During the first three hours of a recent storm the rain fell at a constant rate of 10 mm per hour. The storm stopped for the next 2 hours and then it started raining again at a constant rate of 20 mm per hour for the next 5 hours. Match the pieces of the piecewise function that describes the total rainfall in this situation with the appropriate domain.
f(h)=10h

f(h)=30

f(h)=30+20(h-5)

P=(m+nmx2​+nx1​​,m+nmy2​+ny1​​). The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.

What is the segment ratio formula?

P=(m+nmx2​+nx1​​,m+nmy2​+ny1​​). The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.

A variable is a quality that may be measured and take on several values. A few examples of variables are height, age, salary, province of birth, school grades, and kind of dwelling.

Here,

Given :

A discrete random variable's anticipated value

So, in order to determine the expected value of a discrete random variable,

we may infer from the provided data that it is calculated as a weighting factor of the potential outcomes of that variable,

where weights are the probability of that outcome.

Therefore , the solution of the given problem of variable comes out to be where weights are the probability of that outcome.

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The required Confidence interval for the given data is CI = 0.6 - 0.7 ± 1.96[tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex].

Hypothesis testing is a methodical process for determining whether research study findings are consistent with a specific idea that pertains to a population. To evaluate a hypothesis about a population, hypothesis testing uses sample data.

We have,

x1 = 30,  x2 = 35

n1 = 50, n2 = 50

p1 = x1/n1 = 30/50 = 0.6

p2 = x2/n2 = 35/50 = 0.7

Then,

at α= 0.05, the critical value taken by table of z

Zc = 1.96

CI =[tex]P_{1}-P_{2}[/tex] ±[tex]\sqrt{\frac{P_{1}(1-P_{1})}{n_{1}}+\frac{P_{2}((1-P_{2})}{n_{2}} }[/tex]

CI = 0.6 - 0.7 ± 1.96 [tex]\sqrt{\frac{0.6(1-0.6)}{50}+\frac{0.7((1-0.7)}{50} }[/tex]

This is our needed answer,So option (D) is correct.

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The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

If a road map has a scale of 3 inches to 100 miles.

Then the scale factor is given as,

Sclar factor = 100 / 3

Sclar factor = 33.33 miles per inch

Then the distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be given as,

Distance = 33.33 x 4.5

Distance = 150 miles

The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

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The translation in y = (x + 3)² is of 3 units to the left. The correct option is the last one.

For a general function y = f(x), we define a horizontal translation of N units as:

g(x) = f(x + N)

Here the original function is y = x² and the translated one is:

y = (x + 3)²

So we just added 3 on the argument, so this is a shift of 3 units to the left, the correct option is the last one.

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A collector offers to buy state quarters for 2000% of their face value. The face value of each quarter is 25 cents. At that rate 20 dollars Bryden will get for his four state quarters.

In the given question, a collector offers to buy state quarters for 2000% of their face value.

The face value of each quarter is 25 cents.

We have to find at that rate how many dollars Bryden will get for his four state quarters.

As given that,

Collector buy state quarters = 2000% of their face value

We can write 2000% as 20×100%.

It means that state quarters is 20 times of their face value.

As we know that, 4 quarter is equal to the one dollar. So,

Bryden get for his four state quarters = 20×1 dollars

Bryden get for his four state quarters = 20 dollars

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Answer:

Step-by-step explanation:

Anything raised to the power of 0 equals 1, so we have 1 raised to the power of -3. That's the same thing as

[tex]\frac{1}{1^3}[/tex] which is just 1. The answer is 1.

Answer: y=18

Step-by-step explanation:

Answer:

2x^2 + 8x + 3 in 2( x + 2 )^2 + q form is 2( x + 2 )^2 - 5

The customer rented the car for 8 days.

The total amount paid by the customer, $138, is made up of the initial fee and the daily fee multiplied by the number of days the car was rented.

We can set up the equation as:

138 = 42 + 12x (where x is the number of days the car was rented)

To find the number of days, we can subtract the initial fee from both sides of the equation:

138 - 42 = 12x

96 = 12x

Then we can divide both sides by 12 to solve for x:

x = 8

So the customer rented the car for 8 days.

