The function p, where p (z) = -2² +14z - 40, models the profit from Lindsey's store, in thousands of dollars, after a months of opening the store.
Part A
Based on the function, when did Lindsey's store have a profit of zero dollars?
Enter your answers in the empty boxes to correctly complete the sentence.
The store had $0 profit first in month
and then in month
Part B
When did the store have its maximum profit, and what was the profit?
Enter your answers in the empty boxes to correctly complete the sentence.
The maximum profit of $
occurred in month

The amount of snow that falls from time t = 0 to time t = 5 hours is 20(1-e^(-0.5)) inches.

What is integration ?

Integration is the process of finding an antiderivative of a function. An antiderivative of a function is a function whose derivative is equal to the original function. In other words, integration is the reverse process of differentiation. The process of integration can be thought of as the summing of an infinite number of infinitesimal "slices" of the function being integrated, over a given interval. The symbol ∫ is used to denote integration.

The amount of snow that falls between time t = 0 and time t = 5 hours can be found by evaluating the definite integral of the rate of snowfall with respect to time over the interval [0, 5].

∫[0,5] 2e^(-0.1t) dt

The antiderivative of 2e^(-0.1t) with respect to t is -20e^(-0.1t)

Therefore, the definite integral is

-20e^(-0.15) - (-20e^(-0.10))

= -20e^(-0.5) + 20 = 20(1-e^(-0.5))

Therefore, the amount of snow that falls from time t = 0 to time t = 5 hours is 20(1-e^(-0.5)) inches.

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Answer:

The first one, x+3<16

Step-by-step explanation:

The first one is correct. X represents your friend. In three years, your friend will still not be able to get a license.

Thus, your friend now + three years is STILL LESS THAN SIXTEEN.

X + 3 < 16

That is what that conveys.

Answer:

Step-by-step explanation:

When the digit in the thousands place is < 5, the thousandths place and following digits are replace by 0.

2. When the digit in the thousands place is = or > 5, the digit in the hundredths places is increased by 1 and the following digits become 0.

The radius of the cylinder with a combined volume of 1000 cubic inches is 2.4 inch

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Let r represent the radius of the cylinder/cone.

For the cylinder:

Volume = π * radius² * height

but height is twice the radius, height = 2r, hence:

Volume = π * r² * 2r = 2πr³

For the cube:

Volume = side³

but side is four times the radius, side = 4r, hence:

Volume = (4r)³ = 64r³

The combined volume of a cube and a cylinder is 1000 cubic inches, hence:

1000 = 2πr³ +  64r³

r³(2π + 64) = 1000

r³ = 1000/(2π + 64)

r³ = 14.228

r = 2.4 inch

The radius is 2.4 inch

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the value of cot∅ will be -2√2.

What is trigonometric function?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

Given csc∅ = 3

This is given in 2nd qudrant (90° < 0 <180°).

Sin∅ = 1/3

cos∅ = √1-(1/3)² = -√ (8/9)

cot∅ = cos∅/Sin∅ = -2√2

Hence the value of cot∅ will be -2√2.

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Answer:

18 dollars

Step-by-step explanation:

The easiest way of calculating discount is, in this case, to multiply the normal price $20 by 10 then divide it by one hundred. So, the discount is equal to $2. To calculate the sales price, simply deduct the discount of $2 from the original price $20 then get $18 as the sales price.

The solution to the equation is (3/5, 12/5)

From the question, we have the following parameters that can be used in our computation:

y = 4x

y = -x + 3

substitute the known values in the above equation, so, we have the following representation

4x = -x + 3

Evaluate the like terms

5x = 3

So, we have

x = 3/5

This gives

y = 4 * 3/5

Evaluate

y = 12/5

Hence, the solution is (3/5, 12/5)

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On solving the provided question we can say that - The answer to the question is that all real numbers or domain (−∞,∞)

The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.

The answer to the question is that all real numbers or (−∞,∞)

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On solving the provided question, we can say that Area of rectangular bedroom = 12 X 3.6 = 43.2 cm sq.

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

dimension of rectangular bedroom

L = 12

W = 3.6

Area of rectangular bedroom = 12 X 3.6 = 43.2 cm sq.

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Therefore, using an algebraic method, c = 1/12 in the equation |3/2c - 10| - 9 - 1 is the value of c.

