = (-∞, 3) U (3, ∞)

Step-by-step explanation:

The range is the set of all y-values in a function. The easiest and most straightforward way to find the range is to graph the function and find asymptotes, or locations on the graph where the function lacks y-values.

You can plug in a few points to the equation, as shown in this table below.

After you have your points, you can draw your function following the points, as shown in the next image. Notice the line at y = 3, where the function does not cross. Although it will get infinitely close to the line, the function will never meet or cross this point at any x-value. This is what is known as a "horizontal asymptote", and is not included in the range of the function.

We can represent this asymptote in a range, which is a representation of all possible y-values in the function. The possible y-values for this function start at negative infinity and end at infinity, but do not exist at y = 3, so we represent this through this mathematical expression:

Range = (-∞, 3) U (3, ∞)

g(4) = 1 * g(4), which means that q(4) is equal to g(4). y(-4) = f(-4) * h(-4) = 1 * (-4) = -4. Therefore, the values of q(4), y(-4), and y(4) are determined as follows: q(4) = g(4), y(-4) = -4, and y(4) = 0.

For the first part of the problem, we are given f(t) = u(t), g(t) = 2tu(t), and g(t) = f(t - 1) * g(t). To determine q(4), we need to substitute t = 4 into the equation g(t) = f(t - 1) * g(t). This gives us g(4) = f(3) * g(4). Since f(t) = u(t), we know that f(3) = u(3) = 1 because u(t) is a unit step function that equals 1 for t ≥ 0. Therefore, we have g(4) = 1 * g(4), which means that q(4) is equal to g(4).

For the second part of the problem, we are given f(t) = u(-t), h(t) = tu(-t), and y(t) = f(t) * h(t). To determine y(-4) and y(4), we substitute t = -4 and t = 4 into the equation y(t) = f(t) * h(t). For y(-4), we have y(-4) = f(-4) * h(-4). Since f(t) = u(-t), we have f(-4) = u(4) = 1 because u(t) is a unit step function that equals 1 for t ≥ 0. Similarly, h(-4) = -4u(4) = -4. Therefore, y(-4) = f(-4) * h(-4) = 1 * (-4) = -4.

Similarly, for y(4), we have y(4) = f(4) * h(4). Since f(t) = u(-t), we have f(4) = u(-4) = 0 because u(t) is a unit step function that equals 0 for t < 0. Thus, y(4) = f(4) * h(4) = 0 * h(4) = 0.

Therefore, the values of q(4), y(-4), and y(4) are determined as follows: q(4) = g(4), y(-4) = -4, and y(4) = 0.

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Using the algebraic expression that models the cost of burgers and hotdogs, the cost of 4 burgers and 6 hot dogs is $25.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An algebraic equation is the equality of expressions.

If the expression 3.25b + 2h gives the cost of b burgers and h hotdogs, and we want to determine the cost of 4 burgers and 6 hot dogs, then plug in the values and solve the equation.

cost = 3.25b + 2h

cost = 3.25(4) + 2(6)

cost = 13 + 12

cost = 25

Hence, the cost of 4 burgers and 6 hot dogs is $25.

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Answer:

7/3

Step-by-step explanation:

Answer:

7/3

Step-by-step explanation:

3/7 x 7/3 = 1

Both measurements are below the minimum area of 169 square feet required.

Area is a measurement of size of two dimensional surface such as Square rectangle or Circle. It is calculated by multiplying the length of the surface by width area also can measured in terms of square units such as square feet or square meters area is an important concept in mathematics and is used to measure the size of safe and object it is also used to find the total area of a group of shape.

The measurements of the parking spaces shown do not meet the requirements of the town. The first parking space has an area of 144 square feet, while the second parking space has an area of 128 square feet. Both measurements are below the minimum area of 169 square feet required.