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Answer: m angle3 = 3x - 7 = 3(14) - 7 = 37 degrees

Step-by-step explanation:

Since angles 3 and 9 are complementary, their measures add up to 90 degrees. So, we can set up the equation:

m angle3 + m angle9 = 90

We can substitute in the given values for the measures of each angle:

(3x - 7) + (4x - 1) = 90

Solving for x:

7x - 8 = 90

7x = 98

x = 14

Yes, it is possible to construct a triangle with the given sides 6cm 5 cm and 9 cm.

As given in the question,

Let the triangle with the given side length be ΔABC.

Measure of the side length is equal to :

Side Length 1 ( AB ) = 6cm

Side Length 2 ( BC ) = 5cm

Side Length 3 ( CA ) = 9cm

To construct a triangle following property should satisfied:

Sum of the two side length is always greater than the third side.

AB + BC

= 6cm + 5cm

= 11cm > 9cm

BC + CA

= 5cm + 9cm

= 14cm > 6cm

CA + AB

= 9cm + 6cm

= 15cm > 5cm

Here the required condition to construct a triangle is satisfied.

Therefore, yes it is possible to construct a triangle with the given sides measure .

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The total number of sides and diagonals for a polygon with n sides is given by the equation n(n - 3)/2.

In geometry, a polygon is a two-dimensional closed object with straight sides that is flat or planar. It doesn't have any curved edges. A polygon's sides are also known as its edges. The vertices (or corners) of a polygon are the spots where two sides meet.

Here,

A square has 4 sides and 2 diagonals.

Now, a pentagon will have 5 sides and 5 diagonals

A hexagonal when drawn will have 6 sides and 9 diagonals

Thus, we see that;

When n = 4, d = 2

When n = 5, d = 5

When n = 6, d = 9

Using combination, we will find number of pairs of 2 vertices that can possibly be formed from n-vertices. Thereafter we will subtract n from that since it's neighboring vertices can't combine with the current one.

Thus, we have;

C(n, 2) - n

This gives s;

(n(n-1)/2) - n

Simplifying this gives;

(n(n - 1) - 2n)/2

(n² - n - 2n)/2

(n² - 3n)/2

n(n - 3)/2

The expression that would give you the total number of sides and diagonals for a polygon with n sides is n(n - 3)/2.

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12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.

Given here: Ryan is making a fruit drink. The directions say to mix 3 cups of water with 1 1/2 scoops of powdered fruit mix.

Thus the ratio of the number of cups of water to scoops of powdered fruit mix is equal to 3:3/2=2:1

∴ With 6 scoops of fruit mix we will be required to mix 12 cups of water.

Again unit rate ( scoops of fruit mix / cup of water)= 1.5/3

                                                                                   =0.5 scoops/cup of water

The unit rate means the number of scoops that are required to be mixed with  a cup of water.

Hence, 12 cups of water should be mixed to 6 scoops of fruit mix and the unit rate is 0.5 scoops per cup

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Answer: 20

Step-by-step explanation:

The equation P = -0.02n^2 + 3.4n - 16 represents the profit, P, in thousands of dollars for a small independent movie company as a function of the number of DVD copies produced, n, in thousands.

The equation is a quadratic equation, which means it is a polynomial equation of degree 2. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b and c are constants and x is the variable. In this case, the equation can be written as P = -0.02n^2 + 3.4n - 16, where P is the variable, and -0.02, 3.4, and -16 are the constants.

The first term in the equation is -0.02n^2, which represents the cost of producing the DVD copies. As n increases, the cost of production also increases, and the coefficient -0.02 represents that the cost of production is directly proportional to n^2. The negative sign in front of the term indicates that as the number of copies increases, the cost of production also increases and thus the profit decreases.

The second term in the equation is 3.4n, which represents the revenue generated by the sale of the DVD copies. As n increases, the revenue generated also increases, and the coefficient 3.4 represents that the revenue is directly proportional to n. The positive sign in front of the term indicates that as the number of copies increases, the revenue generated also increases and thus the profit increases.

The last term in the equation, -16, represents the fixed costs associated with producing the DVD copies, such as overhead costs, marketing and distribution costs, etc. These costs are not directly related to the number of copies produced and are constant regardless of how many copies are produced.

In summary, the equation P = -0.02n^2 + 3.4n - 16 represents the profit for a small independent movie company as a function of the number of DVD copies produced. The profit is affected by the cost of production, revenue generated from sales, and fixed costs. As the number of copies increases, the cost of production increases, the revenue generated increases, and the fixed costs remain constant. The profit is the difference between the revenue generated and the costs incurred.

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The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.

The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.

So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.

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Managers must make all the given vital decisions from the options, hence, d) All of the above is the correct answer.

Managers must make a number of important decisions about the use of control charts, some of which include:

These are all important decisions that managers need to make when using control charts to monitor and improve processes in an organization. The right decisions can help ensure that control charts are effective in detecting and addressing issues with processes, while the wrong decisions can lead to control charts being ineffective or even counterproductive.

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The complete question is -

Managers must make a number of important decisions about the use of control charts. what are they?

multiple select questions.

a) what size samples to take and how often samples should be taken.

b) how many control charts to use to monitor the process.

c) what type of control chart to use.

d) what tools to use to take measurements at what points in the process to use control charts.

e) All of the above.

The equation of the circle with center (3, 2) and point (1, 1) is:

(x - 3)² + (y - 2)² = 5.

The equation of a circle with center (h, k) and radius r is given by the equation: (x - h)² + (y - k)² = r²

To find the equation of the circle with center (3, 2) and a point on the circle (1, 1), we first need to find the radius of the circle. We can use the distance formula to find the distance between the center and the point on the circle:

r = √((1 - 3)² + (1 - 2)²) = √((-2)² + (-1)²) = √5

So the radius of the circle is √5

Now we can substitute the center and radius into the equation of a circle:

(x - 3)² + (y - 2)² = (√5)²

Simplifying, we get:

(x - 3)² + (y - 2)² = 5

So the equation of the circle with center (3, 2) and point (1, 1) is:

(x - 3)² + (y - 2)² = 5.

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The length of the median of the trapezoid is 12.

The area of a trapezoid is given by the formula (1/2)h(b1+b2), where h is the height and b1 and b2 are the lengths of the bases. We know that the area is 60, the height is 5 and b1 = b2 + 4.

So, we can write the equation as follows:

(1/2) * 5 * (b1 + b2) = 60

To find the length of the median of a trapezoid, we need to find the length of the mid-segment. The mid-segment of a trapezoid connects the midpoints of the non-parallel sides. The length of the midsegment is the average of the lengths of the bases.

So, the length of the median is (b1 + b2) / 2.

We can substitute the value of the area to find the lengths of the bases and then use that to find the length of the median.

(1/2) * 5 * (b1 + b2) = 60

(1/2) * 5 * (b1 + b2) = 60

b1 + b2 = 24

b1 = b2 + 4

b2 = 24 - b1

b1 = (24 - b1) + 4

b1 = 24 - b1 + 4

b1 = 28 - b1

b1 = 28 - (24 - b1)

b1 = 4 + b1

b1 = b2 + 4

b1 = b1

So, the lengths of the bases are equal to 14 and 10.

Length of median = (14 + 10) / 2 = 12.

Therefore, The length of the median of the trapezoid is 12.

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Answer:

h = 32 cm

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the distance between the parallel sides b₁ and b₂

given A = 1440 , b₁ = 54.6 , b₂ = 35.4 , then

[tex]\frac{1}{2}[/tex] h (54.6 + 35.4) = 1440 ( multiply both sides by 2 to clear the fraction )

h × 90 = 2880 ( divide both sides by 90 )

h = 32

the distance between the parallel sides is 32 cm

TSA = 2πrh + πr² (r = 40/2 = 20)

4715 = 40πh + 400π

4715/(40π) = h + 10

≈ 37.5 = h + 10

h = 27.5 cm

Hope this helped.

Answer:-

h = 17.52cm

Step-by-step explanation:

To find the height, we'll use the formula for a surface area of a cylinder.