Using the equal symbol (=) to indicate equivalence, a mathematical equation is a formula that joins two statements. An equation in algebra is a statement of mathematics proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign places the variables 3x + 5 and 14 apart. The relationship between two sentences on either side of a letter is described by a mathematical formula. A single variable, which also serves as the symbol, is frequently present. like in 2x - 4 = 2, for instance.

given

|3/2c - 10| - 9 ≤ - 1

3/2c-10 -9 = -1

3/2c - 19 = -1

3/2c = 18

36c = 3

c = 1/12

Therefore, using an algebraic method, c = 1/12 in the equation |3/2c - 10| - 9 - 1 is the value of c.

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Using the number line below, where RS=6y+3, ST=4y+8, and RT=61, the value of y was found to be 4.

An area of a line that can connect two points is known as a line segment. A and B, the ends of this line segment, both have fixed lengths. The separation between endpoints A and B is the length of this line segment. An area or portion of a line with two endpoints is known as a line segment. A line segment has a set length as opposed to a line. Both metric measurements, such as millimeters and centimeters, as well as conventional units, such as feet or inches, can be used to measure the length of a line segment. The length of one line segment in comparison to the other when there are two can be determined just by glancing at them. The line segment CD is longer than AB, as can be seen.

given

ST = 2y + 9 RS = 7y + 3

RT = 14y - 8

S lies between R and T, hence we can deduce that:

RS plus ST = RT

Therefore, we can swap out the equations for each of the segments above to obtain:

We can now solve this for y; to do so, let's move all the phrases that begin with y to the left.

14y -7y - 2y = 3 + 9 + 8\s(14 - 7 - 2) (14 - 7 - 2)

*y = 20

5*y = 20

y = 20/5 = 4\

y = 4

The value of y was determined to be 4.

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Answer:

3.64 meters

Step-by-step explanation:

To find the height of the tree to the nearest hundredth of a meter, you can use the principle of similar triangles.

First, we can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the height of the tree, the distance between the base of the tree and the point where the shadows meet, and the length of the shadow of the tree.

c = √(a² + b²)

c = √(h² + 26.2²)

Next, we can use the similar triangles to establish a ratio between the length of the shadow and the height of the tree and the length of the shadow and the distance from the tree.

shadow tree / height tree = shadow person / height person

31.55 / h = 31.55 / 26.2

Now, we can cross-multiply and divide to solve for h

h = 31.55 * 1.35 / 26.2

h = 3.64 meters

We can round it up to the nearest hundredth of a meter:

h = 3.64 meters

Therefore, the height of the tree is 3.64 meters to the nearest hundredth of a meter.

Using Subtraction, Azzata earns $ 10.45 an hour.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.

Any subtraction problem has three components: the minuend, which is the part you start with; the subtrahend, which is the part being subtracted; and the difference, which is the part that is left over.

Emily earns $11.15 an hour at the movie theater.

She earns $0.7 more an hour than Azzata

Azzata earns -

⇒ $11.15 - $ 0.7

⇒ $ 10.45

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Answer:

x = bottles

y = pail

So, originally the pail had 3.68L from the finished bottle

x+3.68L=y

Then the second equation is after Bill spills 1.2L from the pail, the contents are 3 times that of the bottle

y-1.2L=3x

then played first

so

x-y = -3.68

-3x+y= 1,2

__________+

-2x= -2.48

x=1.24L

So the volume of the bottle is 1.24 L

Pail volume: 1.24+3.68= 4.92L

Using the concept of statistics, We are aware about population, sample and data, Variations refers to different forms of same thing.

Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to describe, understand, and make inferences about data sets, and to make predictions and decisions based on that data. Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to describe, understand, and make inferences about data sets, and to make predictions and decisions based on that data.

In statistics, a population is the entire group of individuals or objects that have some common characteristic or that we are interested in studying. For example, the population of a country would be all its citizens, or the population of a certain species of animal would be all the individuals of that species. A sample is a smaller group of individuals or objects selected from the population in order to study or make inferences about the population as a whole.

Variation refers to the degree to which data points in a set differ from one another. In statistics, variation is used to describe the spread or dispersion of a set of data, and is an important aspect of describing and understanding the data. Variation can be measured using different statistical measures such as range, variance, and standard deviation.

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The function is constant in the interval (-6 to 0).

The correct option is (C).

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

If the value of one of the variables does not alter the value of the other, the function is said to be constant.

As we can see, the function is constant in the range from x=-6 to 0, because the value of y in the function does not change as the value of x changes (-6 to 0).

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Answer: 49 Stamps

Step-by-step explanation:

If Lauren gave Kristen and Ethan 12 stamps and 15 stamps respectively, that means that she gave them a total of 27 stamps. This leaves her with 22 stamps left. In order to find the number of stamps she had at the start, add the stamps she gave away to the stamps she had left at the end. So,

15 stamps + 12 stamps + 22 stamps = 49 stamps total at the start

Lauren had 49 stamps in the beginning. Since she gives Kristen 12 stamps, and Ethan 15 stamps, we can add both amounts to assume the total number of stamps she gave away. 15+12=27, so she gave away 27 stamps.  Lauren was left with 22 stamps. We can add 22 to 27 to find out how many stamps she had in all. 27+22=49. Therefore, we can come to the conclusion that Lauren had 49 stamps at the start.

Hope this helps  o(〃＾▽＾〃)o

The tree's shadow at the same time of day was 113.29 foot long.

Foot, plural feet, any of numerous ancient, mediaeval, and modern linear measures (typically 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.

The metre, the fundamental linear unit in the metric system, has largely replaced the foot, with its multiples and subdivisions, in most nations and in all scientific applications. In the United States, the definition of a foot as exactly 30.48 cm went into effect in 1959.

We know that

1 feet = 12 inches

So, 5 feet 8 inches = 5[tex]\frac{2}{3}[/tex] feet

Now, lets find the shadow of tree

5[tex]\frac{2}{3}[/tex]/2 = 321/x

x = 113[tex]\frac{5}{11}[/tex]

x = 113.29

Thus, the tree's shadow at the same time of day was 113.29 foot long

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This problem can be solved using a system of equations.

What is the system of equations?

A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and graphical solutions are possible for these equations. The point of intersection of two lines represents the system of equations' solution.

Line 1

Taking two points on this line (0,300) and (4,450)

Equation of line y = mx+c

m = [tex]\frac{450 - 300}{4 - 0}[/tex] = 37.5

y = 37.5x + c

Substituting (0,300) in the above equation

300 = 37.5 * 0 + c

c = 300

Line equation y = 37.5x + 300

Line 2

Taking two points on this line (0,400) and (5,500)

m = [tex]\frac{500 - 400}{5 - 0}[/tex] = 20

y = 20x + c

Substituting (0,400) in the above equation

400 = 250* 0 + c

c = 400

Line equation y = 20x + 400

a) The solution of the system is when both lines coincide

     37.5 x + 300 = 20x + 400

     17.5 x = 100

           x = 5.7

            y = 20 * 5.7 + 400 = 514

Therefore the solution of the system is ( 5.7 , 514)

b) In terms of saving money scenario. This means that Dave and Joe have the same amount of savings at this point.

Therefore these are the solutions to the above system of equations.

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Answer:

Step-by-step explanation:

Answer:

It looks correct.

Step-by-step explanation:

The other answer choices don't make sense.

The depreciated value in 1990 will be $146.6.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that in 1986 one of the first video games, the Nintendo sold for $180. The depreciation rate per year is 5%.

The price after 1990 will be calculated as,

Price = 180 x ( 0.95 )⁵

Price = $146.6

The complete question is given below.

In 1986 one of the first video games, the Nintendo sold for $180. The depreciation rate per year is 5%. What is the cost at the end of 1990.

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The truth of the table here is r → (р ∨ q). Option b

For rows A and E, we must now choose which of the following statements is true:

We must utilize the P -> Q table shown in the figure to ascertain that.

We are aware that only P -> Q will be true if both of P and Q's hypotheses are true. As a result of utilizing that method, we can see that the final solutions only include the transformations q->r and r->q.

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Answer:A number is divisible by 2 if it ends in 2, 4, 6, 8 or 0. A number is divisible by 5 if it ends in 5 or 0. A number is divisible by 10 if it ends in a 0.Apr 8, 2018

Answer:

7/28 = 1/4

This is because:

7/28 = 0.25

0.25 = 1/4

Step-by-step explanation:

Hope it helps! =D

Answer:

a) 7

Step-by-step explanation:

Given problem,

→ [ ] ÷ 28 = 1/4

Let us assume that,

→ missing number = x

Forming the equation,

→ x ÷ 28 = 1/4

→ x = (1/4) × 28

→ x = 28/4

→ [ x = 7 ]

Hence, the answer is 7.

The proper pairing is as follows:

(1) The factor in an exponential equation that is repeated: Base

(2) The smaller number indicates the number of times a factor is repeated in an exponential expression: Exponent

Exponentiation is a mathematical process that involves the base b and the exponent or power n.

