3:9 and 27:81 are the ratios equivalent or not?

The new image would be smaller in sample size than the original image.

For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be

(200 x 0.5) = 100 x (100 x 0.5)

= 50 pixels.

The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be

(200 x 0.75) = 150 x (100 x 0.75)

= 75 pixels.

In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.

Learn more about sample size here

https://brainly.com/question/25894237

#SPJ4

The amount of silver that  should be added is 48% . A jeweler is said to have 5 rings that weigh 12 g apiece and are composed of an alloy of 20% silver and 80% gold.

What are linear equations?

An equation between two variables that, when plotted on a graph, produces a straight line.

The material will weigh 12 × 5 = 60 grams after melting all 5 rings.

The alloy's 20% silver and 80% gold content have been disclosed to us. Let's further say that the melted material receives an additional x grams of silver, resulting in a composition of 64% gold and 36% silver.

Thus, we can construct the following equation:

Amount of gold before = Amount of gold after mixing

So the equation we get

80% of 60 grams =64% of (X + 60) gram

0.80 × 60 = 0.64 (x + 60)

48 = 0.64x + 38.4

0.64x = 9.6

x = 9.6/0.64

x = 15

So

Amount of silver that needed to be added

= 0.64(15 + 60)

= 0.64(75)

= 48%

To know more about linear equations, visit:

https://brainly.com/question/11897796

#SPJ4

The Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Here, we have,

The Taylor series at x=0 for cos(x) is given by:

cos(x) = ∑(n=0 to infinity) (-1)ⁿ * (x²ⁿ)) / (2n)!

Now, let's find the Taylor series at x=0 for the given function x * cos²((3πx)/2):

To find the Taylor series for the given function, we'll use power series operations.

We'll substitute the Taylor series expansion for cos(x) into the given function and then perform the necessary operations.

Let's start with cos²((3πx)/2):

cos²((3πx)/2) = (cos((3πx)/2))²

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!)²

Expanding the square of the series, we get:

cos²((3πx)/2)

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Now, we'll multiply the x term to obtain the Taylor series for the given function:

x * cos²((3πx)/2) = x * (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Expanding the multiplication and rearranging the terms, we have:

x * cos²((3πx)/2) = ∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Therefore, the Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Learn more about the Power series at

brainly.com/question/32203157

#SPJ4

Stephen makes the mistake in the expression as he uses the 4 in the root and the 3 in the power and the expression actually is: ∛(16)/e

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of Helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

Here is where Stephen makes the mistake, he uses the 4 in the root and the 3 in the power.

The expression actually is: ∛(16)/e

Learn more about expressions on:

https://brainly.com/question/723406

#SPJ1

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.

An event that is certain to happen has a probability of 1.

Answer:

Yes it can!

Step-by-step explanation:

In the given triangles,
∠B = ∠F
Also, ratio of sides given are
2.3/13.8 ≈ 1.67 -> (i)
And 1.9/11.4 ≈ 1.67 -> (ii)
Thus, (i) = (ii)
∴ AB/BF = BC/DF

So we can prove both triangles are similar as the two sides are proportional and the angle between the corresponding sides are equal, so we can use the SAS similarity postulate as the two sets of corresponding sides are proportional and the included angles are congruent .

The single integral in the form y b a fs(x) dx is:

∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx - ∫ y=2 to 5 fs(x) dx - ∫ y=1 to 21 fs(x) dx

To write the given expressions as a single integral in the form y b a fs(x) dx, let's break it down step by step.

1) y = 2 to 22: ∫ fs(x) dx

2) y = 1 to 5: ∫ fs(x) dx

3) y = 21 to 22: ∫ fs(x) dx

Now, to combine these integrals into a single expression, we need to find a common interval that encompasses all three given intervals.

The smallest common interval that covers all three intervals is from 1 to 22.

Therefore, we can rewrite the expressions as:

∫ y=2 to 22 fs(x) dx = ∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx

∫ y=5 to 2 fs(x) dx = -∫ y=2 to 5 fs(x) dx

∫ y=21 to 22 fs(x) dx = ∫ y=1 to 22 fs(x) dx - ∫ y=1 to 21 fs(x) dx

Combining these expressions, we get:

∫ y=2 to 22 fs(x) dx - ∫ y=5 to 2 fs(x) dx + ∫ y=21 to 22 fs(x) dx

= (∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx) - (-∫ y=2 to 5 fs(x) dx) + (∫ y=1 to 22 fs(x) dx - ∫ y=1 to 21 fs(x) dx)

= 2∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx - ∫ y=2 to 5 fs(x) dx - ∫ y=1 to 21 fs(x) dx

Therefore, y b a fs(x) dx, the single integral is:

∫ y=1 to 22 fs(x) dx - ∫ y=1 to 1 fs(x) dx - ∫ y=2 to 5 fs(x) dx - ∫ y=1 to 21 fs(x) dx

Learn more about integration on:

https://brainly.com/question/12231722

#SPJ11

Answer:

between 7 and 8am  ==> answer choice 3

Step-by-step explanation:

The histogram relates the number of cars passing through the school zone at various times of the morning

The height of each bar shows the number of cars

The base of each bar shows the time of passing

The bar with the tallest height is the bar corresponding to the time interval of 7am - 8am

Therefore the correct answer is
between 7 and 8am  ==> answer choice 3

The amount of each trail mix that should be combined to create the special order trail mix are:

6.25 pounds of the trial that contains 75% nuts.

3.75 pounds of the trial that contains 35% nuts.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

Trial mix A = x

= 75% nuts.

Trial mix B = y

= 35% nuts

Now,

Two equations are:

x + y = 10 _____(1)

x = 10 - y _____(2)

0.75x + 0.35y = 10 x 0.60 ______(3)

Substituting (2) in (3)

0.75 (10 - y) + 0.35y = 6

7.5 - 0.75y + 0.35y = 6

7.5 - 6 = 0.75y  - 0.35y

1.5 = 0.40y

y = 1.5/0.40

y = 3.75

Now,

x = 10 - 3.75

x = 6.25

Thus,

6.25 pounds of the trial that contains 75% nuts.

3.75 pounds of the trial that contains 35% nuts.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

the answer is -6,5

Step-by-step explanation:

just look at the left side ( the x axis )first then right(the y axis)

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

Complex numbers are represented on a cartesian coordinate system with a horizontal real axis and a vertical imaginary axis.

Any number that can be expressed as a+bi, where i is the imaginary unit and a and b are the real numbers, is a complex number. The number is made up of two parts: real part (a) and imaginary part (b).

Just like we can use the number line to visualize a set of real numbers, we can use the complex plane to visualize a set of complex numbers. The complex plane consists of two number lines intersecting at a right angle at the point (0,0)(0,0)left parenthesis, 0, comma, 0, right parenthesis.

The horizontal number line (what we know as the xxx-axis on a Cartesian plane) is the real axis. The imaginary axis is the vertical number line (the yyy-axis on a Cartesian plane).A point in the complex plane can represent every complex number.

For example, consider the number 3-5i3−5i3, minus 5, i. This number, also expressed as 3+(-5)i, has a real part of 3 and imaginary part of -5. The location of this number on the complex plane is the point that corresponds to 3 on the real axis and -5 on the imaginary axis.

So the number 3+(-5) corresponds with the point (3,-5). In the general complex number, a+bi corresponds to the complex plane's point(a,b).

Hence, complex numbers are represented on a cartesian coordinate system with a real horizontal axis and an imaginary vertical axis.