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Answer:

(2x-5)^3

Step-by-step explanation:

(((8 • (x3)) -  (22•3•5x2)) +  150x) -  125

 ((23x3 -  (22•3•5x2)) +  150x) -  125

3.1    8x3-60x2+150x-125  is not a perfect cube

Factoring:  8x3-60x2+150x-125

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  150x-125

Group 2:  -60x2+8x3

Pull out from each group separately :

Group 1:   (6x-5) • (25)

Group 2:   (2x-15) • (4x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Answer:

18

Step-by-step explanation:

So you need to do f(x) 5x^2+3x-19+3

You would simplify the equation to get to y=4x+5f(x)+2

Naturally, you would now graph the equation to a linear degree but still inducing a parabellum, y-(d-3)=0

Then solve using the square method (b/2)^2=(6)^2

Then put the 6 on both sides of the equation.

6^2+w0+8x+7t^2

After you get hydrogen oxide as your answer please note: Puenomia can only occur inside the respiratory system.

There ya go: 18.

Answer:

g(1) = 0

Step-by-step explanation:

To evaluate g(1) , substitute x = 1 into g(x), that is

g(1) = 4 - 2(3 - 1)

      = 4 - 2(2)

      = 4 - 4

      = 0

Answer: its 0

Step-by-step explanation:

(a) The average rate of change between a = 0 and b = 1 for RC(x) = 3/4x - 1 is:

RC(1) - RC(0)

= (3/4(1) - 1) - (3/4(0) - 1)

= 3/4 - 1 + 1

= -1/4

So, the average rate of change between a = 0 and b = 1 is -1/4.

(2) As we move point a around on the graph, the average rate of change between a and b = 1 changes.

Specifically, if we move point a to the right, the average rate of change increases, and if we move point a to the left, the average rate of change decreases.

(3) The average rate of change for a straight line equals the slope.

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The 14.9% increase in Sylvia's lead lathe tech's hourly wage of $18.50 results in a $2.75 per hour increase. Assuming the lead lathe tech works 2,080 hours per year, the additional cost to Sylvia's annual wages budget would be approximately $5,720, excluding benefits or taxes.

First, we need to find the percentage increase in the lead lathe tech's hourly wage. The increase requested is $2.75, which is 14.9% of the current wage rate ($18.50). To calculate the percentage increase, we divide the increase by the current wage rate and multiply by 100: ($2.75 / $18.50) * 100 ≈ 14.9%.

To determine the additional cost to Sylvia's annual wages budget, we need to know the total number of hours worked by the lead lathe tech in a year. Let's assume the lead lathe tech works 40 hours per week and there are 52 weeks in a year, resulting in a total of 2,080 hours.

To calculate the annual cost of the wage increase, we multiply the hourly increase ($2.75) by the total number of hours worked (2,080): $2.75 * 2,080 ≈ $5,720.

Therefore, the 14.9% increase in the lead lathe tech's hourly wage will cost Sylvia an additional $5,720 in her annual wages budget, excluding benefits or taxes.

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

We have:

Total number of cards in a pack = 52

Total number of aces in a pack = 4

The probability of drawing an ace is:

The probability that both are aces is:

Answer: the probability is 1/221

The company packs "3" clay pots and "4" plastic pots for maximum packing in one shipment. This will require the fewest shipments.

or,

The company packs "2" clay pots and "6" plastic pots for maximum packing in one shipment. This will require the fewest shipments.

Let, the number of clay flower pots - "c"

the number of plastic flower pots is "p".

We can write:

\(2\leq c + p\leq 8\)

Also,

Weight of clay pot = 15 pounds

Weight of plastic pot = 7.5 pounds

Max Weight of Shipment = 100 pounds

Weight of container = 20 pounds

The weight of Packing material inside the container = 1 pound

Thus, the maximum weight of pots will be less than

                               = 100 - (20+1) = 100 - 21 = 79

We can write another inequality:

\(1.5c + 7.5p < 79\)

To assure the first inequality, we have points,

c = 0, p = 8

p =0, c = 8

c = 1, p = 7

etc. and so on...

