consider the inequality 6x<42.
part A
elizabeth says that any value of x less than 36 makes the equality true.


explain pliss

The scale factor of the dilation must be greater than 1. if the image A'B'C' is bigger than the preimage ABC

If the image A'B'C' is bigger than the preimage ABC, then the scale factor of the dilation must be greater than 1.

In other words, the length of any segment in the image is larger than the corresponding segment in the preimage by the same factor.

Since D is the center of the dilation, we can use the ratio of the corresponding side lengths of the image and preimage triangles to find the scale factor.

For example, if we want to find the scale factor for A', we can use:

scale factor = B'C'/BC

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When the freshly sliced face is set on a table, the height of the remaining cube is 1/3.

The freshly formed face, after the corner is removed, has an area of 1/2 since it traverses three adjacent cube vertices. When the remaining cube is set on the table, this face serves as its basis. The height of the cube is equal to the distance from the table to the opposing vertex.

Because the cube's sides are one length, √(3)/2 separates its center from its opposite vertex. Therefore, (√(3)/2) - (1/3) = (2√(3) - 3)/6, which simplifies to around 0.2113, is the height of the remaining cube.

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Using the circle area formula we know that the required area of the shaded region is (A) 62.8 cm² respectively.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center.

Area of the shaded region:

πr²

Now, insert values:

When r = 6 cm,

πr²

π6²

π36

113.04 cm²

When r = 4 cm,

πr²

π4²

π16

50.24 cm²

Now, the area of the shaded region: 113.04 - 50.24 = 62.8 cm²

Therefore, using the circle area formula we know that the required area of the shaded region is (A) 62.8 cm² respectively.

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Correct question:

Find the approximate area of the shaded part of the circle. Use 3.14 for

cm

a. 62.8 cm²

b. 6.28 cm²

c. 12.56 cm²

d. 125.6 cm

1) The total amount of money in the account at the end of 17 years will be approximately $108,497.62.

2) The amount of money in the account 15 years later at age 55 will be approximately $444,226.91.

3) The total amount of money in the account at the end of 17 years with deposits made at the beginning of the year will be approximately $112,523.50.

4) The amount of money in the account 15 years later at age 55 with deposits made at the beginning of the year will be approximately $461,862.29.

To calculate the total amount of money in the account at the end of 17 years, we can use the formula for future value of an annuity:

FV = PMT x (((1 + r)^n - 1) / r)

where FV is the future value, PMT is the annual deposit, r is the annual interest rate, and n is the number of years. Plugging in the numbers, we get:

FV = $3,000 x (((1 + 0.095)^17 - 1) / 0.095) = $108,497.62

So the total amount of money in the account at the end of 17 years will be approximately $108,497.62.

2) To calculate the amount of money in the account 15 years later at age 55, we need to calculate the future value of the account from the end of year 17 to the end of year 32 (15 years later). We can use the same formula as in part 1, but this time n is 15 and we assume no new contributions are made

FV = PMT x (((1 + r)^n - 1) / r)

FV = $108,497.62 x (((1 + 0.095)^15 - 1) / 0.095) = $444,226.91

So the amount of money in the account 15 years later at age 55 will be approximately $444,226.91.

3) To calculate the total amount of money in the account at the end of 17 years if deposits were made at the beginning of the year, we need to adjust the formula from part 1 to account for the timing of the deposits. We can use the formula for future value of an annuity due:

FV = PMT x (((1 + r)^n - 1) / r) x (1 + r)

where FV is the future value, PMT is the annual deposit, r is the annual interest rate, n is the number of years, and the (1 + r) factor accounts for the fact that the deposits are made at the beginning of the year. Plugging in the numbers, we get

FV = $3,000 x (((1 + 0.095)^17 - 1) / 0.095) x (1 + 0.095) = $112,523.50

So the total amount of money in the account at the end of 17 years with deposits made at the beginning of the year will be approximately $112,523.50.

4) We can use the same formula as in part 2, but this time with the total amount of money calculated in part 3:

FV = $112,523.50 x (((1 + 0.095)^15 - 1) / 0.095) = $461,862.29

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The average distance of electric cars is 275.

The range of the data set is 300.

Given:

To find: Average distance of electric cars

Solution:

The average distance of electric cars can be calculated by finding the average of the data set containing the distances of electric cars. Let's assume that the data set is as follows:

250, 250, 250, 400, 300, 300, 350, 100

To find the average distance of electric cars, we can use the formula:

Average = (Sum of all the data points) / (Number of data points)

Substituting the given values, we get:

Average = (250 + 250 + 250 + 400 + 300 + 300 + 350 + 100) / 8

Average = 2200 / 8

Average = 275

Therefore, the average distance of electric cars is 275.

Now, let's calculate the range of the data set. The range is the difference between the maximum and minimum values in the data set. From the given data set, we can see that the minimum value is 100 and the maximum value is 400.

Range = Maximum value - Minimum value

Range = 400 - 100

Range = 300

Therefore, the range of the data set is 300.

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The solution to the IVP given by y''+y=t, y(0)=1, y'(0)=-2 is y(t) = cos(t) - (3/2) sin(t) + (1/2) t.

To solve the Initial Value Problem, we can use the method of undetermined coefficients, which involves assuming a particular form for the solution to the non-homogeneous equation y'' + y = t, and then finding the coefficients of the terms in that form by substituting it back into the equation.

First, we find the general solution to the homogeneous equation y'' + y = 0

The characteristic equation is r² + 1 = 0, which has solutions r = ±i. Therefore, the general solution to the homogeneous equation is

y_h(t) = c₁ cos(t) + c₂ sin(t),

where c₁ and c₂ are constants determined by the initial conditions.

Next, we assume a particular form for the non-homogeneous solution, based on the form of the right-hand side t. Since t is a linear function, we assume that the particular solution has the form

y_p(t) = a t + b.

Substituting this into the differential equation, we get

y''_p + y_p = t

2a + (at+b) = t.

Equating coefficients, we get

a = 1/2, b = 0.

Therefore, the particular solution is

y_p(t) = (1/2) t.

The general solution to the non-homogeneous equation is then the sum of the homogeneous and particular solutions

y(t) = y_h(t) + y_p(t)

= c₁ cos(t) + c₂ sin(t) + (1/2) t.

To determine the constants c₁ and c₂, we use the initial conditions:

y(0) = c₁ cos(0) + c₂ sin(0) + (1/2) (0) = c₁ = 1,

y'(0) = -c₁ sin(0) + c₂ cos(0) + (1/2) (1) = c₂ - (1/2) = -2,

so c₂ = -3/2.

Therefore, the solution to the IVP is

y(t) = cos(t) - (3/2) sin(t) + (1/2) t.

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Answer: B. 13 - , r

Step-by-step explanation:

The expression that has a solution of 4 when r = 9 is:

B. 13 - r

To ensure that smooth curves have no cusps, we need to require that z'(t) never vanishes. This condition ensures that the tangent line to the curve changes smoothly and continuously as we move along the curve, without any abrupt changes in direction that would create cusps.

To understand why the condition that z'(t) never vanishes is necessary to ensure that smooth curves have no cusps, we first need to understand what a cusp is. A cusp is a point on a curve where the tangent line changes direction abruptly, creating a sharp point or corner in the curve.

Now, let's consider the curve traced by the parametrization z(t) = t^2it^3 with -1 ≤ t ≤ 1. To determine whether this curve has any cusps, we need to calculate the derivative of z(t) with respect to t:

z'(t) = 2it^3 + 3t^2i

If we set z'(t) equal to zero and solve for t, we get:

2it^3 + 3t^2i = 0
t^2(2i t + 3i) = 0

This equation has two solutions: t = 0 and t = -3/2i. These are the points on the curve where z'(t) vanishes.

At t = 0, the curve passes through the origin, which is a smooth point. However, at t = -3/2i, the curve has a cusp. To see why, we can look at the behavior of z(t) near this point.

As t approaches -3/2i from either side, the magnitude of t^2 increases without bound, while the magnitude of t^3 remains constant. This means that z(t) approaches infinity along a straight line with slope -3/2i. In other words, the curve has a sharp corner or cusp at this point.

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Sample mean in sample b to be less variable and more representative of  population mean than sample mean in sample a.

Standard error measures the variability of sample means around the population mean.

It decreases as sample size increases.

Using the formula for the standard error of the mean,

Calculate the standard errors for each sample,

Standard error of sample a

= s/√(n)

= 850/√(9)

= 283.33

Standard error of sample b

= s/√(n)

= 850/√(36)

= 141.67

Where s is the sample standard deviation

And n is the sample size.

The standard error of sample b is smaller than the standard error of sample a.

Sample mean in sample b is more likely to be closer to true population mean than sample mean in sample a.

Therefore, sample mean b is more surprising as larger sample size makes it more likely and accurately represents population mean.

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The correct option is C′(−10.5, 3.5) i.e. the vertex of point C′ is (-10.5, 3.5).

What is dilation?

In mathematics, dilation is a type of transformation that changes the size of a geometric object, but not its shape or orientation. Dilation is similar to scaling, but it involves a fixed point called the center of dilation, and a scale factor that determines the degree of expansion or contraction.

To determine the vertex of point C′, we need to apply the dilation transformation to the coordinates of the original vertex C(-3,1) using a scale factor of 3.5.

The coordinates of C′ can be found by multiplying the coordinates of C by the scale factor:

C′ = (3.5)C = (3.5)(-3,1) = (-10.5,3.5)

Therefore, the vertex of point C′ is (-10.5, 3.5).

Thus, the correct option is C′(−10.5, 3.5).

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p=8h is the equation.This part is represented in tabular form.The coefficient of h. Mark worked 21 hours that week.Yes, the equation is a direct variation.

An equation is a statement that shows the equality of two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, and division. Equations are commonly used in mathematics, science, and engineering to model real-world situations and solve problems.

Direct variation is a mathematical relationship between two variables, where a change in one variable results in a proportional change in the other variable. In other words, if two variables are in direct variation, when one variable increases, the other variable increases as well, and when one variable decreases, the other variable decreases as well, in a constant ratio.

Part A: The equation for this situation is p = 8h, where p represents the pay in dollars and h represents the number of hours worked.

Part B:

| Worked (hrs) | Pay (p) |

|------------------|---------|

| 1                | 8       |

| 2                | 16      |

| 3                | 24      |

| 4                | 32      |

| 5                | 40      |

| 6                | 48      |

and so on.

Part C: The coefficient of h, which is 8, shows the number of hours Mark worked.

Part D: We can use the equation p = 8h and substitute p = 168 to find the number of hours Mark worked.

168 = 8h

h = 21

Therefore, Mark worked 21 hours that week.

Part E: Yes, the equation is a direct variation because the pay (p) is directly proportional to the number of hours worked (h) and the constant of variation is 8.

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The rate at which the base of the triangle is changing when the altitude is 20 cm and the area is 120 cm^2 is 0 cm/s.

To solve this problem, we need to use the formula for the area of a triangle, which is:

A = (1/2)bh

Where A is the area, b is the base, and h is the altitude.

We know that the area is 120 cm^2 and the altitude is 20 cm. So we can plug in these values and solve for the base:

120 = (1/2)b(20)

240 = 20b

b = 12 cm

Now we need to differentiate both sides of the equation with respect to time (t):

dA/dt = (1/2)(db/dt)h

We are given the value of dh/dt (which represents the rate at which the altitude is changing) is 3 cm/s. We need to find db/dt (which represents the rate at which the base is changing).

Plugging in the values we know, we get:

dA/dt = (1/2)(db/dt)(20)

Solving for db/dt, we get:

db/dt = (2dA/dt)/h

Plugging in the values we know, we get:

db/dt = (2)(0)/20

db/dt = 0 cm/s
Since the area is constant (120 cm²) and the altitude is constant (20 cm), the base of the triangle is not changing. Therefore, the rate at which the base is changing is: 0 cm/s

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A scatter plot chart of stock returns versus past stock returns will typically appear as a random pattern mostly concentrated in the top-right and lower-left quadrants.

This pattern indicates that there is a positive correlation between past and current stock returns, but there are also instances where current returns are negative despite past positive returns.

The top-right quadrant represents instances where both past and current returns are positive, while the lower-left quadrant represents instances where both past and current returns are negative.

The random pattern indicates that stock returns cannot be predicted with certainty based on past returns alone.

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the length of each Segment WY = 7.2 .

What is line Segment?

A portion of a straight line or curve between two points. A portion of a plane or solid figure truncated by intersecting lines, planes, or planes, especially between chords and arcs of a circle.

                                      In geometry, a line segment is bounded by two different points on the line. Or we can say that the line segment is part of the line connecting his two points. Lines have no endpoints and extend infinitely in either direction, while lines have two fixed or definite endpoints. 

In both triangles

        VW/WX = YW/WU

         7/8.75 =  YW/9

           9 * 7/8.75  = YW

               7.2 = WY

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The theorem is shown in a pythagoras theorem is c² = a² + b²

The theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.

The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Mathematically, we can express this as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.

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Answer:

Yo wassup bro, at this computer factory, they be making two types of computers, laptops and desktops. They churn out 70 laptops a day and 55 desktops a day. They got a total of 14 machines to make these computers. And they make a total of 905 computers a day. We gotta figure out how many machines are making laptops and how many are making desktops, ya know?

Alright, let's set up a system of equations to solve this. Let's call the number of machines making laptops "x" and the number of machines making desktops "y".

So, we got two equations here:

The total number of computers they make in a day is 905, so we can write: x laptops + y desktops = 905.

They got a total of 14 machines, so we can write: x + y = 14.

Now, let's solve this system of equations to find the values of x and y, man. Once we got those, we'll know how many machines are making laptops and how many are making desktops at this computer factory, yo!

The crude death rate for all causes in Metroville is 1 per 1,000 residents if the total number of deaths from all causes is 900.

total number of residents injured from roller-skating = 1,800

total number of deaths = 90

deaths from all causes  = 900

Therefore, we can set up a proportion:

90 deaths / x residents = 1,000 deaths per 1,000 residents

x = 90,000 / 1,000

x = 90

The total population of Metroville is 90,000 residents.

The crude death rate for all causes is then:

Crude death rate = (total number of deaths / total population) * 1,000

Crude death rate = [tex](90 / 90,000) * 1,000[/tex]

Crude death rate = 1 per 1,000 residents

Therefore, we can conclude that the crude death rate for all causes in Metroville is 1 per 1,000 residents.

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The volume of water in the tank won't be enough for the fish.

A cuboid is a solid shape or a three-dimensional shape. The volume of a cuboid is expressed as;

V = l×w× h

where l is the length, w is the width and h is the height.

The volume of water needed by the fish is 700,000× 1litre = 700,000 litres.

The volume of water the tank can occupy is

V = l× b× h

V = 80× 1200× 70

V = 6,720,000cm³

in litres ;

V = 6,720,000/1000

V = 6720litres

therefore the volume water in the tank is not enough for the fish

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Thus, the correct Percent response is B) 79%.

Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".

If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.

We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:

$2644 - $548.30 = $2095.702.

By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:

($2095.70 / $2644) * 100% = 79%

Thus, the correct response is B) 79%.

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In a speculation test, a blunder happens when we dismiss invalid speculation that's really genuine, whereas a Sort II mistake happens when we fall flat to dismiss a null theory that's really wrong.

Since a Sort I error is more genuine in this situation, we need to play down the likelihood of making such a mistake. This implies we ought to select a lower level of noteworthiness, which decreases the likelihood of dismissing genuine invalid speculation.

In rundown, the leading choice of level of noteworthiness for this double-blind therapeutic test would be a lower level, such as 0.01 or 0.001, to minimize the likelihood of making a Sort I mistake, which is more genuine in this situation.

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Step-by-step explanation:

When adding or subtracting fractions, they must have a common denominator....20 is the easiest for these...this then becomes

b +  16/20  = 35/20     now subtract 16/20 from both sides of the equation

b = 35/20 - 16/20

b = (35-16)/20 =  19/20      

the 11th term in the given geometric sequence is equal to [tex]-9216x^{52}[/tex]

A sequence is a list of numbers indexed by the natural numbers 1,2,3,4,5.. A common notation for a sequence is [tex]a_1,a_2,a_3,\cdots[/tex]. Most often for interesting sequences there is some pattern in the list of numbers, and there is some formula to generate the nth number in the sequence. A sequence is called a geometric sequence if the next number number is got from the previous number by multiplying it by a fixed number r. This number is called the common ratio r of the sequence. So if the first number is a, then the second number is ar, the third is [tex]ar^2[/tex]... So that the nth number [tex]a_n = ar^{n-1][/tex].  

For example 1 ,3,9,27,81,.... The sum of the first n terms of such a sequence is equal to [tex]$S_n = \frac{a(r^n-1)}{r-1}$[/tex]. if the absolute value of r, [tex]|r| < 1[/tex], then the sum to infinity is [tex]$S = \frac{a}{1-r}$[/tex].

In our question we are given a geometric sequence whose first term :

[tex]$a = -9x^2\,,\textrm{ and common ratio : r } = 2x^5$[/tex] .

So the 11th term is [tex]$ar^{10} = (-9x^2){(2x^5)}^{10} = (-9x^2)(1024x^{50}) = -9216x^{52}$[/tex]

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I'm sorry, but I cannot provide a definitive answer to your question as I do not have access to the table you are referring to.

However, in general, to find the price per spool of each kind of thread, you would need to know the total price of the package and the number of spools in the package.

To calculate the price per spool, you would divide the total price of the package by the number of spools in the package. For example, if a package costs $10 and contains 50 spools of thread, the price per spool would be $0.20 ($10 ÷ 50 = $0.20).

You can use this method to find the price per spool for each type of thread in the table you are looking at.

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Answer:

Step-by-step explanation:

Graph #          Matching equation

1                             |-3x|

2                            |-x|

3                           -|2x|

You can tell which one matches by finding the slope and whether the V points up or down

the answer would be $108

because if you divide 18 by 2

18÷2=9

so,one rocking horse is $9

if you say 12x9= 108

Answer:

Harry can buy 5 gallons of lemonade and 5 gallons of iced tea and still have $1.50 left over from his original $24 dollar budget

Step-by-step explanation:

The volume of the prism is gotten as 312 cm³.

Volume is described as a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units.

The basic formula for volume is length × width × height.

The formula for the volume of triangular prism = area of triangle x length

area of triangle = 1/2 x base x height

⇒ area of triangle = 1/2 x 8 x 6 = 24 cm²

Therefore, volume of the prism = 24 x 13 = 312 cm³

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The probability of getting a 5 or a divisor of 16 when spinning the spinner is 1/2 or 50%.

To find the probability of getting a 5 or a divisor of 16, we need to first understand what the spinner looks like. Assuming that the spinner has equally sized sections labeled 1 through 8, we can see that a divisor of 16 would be either 1, 2, or 4.

So, out of the eight possible outcomes, there are three that are divisors of 16 (1, 2, and 4) and one that is a 5. Therefore, there are four possible outcomes that satisfy the condition of getting a 5 or a divisor of 16.

To calculate the probability of getting a 5 or a divisor of 16, we divide the number of favorable outcomes (4) by the total number of possible outcomes (8). This gives us:

P(5 or divisor of 16) = favorable outcomes / total outcomes

= 4/8

= 1/2 or 50%

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The probability of the teacher pulling out two red markers is 1/9 or approximately 0.1111 when rounded to four decimal places.

Since the teacher puts the marker back before drawing again, each draw is independent of the other. Therefore, the probability of getting a red marker on the first draw is 5/15 or 1/3. The probability of getting a red marker on the second draw is also 1/3, since the probabilities are the same for each draw.

To find the probability of getting two red markers, we need to multiply the probability of getting a red marker on the first draw by the probability of getting a red marker on the second draw.

Probability of getting two red markers = (1/3) * (1/3) = 1/9

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Thus, the number of current lawnmowers in the Springtown Hardware is 864,900.

In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. The Latin word "per centum," which meaning "per 100," is where the word "percent" comes from. % is the symbol used to represent percentages.

When a number is expressed in decimal form, you can calculate its percentage by multiplying it by 100. For instance, multiplying 0.5 by 100 gives you the percentage 50%.

Given data:

Springtown Hardware's inventory - 697,500 lawnmowers.

Current inventory of 24% more lawnmowers.

Current inventory = old inventory  + 24% of old inventory

Current inventory =  697,500 + 24 % of  697,500

Current inventory =  697,500 + 24 *  697,500/ 100

Current inventory =  697,500 + 24* 6,975

Current inventory = 864,900

Thus, the number of current lawnmowers in the Springtown Hardware is 864,900.

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