Learn more about Cartesian plane:

https://brainly.com/question/28574364

Answer:

\(Meeting\ Time = 6:03\ pm\)

Step-by-step explanation:

Given

\(Start\ Time= 5:45pm\)

\(Lixin = 18\ min/round\)

\(Khairul = 360\ seconds/round\)

\(Devi = 4minutes/2\ rounds\)

Required

Determine their next meeting time

First, we need to get their unit rate in minutes per round

\(Lixin = 18\ min/round\)

\(Khairul = 360\ seconds/round\)

Convert 360 seconds to minutes

\(Khairul = \frac{360}{60} min/round\)

\(Khairul = 6 min/round\)

\(Devi = 4minutes/2\ rounds\)

Divide by 2/2

\(Devi = 2mins/round\)

So, we have:

\(Lixin = 18\ min/round\)

\(Khairul = 6 min/round\)

\(Devi = 2mins/round\)

Next, is to determine the LCM of 18, 6 and 2

\(18=2 * 3 * 3\)

\(6 = 2 * 3\)

\(3 = 3\)

Their LCM is:

\(LCM = 2 * 3 * 3\)

\(LCM = 18\)

This means that they will meet 18 minutes after their initial time of departure.

So:

\(Meeting\ Time = 5:45\ pm + 18\ minutes\)

\(Meeting\ Time = 6:03\ pm\)

Answer:

114.12

Step-by-step explanation:

Answer:

x = 4 , ∠ A = 65° , ∠ B = 88° , ∠ C = 23°

Step-by-step explanation:

∠ A + ∠ C = 88 , substitute values for A and C

5x + 3 + 15x + 5 = 88

20x + 8 = 88 ( subtract 8 from both sides )

20x = 80 ( divide both sides by 20 )

x = 4

Then

∠ A = 15x + 5 = 15(4) + 5 = 60 + 5 = 65°

∠ A + ∠ C = 88° , that is

65° + ∠ C = 88° ( subtract 65° from both sides )

∠ C = 23°

∠ B = ∠ A + ∠ C ( vertically opposite angles )

∠ B = 88°

The indicated measure is:55⁰

To prove that thry are the circles diameters you can do it by two methods.One is calculating all the angles and the sum of all angles of it equals 360⁰.The one that is the opposite point of 55⁰ is 55⁰ so we need to find the other by : 180⁰-55⁰=125⁰. So 125⁰×2+55⁰×2=360⁰.

The second method is by knowing the rule that applies to diameters of a circle and that says that : a diameter is formed when a line goes from a point to the circle and passes the main point and then finishes to another point in the cirlcle.

y=12x-16

that's the answer

The employee's net take-home pay is $2597.

The gross salary is the total salary before any deductions are made.

In this case, the employee's bi-weekly gross salary is $3000.

Deductions are made from the gross salary to arrive at the net take-home pay.

The deductions include income tax, CPP, El, and union dues.

The total deductions can be calculated by adding the individual deductions:

Total deductions = Income tax + CPP + El + union dues

Total deductions = $218 + $99 + $36 + $50Total deductions = $403

The net take-home pay is the amount that the employee receives after all the deductions have been made.

It can be calculated by subtracting the total deductions from the gross salary:

Net take-home pay = Gross salary - Total deductions

Net take-home pay = $3000 - $403Net take-home pay = $2597

Therefore, the employee's net take-home pay is $2597.

For more questions on gross salary

https://brainly.com/question/25267964

#SPJ8

Answer:

x = 100

Step-by-step explanation:

You have to use the equation 15x + 10 = 6x - 6 + 70. This equation finds out that x = 6. Then, you would multiply 6 by 15. This gets 90. Finally, add 10 to that.

A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.

A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

Total amount of book in library are 2500 ,

Out of that 40% are fiction so the number of the non fiction books are 60%

so 60% of 2500 will give us the value of non fiction books,

Number of non fiction = 2500 x 60%

= 2500 x 60/100

= 25 x 60

= 1500

Therefore,  Number of non fiction books are 1500.

Learn more about Percentages problem:

https://brainly.com/question/29393986

#SPJ4

The measure of n of the sector with the given area is: 100°

The area of a sector of a circle = ∅/360 × πr².