[tex]\boxed{\sf SA=2\pi rh+2\pi r^2}[/tex]

Since the diameter is 40 cm, than the radius is :-

Now, let's substitute the values to the SA formula:-

[tex]\sf 4715\;cm^2=2\pi (20cm)h+2\pi (20cm)^2[/tex]

[tex]\sf 4715cm^2=40\pi cmh+800cm^2\pi[/tex]

[tex]\sf \cfrac{4715cm^2-800cm^2\pi }{40\pi cm} =\cfrac{40\pi cm(h)}{40\pi cm}[/tex]

[tex]\sf h=\cfrac{2,201.725877cm^2}{40\pi cm}[/tex]

[tex]\sf h=17.52\; cm[/tex]

____________________

Hope this helps!

Have a great day!

Answer:

1. 10

2. 12

Step-by-step explanation:

1. 8² + 6² = y² (Taking the unknown side as y)

64 + 36 = 100

y² = 100

y = 10

2. 5² + x² = 13² (Taking the unknown side as x)

x² = 13² - 5²

= 169 - 25

= 144

x² = 144

x = 12

Step-by-step explanation:

f(x) = 0.5 ∛(x − 4) − 5

As x approaches ∞:

f(∞) = 0.5 ∛(∞ − 4) − 5

f(∞) = 0.5 ∛(∞) − 5

f(∞) = 0.5 (∞) − 5

f(∞) = ∞ − 5

f(∞) = ∞

As x approaches -∞

f(-∞) = 0.5 ∛(-∞ − 4) − 5

f(-∞) = 0.5 ∛(-∞) − 5

f(-∞) = 0.5 (-∞) − 5

f(-∞) = -∞ − 5

f(-∞) = -∞

The image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

What is rotation?

The term "rotation" refers to an object moving in a circle around its center. Different forms can be rotated at an angle around the centre. A rotation is a map in mathematics. The term "rotation group of a unique space" refers to all rotations that revolve around a fixed point and form a group beneath a structure. With respect to three-dimensional shapes, we can turn or rotate the elements about an endless number of fictitious axes.

Here When rotating a point 270 degrees counterclockwise about the origin our point A( x , y) becomes A'(y,-x). Then

=> (x , y) = (-8,0)

Now 270 degrees counter clockwise rotation then,

=> (y,-x) = (0,-(-8))

=> (y,-x)=(0,8)

Hence the image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

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Two lines represented by the following equations are perpendicular to each other. Explanation is given below.

Those lines that are perpendicular to each other that means create an angle of 90° at intersecting point are perpendicular lines.

We have the equations:

a)6x²-5xy-6y² = 0

b) x²-y²+x+y=0

c) x² - y² = 0​

The above lines are the product of two separate lines.

To prove that the two lines represented by the following equations are perpendicular to each other:

We have drawn the graphs of all the three equations.

The attached images are equation 1, equation 2, equation 3 are in the order of a, b and c.

And we can clearly see that the lines are perpendicular.

The general formula of the equation,

ah²+ 2hk + bk² = 0.

When a+b = 0,

Then the lines are perpendicular.

The sum of the coefficients of order 2 variable is zero.

a). 6 - 6 = 0

b). 1-1 = 0

c). 1-1 = 0

Therefore, the proof is given above.

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Answer: y=25x+80

Step-by-step explanation:

The explanation of each of the term are defined below.

The order of each reactant is known as the reaction orders in a rate law describe the mathematical dependence of the rate on reactant concentrations.

The term rate law expression in math is defined as the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power in which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced chemical equation.

The term overall order of the reaction is known as  the sum of orders for each reactant.

Finally value of the rate constant means the rate constant is temperature dependent.

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The two numbers are 4 and -4, and their product is 4 * -4 = -16, which is the minimum value.

Generally, To find two numbers whose difference is 8 and whose product is a minimum, we can use algebra. Let's call the two numbers x and y. We know that:

x - y = 8 (the difference between the two numbers is 8)

To find the product of the two numbers, we can multiply x and y:

xy = x(x - 8) = x^2 - 8x

To find the minimum value of the product, we can take the derivative of this expression with respect to x and set it equal to 0:

d(xy)/dx = 2x - 8 = 0

Solving for x, we find that x = 4.

Therefore, one of the numbers is 4. We can use the equation x - y = 8 to find the other number:

4 - y = 8

y = -4

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This is all I coulf find hope it helps! :')