It is represented as bn and is pronounced as "b to the n."

The formula for an exponential function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0.

The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

The correct matching will be as follows:

(1) The number that is repeated as a factor in an exponential expression: Base

(2) The smaller number in an exponential expression; tells how many times a factor is repeated: Exponent

Therefore, the proper pairing is as follows:

(1) The factor in an exponential equation that is repeated: Base

(2) The smaller number indicates the number of times a factor is repeated in an exponential expression: Exponent

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In the ΔWXY, with the incenter of the triangle being Z.

1. The measure of m∠WYZ = 43°.

2. The measure of m∠WXY = 66°.

3. The measure of m∠YWX = 28°.

4. The measure of m∠ZWX = 14°.

What is an incenter?

The intersection of the triangle's three interior angle bisectors forms the triangle's incenter. Due to the junction point of the central axis being the centre of the triangle's inscribed circle, this point is equally spaced from the sides of a triangle.

In ΔWXY, the incenter of the triangle is Z.

This means that ∠W, ∠Y and ∠X are equally bisected angles.

It is given that the measurement of ∠WYX = 86° and ∠WXZ = 33°

1. The measure of angle ∠WYZ.

The angle ∠WYX is bisected by the line segment YZ.

It forms two angles ∠WYZ and ∠XYZ.

So, the measurement of ∠WYZ = ∠WYX/2

∠WYZ = 86°/2

∠WYZ = 43°

Therefore, the measurement of ∠WYZ = 43°.

2. The measure of angle ∠WXY.

The angle ∠WXY is bisected by the line segment XZ.

It forms two angles ∠WXZ and ∠ZXY.

The measurement of angle ∠WXZ = 33°.

So,  the measurement of ∠WXY = ∠WXZ × 2

∠WXY = 33° × 2

∠WXY = 66°

Therefore, the measurement of ∠WXY = 66°.

3. The measure of angle ∠YWX.

According to the properties of the triangle, the sum of three angles of triangle is 180°.

So, the equation will be -

∠YWX + ∠WXY + ∠XYW = 180°

∠YWX + 66° + 86° = 180°

∠YWX + 152° = 180°

∠YWX = 180° - 152°

∠YWX = 28°

Therefore, the measurement of ∠YWX = 28°.

4. The measure of angle ∠ZWX.

The angle ∠YWX is bisected by the line segment WZ.

It forms two angles ∠YWZ and ∠ZWX.

So, the measurement of ∠ZWX = ∠YWX/2

∠ZWX = 28°/2

∠ZWX = 14°

Therefore, the measurement of ∠ZWX = 14°.

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If the acceleration of the object becomes 9m/s², the force will be 24N

From the information, the moving object, the force acting on the object varies directly with the object's acceleration. When a force of 36N acts on a certain object, the acceleration of the object is 6m/s². The constant will be:

y = k/x

y = force.

x = acceleration

k = constant of proportionality.

k = 36 × 6

k = 216

If the acceleration of the object becomes 9m/s², the force will be:

= 216 / 9

= 24

The force is 24N.

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1) Orders between 186 and 187 is zero

2) Common order weight is 183.8.

3) Average is 183.6625

A dot plot is defined as a simple plot that displays data values as dots above a number line. Dot plots show the frequency with which a specific item shows in a data set. Dot plots simply show the distribution of the data.

A manufacturing company is shipping a certain number of orders that need to weigh between 184 and 184 pounds in order to ship.

Data is given below;

Arranged in ascending order this would be

183.2, 183.2, 183.3, 183.3, 183.7, 183.7, 183.8, 183.8, 183.8, 183.8, 183.8, 183.8, 183.8, 183.8, 183.9, 183.9

Min is 183.2 and max is 183.9

1) Orders between 186 and 187 is nil

2) Common order weight is one which is maximum repeated and in this case, the common order weight is 183.8.

3) Average = sum/16

Average = 183.2 + 183.2 + 183.3 + 183.3 + 183.7 + 183.7 + 183.8 + 183.8 + 183.8 +  183.8 + 183.8 + 183.8 + 183.8 + 183.8 + 183.9 + 183.9

Average = 2,938.6/16

Average = 183.6625

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Answer:

Step-by-step explanation:

The amount in dollars is represented by d, and the amount of months is represented by the letter t. Using this, you can construct an equation using the given values in the form of f(x) = a - b(c). This equation represents the decrease in Malik's income after one month.

Hope this helps! :)