Identify the domain and range of the function domain

the z-value for an apple that weighs 140 grams is 1.5.

The z-value is used to determine how many standard deviations an observation is from the mean of a normal distribution. To find the z-value for an apple that weighs 140 grams, we need to calculate the difference between the apple's weight and the mean weight, and divide by the standard deviation.

Given that the average weight of a honeycrisp apple is 110 grams and the standard deviation is 20 grams, we can calculate the z-value as follows:

(140 - 110) / 20 = 1.5

This means that the apple that weighs 140 grams is 1.5 standard deviations above the mean weight of 110 grams. This information can be used to calculate the probability of finding an apple with a weight of 140 grams. For example, if we use a standard normal distribution table, we can find that the probability of finding an apple with a weight greater than 140 grams is 0.0668, or 6.68%.

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Line through (2,4,5) perpendicular to plane 3x-7y+5z=21 found by finding normal vector <3,-7,5> and direction vector <0,5,-3> from cross product. Parametric equation is r(t)=<2,4,5>+t<0,5,-3>.

What is plane ?

A plane is a Euclidean, two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point, a line and three-dimensional space.

The normal vector is given by the coefficients of x, y, and z in the equation of the plane:

n = <3, -7, 5>

Next, we need to find a point on the line and a direction vector for the line. The point on the line is (2, 4, 5) and the direction vector can be found by taking the cross product of the normal vector and an arbitrary vector not parallel to the normal vector.

An arbitrary vector not parallel to the normal vector could be <1, 0, 0>. Taking the cross product, we get:

d = n x <1, 0, 0> = <0, 5, -3>

So, the line through (2, 4, 5) perpendicular to the plane 3x - 7y + 5z = 21 is given by:

r(t) = <2, 4, 5> + t<0, 5, -3> = <2 + 0t, 4 + 5t, 5 - 3t>

Line through (2,4,5) perpendicular to plane 3x-7y+5z=21 found by finding normal vector <3,-7,5> and direction vector <0,5,-3> from cross product. Parametric equation is r(t)=<2,4,5>+t<0,5,-3>.

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The volume of the cube as a polynomial is 8x³ + 12x² + 6x + 1.

The volume of a cube is expressed as;

V = a³

Where a is the side of the cube.

Given that;

Plug the given value into the above equation and simplify.

V = a³

V = ( 2x + 1 )³

Expand using FOIL method

V = ( 2x + 1 )( 2x + 1 )( 2x + 1 )

V = ( 2x( 2x + 1 ) + 1( 2x + 1 ) )( 2x + 1 )

V = (4x² + 4x + 1 )( 2x + 1 )

V = 2x(4x² + 4x + 1 ) + 1(4x² + 4x + 1 )

V = 8x³ + 8x² + 2x + 4x² + 4x + 1

Collect and add like terms

V = 8x³ + 12x² + 2x + 4x + 1

V = 8x³ + 12x² + 6x + 1

Therefore, the volume is 8x³ + 12x² + 6x + 1.

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Option C is correct.  Less than 100  is closest to total deaths resulting from ladder misuse each year.

According to the Consumer Product Safety Commission (CPSC), on average, approximately 300 people die each year in the United States from falls involving ladders.

However, not all of these deaths are due to ladder misuse. In fact, the number of deaths resulting specifically from ladder misuse is likely to be lower. It is estimated that a significant portion of ladder-related fatalities are caused by factors such as overreaching, misusing the ladder, or failing to follow proper safety guidelines.

To reduce the number of deaths and injuries resulting from ladder misuse, it is important to follow safety guidelines and to choose the right ladder for the job, taking into consideration factors such as height, weight, and stability.

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Expected length = 6 meter.

Using the formula,

  A = W × L

where,

Area (A) = 24

Width (W) = 4

Length (L) = ?

so, A/W = 24/4 = 6

Hence, length of the rectangle is 6 meter.

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For given expression n-8>=10 to be true, n>=18.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.

e.g. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the expression x/2 + 6. Complex riddles are solved using mathematical expressions.

Now

Given

The difference of a number (n) and 8 is no less than 10.

We can write this as expression n-8>=10,

and for this to be true n>=18.

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The value of derivative is approximated by tan(pi/4 + 0.0001) - 1 / 0,0001 is pi / 4 by limits and continuity.

Let the given expression be some I (say)

then , I = tan(pi/4 + 0.0001) - 1 / 0,0001

         we know that tan(pi/4) = 1

hence replace 1 by tan(pi/4) in the above expression,

         I = tan(pi/4 + 0.0001) - tan(pi/4) / 0,0001

Now, tan (I) = limx→0 tan(I+x) - tan(I) / x

in this case , x = 0.0001 and I = pi/4

Therefore , the derivative is approximated by tan(pi/4 + 0.0001) - 1 / 0,0001 is at pi/4.

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Answer:

Third option

Step-by-step explanation:

If the polynomial has a factor of the form  [tex](x - h)^p,[/tex] the behavior of its graph is determined by the value of p. p .

One zero of the polynomial is x = h

x - h is a zero of multiplicity p

The following is a summary of rules regarding multiplicities and x-intercepts.

The given polynomial is:
[tex]\mbox {\large \textsf(x - 1)^2(x+3)(x + 5)^5}}[/tex]

The zeros can be found by setting each of these factors to 0 and solving for x
x - 1 = 0 ==> x = 1
x + 3 = 0 ==> x == -3

x + 5 = 0 ==> x = -5

Hence, the zeros of this polynomial are

Using the rules provided we see that the graph

This corresponds to
Third option

According to Chebyshev's theorem, at least 69 percent of any set of observations will be within 1.8 standard deviations of the mean.

Standard deviations of the mean = 1.8 s

According to Chebyshev's theorem at least (1 - 1/k^2)×100% observations will lie within k standard deviation from the mean.

The proportion of observations that will be within 1.8 standard deviations of the mean = (1 - 1/(1.8)^2)×100%

The proportion of observations that will be within 1.8 standard deviations of the mean = (1 - 1/3.24)×100%

The proportion of observations that will be within 1.8 standard deviations of the mean = (1 - 0.31)×100%

The proportion of observations that will be within 1.8 standard deviations of the mean = 0.69 × 100%

The proportion of observations that will be within 1.8 standard deviations of the mean = 69%

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Answer: 2x + 4mi >=10 , 3

Step-by-step explanation:
x=days after monday

Since Joseph ran 4 miles the first day, that number stays constant. The 2miles depends on the amount of days he runs for so that is the coefficient. Atleast means greater than or equal to. Using the inequality, we can solve that x >= 3.

2x+4>=10

    -4    -4

2x>=6

/2     /2

x>=3

Hire purchase is a method of purchasing goods in which the retailer arranges for a lending firm to collect a down payment from you and you pay the remaining balance in monthly instalments.

A hire purchase, often referred to as an instalment plan, is a deal where a client accepts a contract to buy an item by making a down payment and paying the remaining amount of the asset's price plus interest over time.

Hire purchase is a method of purchasing goods in which the retailer arranges for a lending firm to collect a down payment from you and you pay the remaining balance in monthly instalments.

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The percentage of 7th graders students that spend less than an hour a day on social media is 51.8%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

7th graders:

Number of students that spend less than an hour = 29

Number of students = 56

The percentage of students that spend less than an hour.

= 29/56 x 100

= 51.785

= 51.8 %

Thus,

The percentage of students that spend less than an hour is 51.8%.

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The new coordinates of the point will be (2, -3).

Coordinate is a system used to determine the exact location of a point on a 2-dimensional plane or 3-dimensional space. It is typically used to pinpoint a specific spot on a map or graph. Coordinate systems are usually written in two or three numbers, representing the x, y and z positions of the point. These coordinates can then be used to calculate distances, angles and other measurements.

After the transformation D5 o R270-, the image point of (-3, 4) will be (2, -3). The transformation D5 is a dilation, which changes the distance between the origin and the point by a factor of 5. The transformation R270- is a rotation by 270 degrees counter-clockwise, which moves the point to the left and up by the same distance. Therefore, the new coordinates of the point will be (2, -3).

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The correct option:  A) Completely randomized design: Randomly assign the treatments to the dogs.

"Any randomized design is regarded as a form of experiment that is assigned to various treatments by carrying out various experiments on various groups.

The answer to the query is

Therefore, we get to the conclusion that the treatment given to the dogs at random is the best course of action.

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The values of x = 10√3 derived using the trigonometric ratio of cosine.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent x and hypotenuse 30;

cosθ = x/30

for the smaller right triangle with adjacent 30 - 20 = 10 and hypotenuse x

cosθ = 10/x

x/30 = 10/x

x² = 300 {cross multiplication}

x = √300 {take square root of both sides}

x = √100 × √3

x = 10√3.

Therefore, the values of x = 10√3 derived using the trigonometric ratio of cosine.

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The displacement made by the cyclist is 0, this is caused by the same path traveled by the cyclist.

Displacement is the change in position of a moving object relative to a frame of reference. That is, locking is a change in the initial position of the object to the final position of the object.

The displacement in this case is calculated by the Pythagorean theorem.

Displacement² = S₁² + S₂²

The displacement will be zero when the start and end points are the same, that's what makes the problem zero. In the question, the distance traveled by the rider is 45 km, but because there is no position lock because the rider is traveling the same path, the closing done by the cyclist is 0.

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P-values that are precise serve as a measure of statistical significance is important to include on the box-whisker plot.

In a clinical trial, research is conducted on human participants (sometimes known as volunteers) with the goal of advancing medical knowledge.

Clinical trials also known as interventional studies and observational studies are the two primary categories of clinical research. Medical products, such as medications or gadgets, surgeries, or adjustments to participants' behavior, including dietary changes, can all be considered treatments.

The null hypothesis should be rejected if the p-value is less than 0.05, which is commonly regarded as statistically significant. The null hypothesis is not rejected if the p-value is greater than 0.05 since it indicates that the divergence from the null hypothesis is not statistically significant.

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The two equations representing the costs are 10 + 5x and 15 + 4.5x.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Let, 'x' be the number of pizzas.

Therefore, From the given information the two linear equations we can form is, 10 + 5x and 15 + 4.5x.

As the delivery charges for both the stores is a constant.

We can determine the number of pizzas when the cost for both options would be the same by equating these two equations.

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This cannot be determined with the information given. To calculate the sample size, we would need to know the population means, the population standard deviation, and the confidence interval.

The confidence interval is 97%, which is the likelihood that the mean of the receipts is less than $38. We can use this information to calculate the margin of error and then use this to calculate the sample size.   The margin of error is calculated by taking the critical value (in this case, 1.96) and multiplying it by the standard deviation of the population. We then divide this by the square root of the sample size to get the margin of error.  

Once we have the margin of error, we can then calculate the sample size by taking the population means minus the margin of error and dividing this by the desired confidence interval. In this case, the desired confidence interval is 97%.   Therefore, without the population means, standard deviation, and confidence interval, it is impossible to calculate the sample size.

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Answer:

I think the answer is 5y-8-2.5z

All of the y-values are not a constant multiple of the corresponding x-values, so the relationship is not a proportional relationship.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between the x-values and y-values in this table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/1 ≠ 5/2 ≠ 6/3

Since the constant of proportionality (k) for the relationship between the x-values and y-values are different, we can logically deduce that this is not a proportional relationship.

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Answer:

SAS because you have two congruent sides surrounding one congruent angle

After 30 minutes, the amount of salt remaining in the tank is 18.75 kg. This is because the brine entering the tank contains 0.03 kg of salt per liter of water, and 25 liters of brine are entering the tank every minute.

Thus, in 30 minutes, 750 liters of brine will have entered the tank, bringing with it 22.5 kg of salt. Since the tank initially contained 20 kg of salt, the amount of salt remaining after 30 minutes is 18.75 kg.

The theory behind the amount of salt remaining in the tank after a given amount of time is based on the idea that the amount of salt entering the tank is equal to the amount of salt leaving the tank. The amount of salt entering the tank is determined by the concentration of salt in the brine solution and the rate at which the brine enters the tank. The amount of salt leaving the tank is determined by the same rate at which the brine enters the tank.

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The double integral is used to calculate the area of a region enclosed by two curves.

The region is bounded by the curves x = 1, y = 0, x = 3 and y = [tex]3x2 - 9x2y2[/tex]. In this case, the double integral is given by the expression [tex]∫10∫312x3 - 9x2y2 dy dx.[/tex]

In order to calculate the double integral, the iterated integral method is used. This involves integrating the inner integral with respect to y first, and then integrating the outer integral with respect to x.

The first step is to integrate the inner integral with respect to y. This gives us the expression [tex]∫0 3 (12x3 - 9x2y2) dy[/tex]. After integrating with respect to y, we then integrate the outer integral with respect to x. This gives us the expression [tex]∫10 ∫0 3 (12x3 - 9x2y2) dy dx.[/tex]

The result of this double integral is the area of the region bounded by the two curves. The result of the double integral is therefore the area of the region bounded by the two curves. The result of the double integral is therefore the area of the region enclosed by the two curves. The result of this double integral is the area of the region bounded by the two curves.

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Answer:

The area of a trapezium with parallel sides of length 19 cm and 21 cm, and a distance of 14 cm between them, is 280 square cm.

Step-by-step explanation:

The probability the that red ball was moved is 1/100

Given that there are two bags. Bag A contains 1 red ball and 9 blue balls. Bag B contains 10 blue balls. A ball is chosen at random from bag A and placed into bag B. Then a ball is chosen at random from bag B and placed into bag A. After this process, the red ball is in bag A and we are asked to find the probability that it was moved.

Probability of the red ball chosen from bag A = 1/10

Probability of the red ball chosen from bag B = 1/10

After this process, the red ball is in bag A, the probability that it was moved.

                              1/10 × 1/10 = 1/100

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For the slope of -3, the altitude where the average temperature is -50°C is 70 km.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

At 50 kilometer from earth's surface, the temperature is 10°C.

At 80 kilometer from earth's surface, the temperature is -80°C.

The given temperature for unknown altitude is -50°C.

We are told that the temperature varies linearly with altitude, so if y represents the temperature (in °C) and x represents altitude (in km), these variables are related by the equation y = mx + b, where m (the slope) and  b (the y-intercept) are constants.

The two points on this line are (50 km , 10°C) and  (80 km , -80°C).

Use these points to find the slope m -

m = (y2 - y1)/(x2 - x1)

m = (-80 - 10)/(80 - 50)

m = -90/30

m = -3

Recall that the slope of a linear relationship is the "unit rate of change". In other words, the slope of -3 means that the temperature declines by 3°C for every 1 km of additional altitude.

Since the altitude at which the temperature is -50°C is needed, the value of x such that (x, -50°C) is on this line is needed. To find x, simply use the slope formula again, using either of the other two points:

Slope formula using (50,10) and (x,-50) -

m = (y2 - y1)/(x2 - x1)

-3 = (-50 - 10)/(x - 50)

-3(x - 50) = -60

-3x + 150 = -60

-3x = -60 - 150

-3x = -210

x = -210/-3

x = 70

Therefore, the altitude will be 70 km.

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The admissions office wishes to estimate the average cost of textbooks for all students, represented by the parameter μ (the population mean).

There are steps followed to determine the parameter the admissions office wishes to estimate:

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The measure of the angle JKH is 19 degrees

The complete question is added as an attachment

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

m/LJK= 38° and m/KLJ= 71°.

Start by calculating the external angle of  JKL

So, we have

External = LJK + KLJ

External = 38 + 71

External = 109

The measure of angle JKH is then calculated using:

JKH + 90 = External

This gives

JKH + 90 = 109

Evaluatet the like terms

JKH = 19

Hence, the angle has a value of 19 degrees

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