So,

The company packs "3" clay pots and "4" plastic pots for maximum packing in one shipment. This will require the fewest shipments.

or,

The company packs "2" clay pots and "6" plastic pots for maximum packing in one shipment. This will require the fewest shipments.

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The complete question is:

A gardening company sells clay flower pots and plastic flower pots. There must be at least 2 pots in each shipment, but there cannot be more than 8 in a shipment. Additionally, the shipment must weigh less than 100 pounds. Each shipment container weighs 20 pounds, and there is 1 pound of packing material. A clay flower pot weighs 15 pounds, whereas a plastic flower pot weighs 7.5 pounds. The company wants to fill each shipment as full as it can get when they send shipments to garden supply stores. There is a similar demand for each type of pot. What is the best solution for the company if they want to ship the fewest shipments? Justify your reasoning.

Count is incremented by 1 before returning the result because we want to count the number of trials needed to achieve the first success.

To create a Geometric random variable with a probability of success equal to p, you can use the following algorithm:

Initialize a counter variable, let's call it count, to 0.

Generate a random number between 0 and 1, let's call it rand_num.

Set the initial probability of success, prob_success, to p.

While rand_num is greater than prob_success, do the following steps:

Increment count by 1.

Generate a new rand_num between 0 and 1.

Update prob_success by multiplying it with (1 - p).

Return count + 1 as the generated Geometric random variable.

This algorithm works by repeatedly generating random numbers until a success occurs. Each time a failure occurs (when rand_num is greater than prob_success), the probability of success is updated to account for the remaining trials.

Note that count is incremented by 1 before returning the result because we want to count the number of trials needed to achieve the first success.

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Answer:

x^4

Step-by-step explanation:

Answer:

15 m, 20 m, 25 m forms a right triangle.

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1:8

Step-by-step explanation:

for every one cup of milk, there is 8 grams of protein

Answer:

√2-√3

Step-by-step explanation:

√3 (√2 -1 ) + √2 (1-√3)

= √3 x √2 - √3 + √2 - √2 x √3

= √6 - √3 + √2 - √6

= √2 - √3

Answer:

36,000 meters

Step-by-step explanation:

We can use the polar equation r = f(θ) to sketch the curve. However, since you have only provided the value of θ as −π/6, we cannot determine the shape of the curve without knowing the equation of the function f(θ).

In order to sketch the curve, we need to plot at least three points on the polar coordinate plane. We can do this by selecting three different values of θ, plugging them into the polar equation, and finding the corresponding values of r. We can then plot these points and connect them to form the curve.

Answer:
1. First, recall that in polar coordinates, a point is represented by (r, θ), where r is the distance from the origin, and θ is the angle measured counter-clockwise from the positive x-axis.
2. In this case, the polar equation is given as θ = -π/6, which means the angle is fixed at -π/6 radians, or -30 degrees.
3. Since r can take any value, this curve is a straight line consisting of all points that are located at a -30-degree angle from the positive x-axis. To visualize this, imagine a ray starting at the origin and rotating -30 degrees in the clockwise direction.

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Answer:

There are 3 friends (Judy + 2 friends) who won $145.00

They want to share the winnings equally, but they got:

one $100 bill

four $10 bills

five $1 bills.

Assuming that they can share only those bills, the only way to share the winnings equally is:

Each friend gets one $10 bill

Each friend gets one $1 bill

Then each one gets $11.

And there is a surplus of:

one $100 bill (that can't be divided)

one $10 bill (that can't be divided)

two $1 bill (that can't be divided)

Then:

There is a common pool of $100 + $10 + 2*$1  = $112

And each one of the 3 friends gets $10 + $1 = $11

In the case where they can change the bills, each friend will get:

$145/3 = $48.33

Answer: 4/5

Step-by-step explanation: