Question 4 [14 marks]
Part a) (6 marks)
Find the following probabilities by checking the z table i) P(-1.5 ii) P((1.15 Z0.35
Part b) (8 marks)
Battery manufacturers compete on the basis of the amount of time their products last in cameras and toys. A manufacturer of alkaline batteries has observed that its batteries last for an average 26 hours when used in a toy racing car. The amount of time is normally distributed with a standard division of 2.5 hours.
What is the probability that the battery lasts between 25 and 29 hours?
What is the probability that the battery lasts longer than 29 hours
What is the probability that the battery lasts less than 25 hours.

The y-intercept of the graph is located at (0, 0). So, the value of c is 0.

What is graph?

A graph is a visual representation of data that displays the relationship between two or more variables. It consists of a set of points, called vertices or nodes, which are connected by lines or curves, called edges or arcs. The vertices represent the variables, while the edges represent the relationship between them.

To find the y-intercept of the graph of y = -7x + 140y, we need to substitute x = 0 into the equation and solve for y. This will give us the y-coordinate of the point where the graph intersects the y-axis.

Substituting x = 0, we get:

y = -7(0) + 140y

y = 140y

Simplifying the equation, we get:

139y = 0

Dividing both sides by 139, we get:

y = 0

Therefore, the y-intercept of the graph is located at (0, 0). So, the value of c is 0.

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Answer:

блина я сама не

Step-by-step explanation:

Answer: 32

Step-by-step explanation:

the min is 54 while the max is 86

86-54 is the range which is 32

Answer:

Step-by-step explanation:

to factorize [tex](x-4)^{2} -36[/tex]
(x-4-6) * (x - 4 / 6)
(x-10) * (x+2)

Answer:

Step-by-step explanation:

So first you would combine like terms which in this case are 9x, -6x, y, and y

So: 9x+y-6x+y

(9x-6x)+(y+y)

3x+2y is the final answer

hope this helped

Answer:

Step-by-step explanation:

To calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.

What is rate ?

In mathematics, a rate is a ratio that compares two quantities with different units. It is typically expressed as the amount of change of one quantity with respect to another quantity. Rates are often used in the context of describing how quickly or slowly something changes over time or space.

To calculate a rate, we need to divide two quantities that have different units. For example, if we want to find the rate of a car's speed, we divide the distance traveled (in miles) by the time taken to travel that distance (in hours).

The formula for rate is:

rate = quantity / time

To calculate a unit rate, we need to divide a rate by the quantity being measured. For example, if the rate is the number of miles traveled per hour, the unit rate would be the number of miles traveled in one hour. To find the unit rate, we divide the rate by 1 hour.

The formula for unit rate is:

unit rate = rate / 1

When calculating rates or unit rates, it is important to make sure that the units of the quantities being divided are consistent. If the units are not the same, we need to convert them to the same unit before performing the division.

Therefore, to calculate a rate, divide two quantities with different units; to calculate a unit rate, divide a rate by the quantity being measured.

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the perimeter of D'E'F is 5 times larger than the perimeter of DEF.

If the scale from DEF to D'E'F is 5:1, then the corresponding side lengths are multiplied by a factor of 5 when going from DEF to D'E'F. This means that if the perimeter of DEF is P, then the perimeter of D'E'F is 5P.

To see why this is true, consider the perimeter of DEF:

P = DE + EF + FD

When we scale up by a factor of 5, we get:

D'E' + E'F' + F'D' = 5DE + 5EF + 5FD

= 5(DE + EF + FD)

= 5P

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The price per unit that yields maximum revenue is $400.

We can start by finding the demand function for the product. Since the demand is assumed to be linear, we can use two data points to find the equation of the line:

(40, 300) and (45, 275)

Using the point-slope form of a line, we get:

(275 - 300) / (45 - 40) = -5/25 = -1/5

y - 300 = (-1/5)(x - 40)

y = (-1/5)x + 320

where y is the number of units sold per week and x is the price per unit.

The revenue function is simply the product of the price and the number of units sold:

R = xy

Substituting the demand function, we get:

R = x(-1/5)x + 320x

Simplifying, we get:

R = -1/5x^2 + 320x

To find the price per unit that yields maximum revenue, we need to take the derivative of the revenue function with respect to x and set it equal to zero:

dR/dx = -2/5x + 320 = 0

Solving for x, we get:

x = 800/2 = $400

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Answer:

the actual distance is 2 kilometer.

Step-by-step explanation:

The Answer should be 4:1 it's the half of the 8 to 2

The surface area of the prism is 210.4 in².

The surface area of a prism is the sum of the areas of all of its faces.

For a right prism (a prism with rectangular bases), the formula for the surface area is:

Surface Area = 2(length x width) + (height x perimeter of base)

where;

The surface area of the prism is calculated as;

S.A = 2 (9 in x 5 in) + ( 4.3)(2 (9 in + 5 in )

S.A = 90 in²  +  120.4 in²

S.A = 210.4 in²

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97 bielorrusias hacen falta para comprarte un perro

The value of distance between city B to city C given by 'x' is found as: 41 miles.

Distance in air miles from city A to each city B and city C are-

City A to City B= 11

City A to city C= 29

City B to City C= X

Then,

Distance between city B to city C = distance between city A to city B +  between city A to city C

x = 29 + 11

Solving the linear equation:

x = 41

Thus, the value of distance between city B to city C given by 'x' is found as: 41 miles.

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For Milton to fill the 3-gallon aquarium with water, the 1-quart container will need to be filled and emptied 12 times.

The 3-gallon aquarium must first be converted to quarts. A 3-gallon aquarium holds 12 quarts since 1 gallon equals 4 quarts.

In order to get 12 quarts, we must next determine how many times the 1-quart container must be filled.

12 quarts divided by one quart equals 12 containers.

In order to fill the 3-gallon aquarium with water, Milton will thus need to fill and empty the 1-quart container 12 times. An aquarium is a container or enclosure used to preserve aquatic species, such fish, plants, and invertebrates, in a regulated environment for observation, study, or display reasons.

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The correct answer is C. 6 seconds.

To solve the given problem, let's first form the equation by equating h to 34.48 (since this is the height we are looking for):34.48 = 14.5 cos(2πt/5) + 30Next, let's subtract 30 from both sides:4.48 = 14.5 cos(2πt/5)Now, let's divide both sides by 14.5:cos(2πt/5) = 4.48/14.5Now we can solve for t:2πt/5 = cos^-1(4.48/14.5)t = (5/2π) cos^-1(4.48/14.5)Using a calculator, we can evaluate this expression to get t ≈ 3.59 seconds. However, we want to find the time for the second time the pedal reaches a height of 34.48 inches. Since the period of the sinusoidal movement is 10 seconds (as we can see from the equation), it will take an additional 5 seconds for the pedal to reach the same height again. Therefore, the total time for the pedal to reach a height of 34.48 inches for the second time is:t = 3.59 + 5 = 8.59 seconds Rounding to the nearest second, we get an answer of C. 6 seconds. Therefore, the correct answer is C. 6 seconds.

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Therefore , the solution of the given problem of cardinality comes out to be A×B×C is 3 .

A's cardinality is equivalent to its element count if A has a finite amount of elements. Say |A|=5 if A=2, 4, 6, 8, 10. The outcome of a numbering process is referred to as "cardinality". A set's cardinality is determined by the number of components in it. For illustration, the group 1, 2, 3, 4, and 5 has a greater cardinality of five than the set 1, 2, 3, and 5, each of which has an attributes of three.

Here,

a)

I "Chinese New Year of 2023" has one cardinal element, making it one-dimensional.

ii) Since there are three elements in S and each element can either be included in a subset or not, the power set P(S) of S=1,,apple has 23 = 8 elements.

iii) xRx2=3 has two components because the squares of two real numbers, 3 and -3, are both 3.

iv) Since "0" is regarded as one element and there are five other distinct elements in the collection,  {{0,1,2},3,4,5,∅,{{0}}}  has six elements.

b)

=> A={0,1,2}, B={apple}, and C={apple}

The set difference between C and A is only the element 0, which is absent from C, so A=apple0,1,2=apple.

Consequently, A, B, and C include the following components:

=> {(0,apple,apple), (1,apple,apple), (2,apple,apple)}

=>  A×B×C is 3 .

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The answer will be as follows after answering the supplied question As a coordinates result, Anew "'s ordered pair is (-1/2 * x, 1/2 * y).

In geometry, a coordinate system is a method that uses one or more numbers or coordinates to determine the precise arrangement of points or other geometrical objects on a manifold, such as Euclidean space. Coordinates are pairs of numbers that are used to locate a point or object on a two-dimensional plane. A point's location on a 2D plane is represented by two numbers known as the x and y coordinates. a set of digits that represent precise locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second number represents the top-to-bottom distance. As in (12.5), when there are 12 units below and 5 above.  

To conduct a dilation with a scale factor of 1/2 around the origin, multiply each point's coordinates by 1/2. If the initial coordinates of point A are (x,y), then the dilated point A' coordinates are:

A' = (1/2 * x, 1/2 * y)

We negate the x-coordinate while keeping the y-coordinate constant to represent the dilated point A' over the y-axis. As a result, the final coordinates of A" are:

A'' = (-1/2 * x, 1/2 * y)

As a result, Anew "'s ordered pair is (-1/2 * x, 1/2 * y).

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a. Simplified equivalent expressiοns: A = 3x + 15

b. The expressiοn that represents this situatiοn is: 6x - 4

c. The expressiοn that represents the tοtal number οf items in these fοur rοws is: 4(2x+1)

d. The expressiοn that represents this situatiοn is: 3(x+1)

Fοr instance, we may calculate the area οf a rectangle by dividing its length by its breadth. The surface area οf the rectangle is either 24 οr 8. There are a tοtal οf eight tiny squares, if yοu cοunt them. (See Rectangle's Area.)

a. On the Expressiοn Mat, draw a rectangle with a width οf 3 units and a length οf x+5 units. The expressiοn that represents the area οf this rectangle is:

A = 3(x+5)

Simplified equivalent expressiοns:

A = 3x + 15

b. On the Expressiοn Mat, draw twο equal grοups οf 3x-2. The expressiοn that represents this situatiοn is:

(3x-2) + (3x-2)

6x - 4

c. On the Expressiοn Mat, draw fοur rοws οf 2x+1. The expressiοn that represents the tοtal number οf items in these fοur rοws is:

4(2x+1)

Simplified equivalent expressiοns:

8x + 4

d. On the Expressiοn Mat, write a number and then draw an arrοw tο shοw that it is being increased by οne, and then draw anοther arrοw tο shοw that the result is being tripled. The expressiοn that represents this situatiοn is:

3(x+1)

Simplified equivalent expressiοns:

3x + 3

3(x + 1)

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The cοrrect answer is A, E and F. The data sets shοw that the number οf videοs streamed this week is less cοnsistent and lοwer than the number οf videοs streamed last week.

Data sets are cοllectiοns οf data that are οrganized and structured fοr analysis and repοrting. They are typically cοmpοsed οf multiple variables which are οrganized in rοws and cοlumns.

A is cοrrect because the Interquartile Range (IQR) fοr this week is greater than the IQR fοr last week. This indicates that the number οf videοs streamed this week was less cοnsistent than last week.

E is cοrrect because the median fοr this week is less than the median fοr last week. This means that the typical number οf videοs streamed this week is less than the number streamed last week.

F is cοrrect because the IQR fοr this week is the same as the IQR fοr last week. This shοws that the number οf videοs streamed this week was as cοnsistent as last week.

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The area of one slice of a large pizza with a diameter of 24 inches is 56.52 square inches.

The formula for calculating the area of a circle is A = πr^2, where A is the area of the circle, π is the constant pi (3.1415) and r is the radius of the circle. To calculate the area of a slice, we must first calculate the radius of the pizza. To do this, we divide the diameter of the pizza (24 inches) by 2, which yields a radius of 12 inches.

Now that we have the radius, we can calculate the area of one slice. Plugging the radius of 12 inches into the equation, we get A = 3.1415*12^2 = 452.16 square inches. Since each pizza is cut into 8 equal slices, each slice would have an area of 452.16/8 = 56.52 square inches.

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Answer: To solve the inequality x − (5 − 3x) ≤ 2x − 1, we need to simplify it by first distributing the negative sign in front of the parentheses, and then combining like terms. This gives us:

x - 5 + 3x ≤ 2x - 1

4x - 5 ≤ 2x - 1

Next, we can isolate the variable on one side of the inequality by subtracting 2x from both sides:

4x - 2x - 5 ≤ -1

2x - 5 ≤ -1

Finally, we can isolate x by adding 5 to both sides and dividing by 2:

2x ≤ 4

x ≤ 2

So the solution to the inequality is x ≤ 2.

To graph this solution on a number line, we can put a closed dot at 2 and shade to the left of it, since all values less than or equal to 2 satisfy the inequality. Therefore, the correct graph is A, a number line with a closed dot at 2 shaded to the left.

Step-by-step explanation:

(a) The solution of the seasonal-growth model is

P(t) = P0[tex]e^{(k/r sin(rt))}[/tex]

(b) After solving we get [tex]\lim_{t \to \infty} P(t)[/tex] = NONE . As, t approaches to infinity

(a) To solve the differential equation DP/dt = kPcos(rt-[tex]\theta[/tex]),

The variables can be split apart and integrat:

∫(1/P) dP = ∫k cos(rt-[tex]\theta[/tex] ) dt

ln|P| = (k/r)sin(rt- [tex]\theta[/tex] ) + C

where

C is the constant of integration.

By solving for P, we get:

P(t) = [tex]e^{(k/r sin(rt- \theta ) + C)}[/tex]

We can determine the value of C by using the initial condition P(0) = P0:

P(0) = [tex]e^{(k/r sin(- \theta) + C)}[/tex]= P0

C = ln(P0) - (k/r)sin(-[tex]\theta[/tex] )

C = ln(P0) + (k/r)sin([tex]\theta[/tex] )

By substituting this into the expression for P(t), we get:

P(t) = [tex]e^{(k/r sin(rt-\theta) + ln(P0) + (k/r)sin(\theta))}[/tex]

By simplifying, we get:

P(t) = P0[tex]e^{(k/r sin(rt-\theta) + k/r sin(\theta))}[/tex]

P(t) = P0[tex]e^{(k/r sin(rt))}[/tex]

(b) We must take into account the behavior of sin(rt) as t approaches infinity in order to determine the limit of P(t) as t approaches infinity. Sin(rt) will fluctuate between -1 and 1 as t grows because the sine function oscillates between -1 and 1.

As a result, the term [tex]e^{(k/r sin(rt))}[/tex] will bounce between [tex]e^{(-k/r)}[/tex] and [tex]e^{(k/r)}[/tex] as t approaches infinity, but it won't converge to a single value.

As a result, there is no P(t) limit as t approaches infinity.

Hence, the answer is:

[tex]\lim_{t \to \infty} P(t)[/tex] = NONE.

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we can deduct that the angle on the L vertex is 25°, because that way all three angles will result in 180°.

We know that JKLM is a parallelogram, which means that its opposite sides are parallels, such that: JK // ML and JM // KL.

So, we know that the angle MLJ equals 25°, and JK // ML, from this we can say that angles LJK and MLJ are equal, because they are ''internal alternate angles'', since that they are inside the parallels.

So, angle LJK is 25, and JKL is a triangle, which has the angle at K vertex equal to 130°. We know that internal angles in a triangle must sum 180°.

Since that, two angles, in the triangle JKL, measure 130° + 25° = 155°; we can deduct that the angle on the L vertex is 25°, because that way all three angles will result in 180°.

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i have no idea what that is

The gross earning per week is = $ 495.56.

The salary to hourly wage calculator allows you to view your earnings over several time frames. It is a versatile tool that enables you to change your annual salary into an hourly payout, compute your monthly salary into an hourly rate, change your weekly rate into an annual salary, etc. You will save time and effort by using our salary converter, which completes all tasks fast and easily.

Joseph works 5 hours on Monday

10 hours on Tuesday,

9. 5 hours on Wednesday

8. 25 hours on Thursday

6 hours on Friday

7. 5 hours on Saturday

He is paid $9. 85 per hour and time and a half for all hours over 40 per week.

Total working hour= 5+10+9.5+8.25+6+7.5=46.25

Earning per hour is = 9.85

total earning= 46.25*9.85=$455.56

total gross earning= $ 455.56+40=495.56

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Answer:

18x + 22y

Step-by-step explanation:

4x (3) + 5y (3) + 2x (3) + 7y

Multiply the coefficients of the variables x and y with the constants, so that:

4x (3) + 5y (3) + 2x (3) + 7y

= 12x + 15y + 6x + 7y

Then just add up the coefficients with the same variable:

12x + 6x = 18x

15y + 7y = 22y

So the final answer is:
18x + 22y

[tex]\huge\text{Hey there!}}[/tex]

[tex]\mathsf{4x^3 + 5y^3 + 2x^3 + 7y}[/tex]

[tex]\large\textsf{COMBINE the LIKE TERMS (if you have any):}[/tex]

[tex]\mathsf{= (4x^3 + 2x^3) + (5y^3) + (7y)}[/tex]

[tex]\mathsf{= 4x^3 + 2x^3 + 5y^3 + 7y}[/tex]

[tex]\mathsf{= 6x^3 + 5y^3 + 7y}[/tex]

[tex]\large\textsf{Therefore your ANSWER should be:}[/tex]

[tex]\huge\boxed{\mathsf{6x^3 + 5y^3 + 7y}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:  It will take 4.5 hours to travel 432 kilometers at an average speed of 96 kilometers per hour

Step-by-step explanation:

The normal curve can be used to approximate the binomial probability as all conditions are met, with at least 10 successes and failures, a success rate of less than 10%, and a sample size of at least 20.

Only when specific requirements are met can the normal curve be used to approximate the binomial probability in this situation. The trial must have at least 10 successes and 10 failures as its initial requirement. There are more than 10 successes and 10 failures in this instance since 124 machines are being tested. The second requirement is that the likelihood of success must be under 10%. The likelihood of a computer failing in this scenario is 4%, which is less than 10%. The sample size needs to be at least 20, which is the third requirement. The sample size in this instance is 124, which is more than 20.

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225 hamburgers were sοld οn Saturday

A linear equatiοn is an equatiοn οf a straight line in twο variables, usually written in the fοrm y = mx + b, where m is the slοpe and b is the y-intercept. It represents a relatiοnship between twο variables that is linear, meaning that as οne variable changes, the οther changes at a cοnstant rate.

Let's use algebra tο sοlve the prοblem.

Let x be the number οf hamburgers sοld οn Saturday.

Then, accοrding tο the prοblem, the number οf cheeseburgers sοld οn Saturday is 73 mοre than the number οf hamburgers sοld, sο the number οf cheeseburgers sοld is x + 73.

The prοblem alsο tells us that the tοtal number οf hamburgers and cheeseburgers sοld is 523. Sο we can set up an equatiοn:

x + (x + 73) = 523

Simplifying the left side οf the equatiοn:

2x + 73 = 523

Subtracting 73 frοm bοth sides:

2x = 450

Dividing bοth sides by 2:

x = 225

Therefοre, 225 hamburgers were sοld οn Saturday.

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