We are given that:

Area of the sector = 40π

Radius (r) = 12 units

∅ = n°

Plug in the values and solve for n

40π = n/360 × π(12²)

40π = n/360 × π144

Divide both sides by 144π

40π/144π = n/360 × 144π/144π

40/144 = n/360

40(360) = n(144)

14,400/144 = n

n = 100°

Learn more about the area of sector on:

https://brainly.com/question/22972014

#SPJ1

Answer:

(-3,-4)

Step-by-step explanation:

The vertex is the point where the two rays meet

The vertex is x=-3, y= =-4

(-3,-4)

Answer:

(-3,-4)

Step-by-step explanation:

The vertex is the point where the two rays meet

The vertex is x=-3, y= =-4

(-3,-4)

(a) We have shown that there exists an element b ∈ B that is an upper bound for A.

(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.

(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.

Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).

Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.

(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.

Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.

This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.

Visit here to learn more about upper bound:

brainly.com/question/22965427

#SPJ11

This approximates to roughly 6/7 = 0.8571

========================================================

Explanation:

Let's define the following

There are 30 students in the class total. This must mean A+B+C+D = 30.

We know that "There were 7 students who failed the test and also did not complete the assignment", meaning we can say D = 7.

We can also say A+B = 21 because this is the entire group of people who passed the test (whether they did the hw or not).

This means:

A+B+C+D = 30

(A+B)+C+D = 30

(21) + C + 7 = 30

C+28 = 30

C = 30-28

C = 2

We have 2 people who failed the test, but did the hw.

Because 20 students did the hw, we know that

A+C = 20

A+2 = 20

A = 20-2

A = 18

We have 18 students who passed the test and did the hw. This is out of 21 students who passed. From here on out, we only focus on this group of students because of the phrasing "given that they passed the test". This means we know 100% that whoever we picked, they passed the test.

The probability we're after is therefore:

18/21 = (3*6)/(3*7) = 6/7

Side note: It might help to sort the data into a table as shown below. Start with table 1, and the goal is to replace the placeholder letters with the proper numbers, to arrive at table 2. You'll have to use algebra as shown earlier to fill out the table.

Answer:

6/7

Step-by-step explanation:

It's correct trust me.

The sine function oscillates between -1 and 1, the limit does not exist as b approaches infinity. Therefore, the improper integral diverges. The answer is: DIVERGES

The given improper integral is ∫19^∞cos(πx)dx. To determine whether it converges or diverges, we can use the following theorem:

If f(x) is continuous, positive, and decreasing on [a, ∞), then the improper integral ∫a^∞ f(x)dx converges if and only if the corresponding improper sum ∑n=a to ∞ f(n) converges.

In this case, f(x) = cos(πx), which is not positive and decreasing on [19, ∞). Therefore, we cannot use this theorem to determine whether the integral converges or diverges.

Instead, we can use the following test for convergence:

If f(x) is continuous and periodic with period p, and ∫p f(x)dx = 0, then the improper integral ∫a^∞ f(x)dx converges if and only if ∫a^(a+p) f(x)dx = ∫0^p f(x)dx converges.

In this case, f(x) = cos(πx), which is continuous and periodic with period 2. Also, we have ∫0^2 cos(πx)dx = 0. Therefore, we can apply the test for convergence and write:

∫19^∞cos(πx)dx = ∫19^(19+2) cos(πx)dx + ∫(19+2)^(19+4) cos(πx)dx + ∫(19+4)^(19+6) cos(πx)dx + ...

= ∫0^2 cos(πx)dx + ∫0^2 cos(π(x+2))dx + ∫0^2 cos(π(x+4))dx + ...

= ∑n=0^∞ ∫0^2 cos(π(x+2n))dx

Since ∫0^2 cos(π(x+2n))dx = 0 for all n, the improper integral converges by the test for convergence.

Therefore, ∫19^∞cos(πx)dx converges, and its value is equal to 0.

The improper integral in question is:

∫(19 to ∞) cos(πx) dx

Learn more about integration here: brainly.com/question/18125359

#SPJ11

Answer:

x= -27/20

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

Answer:

g + 2/3 \(\geq\) -6

Step-by-step explanation: