Triangle PQR is transformed to similar triangle P’Q’R’:

A coordinate plane is shown. Triangle ABC has vertices A at 2 comma 6, B at 2 comma 4, and C at 4 comma 4. Triangle A prime B prime C prime has vertices A prime at 1 comma 3, B prime at 1 comma 2, and C prime at 2 comma 2.

What is the scale factor of dilation?

1 over 2
1 over 3
1 over 4
1 over 5

Answer:

I think 3.200 has four significant figures

Answer:

38 cm²

Step-by-step explanation:

Given that,

→ Length (l) = 4 cm

→ Breadth (b) = 3 cm

→ Height (h) = 1 cm

Formula we use,

→ 2(lb + bh + lh)

The surface area of cuboid will be,

→ 2(lb + bh + lh)

→ 2{(4 × 3) + (3 × 1) + (4 × 1)}

→ 2(12 + 3 + 4)

→ 2 × 19

→ [ 38 cm² ]

Hence, the surface area is 38 cm².

Answer:

Step-by-step explanation:

I believe the correct answer from the choices listed above is option D. The expression that could be used to determine the average rate at which the object falls during the first 3 seconds of its fall would be  (h(3)-h(0))/3. Average rate can be calculated by the general formula:

Average rate = (change in y-axis) / (change in x-axis)

In this case,

Average rate = (change in height) / (change in time)

Given:

The equation of given line is

\(y=3x-4\)

A line is perpendicular to the given line and passes through the point (9,5).

To find:

The equation of the perpendicular line.

Solution:

We have,

\(y=3x-4\)

On comparing this equation with slope intercept form \(y=mx+b\), we get

\(m=3\)

It means, the slope of the given line is 3.

The product of slopes of two perpendicular lines is -1.

\(m\times m_1=-1\)

\(3\times m_1=-1\)

\(m_1=-\dfrac{1}{3}\)

Point slope form of a line is

\(y-y_1=m(x-x_1)\)

Where, m is the slope.

The slope of perpendicular line is \(-\dfrac{1}{3}\) and it passes through the point (9,5). So the equation of the line is

\(y-5=-\dfrac{1}{3}(x-9)\)

\(y-5=-\dfrac{1}{3}(x)-\dfrac{1}{3}(-9)\)

\(y-5=-\dfrac{1}{3}x+3\)

Adding 5 on both sides, we get

\(y-5+5=-\dfrac{1}{3}x+3+5\)

\(y=-\dfrac{1}{3}x+8\)

Therefore, the equation of required line is \(y=-\dfrac{1}{3}x+8\).

The decimal as a fraction is 24/25 pounds

A fraction can be defined as the part of a whole number, a whole element or a whole variable.

In mathematics, there are different types of fractions.

These fractions are listed as;

From the information given, we have that;

0. 96 pounds

Divide the decimal by 100, we get;

96/100

Divide the values by a common factor of 2,  we have;

48/50

Divide further

24/25

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The 95% confidence interval for the average number of units that students in their college are enrolled in is (11.46,12.53)

We are given the number of students, n =  46, and  the mean of the sample which is x= 12.5, and the standard deviation of the sample which is s= 1.8 , the formula  we are referring to for calculating the confidence interval which is :

x ± t (s/√(n))

since for  this case, the degree of freedom is one less than the mean, which is 45, the critical value for the confidence of 95% with  the degree of freedom of 45 is 2.015

x + t(s/√(n)) = 12.5 +2.015*(1.8/6.78)=  12.53

x - t(s/√(n))= 12.5 -2.015*(1.8/6.78)= 11.46

The interval is (11.46,12.53)

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Answer:

17.32 minutes

Step-by-step explanation:

The standard deviation for a uniform distribution is:

\(\sigma =\frac{b-a}{\sqrt12}\)

If a = 20 minutes and b = 80 minutes, the standard deviation is:

\(\sigma =\frac{80-20}{\sqrt12} \\\sigma=17.32\ minutes\)

The standard deviation of the distribution of consumer usage time of computers in the public library is 17.32 minutes.

To declare a variable named apple of the class named "apple" and initialize it to a new object, we can use the following statement in most programming languages:

apple apple = new apple();

Here, the first "apple" is the class name, and the second "apple" is the name of the variable we are declaring. The "new" keyword is used to create a new object of the class, and the parentheses indicate that no parameters are being passed to the constructor.

This statement creates a new instance of the class named "apple" and assigns it to the variable also named "apple". The variable can now be used to access the properties and methods of the object, allowing us to manipulate and work with the data stored within it.
```java
Apple apple = new Apple();
```

This statement creates a new instance of the "Apple" class and assigns it to the variable "apple." The "new" keyword is used to create a new object, and "Apple()" calls the constructor for the class.

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Answer:

Step-by-step explanation:

The missing reasons are Cofunction identity, Cosine difference identity, Cofunction identity, Cosine function is even and sine function is odd respectively.

Given:

The given expression is \(\sin (x-y)\).

To find:

The justification for each step.

Explanation:

Cofunction identities:

\(\sin\left(\dfrac{\pi}{2}-x\right)=\cos x\)

\(\cos\left(\dfrac{\pi}{2}-x\right)=\sin x\)

Cosine difference identity:

\(\cos(x-y)=\cos x\cos y+\sin x\sin y\)

Cosine function is even, so \(\cos(-x)=\cos x\).

Sine function is odd, so \(\sin(-x)=-\sin x\).

We have,

\(\sin (x-y)\)

\(=\cos\left|\dfrac{\pi}{2}-(x-y)\right|\)                                             Step 1: Cofunction identity

\(=\cos\left|\dfrac{\pi}{2}-x+y\right|\)                                                 Step 2: Distributive property

\(=\cos\left|\left(\dfrac{\pi}{2}-x\right)+y\right|\)                                            Step 3: Associative property

\(=\cos\left|\left(\dfrac{\pi}{2}-x\right)-(-y)\right|\)                                        Step 4: Factoring out   

\(=\cos\left(\dfrac{\pi}{2}-x\right)\cos(-y)+\sin\left(\dfrac{\pi}{2}-x\right)\sin(-y)\)       Step 5: Cosine difference identity

\(=\sin(x)\cos(-y)+\cos(x)\sin(-y)\)                           Step 6: Cofunction identity

\(=\sin(x)\cos(y)-\cos(x)\sin(y)\)                                Step 7: Cosine function is even, sine function is odd

Therefore, the missing reasons are Cofunction identity, Cosine difference identity, Cofunction identity, Cosine function is even, sine function is odd respectively.

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In the basis step of the mathematical induction proof for P(n), we show that the equation is true for n = 1. The equation of the inductive hypothesis (IH) is P(k), where k is an arbitrary natural number. In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true.

In the basis step, we substitute n = 1 into the equation 11⋅2+12⋅3+⋅⋅⋅+1n⋅(n+1)=nn+1. This gives us the equation 1⋅2 = 1+1, which is true.

The inductive hypothesis (IH) is denoted as P(k), where k is an arbitrary natural number. We assume that P(k) is true, meaning that 11⋅2+12⋅3+⋅⋅⋅+1k⋅(k+1)=kk+1 holds.

In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true. This involves substituting n = k+1 into the equation 11⋅2+12⋅3+⋅⋅⋅+1n⋅(n+1)=nn+1 and demonstrating that the equation holds for this value. The specific equation we need to show in the inductive step is 11⋅2+12⋅3+⋅⋅⋅+1(k+1)⋅((k+1)+1)=(k+1)(k+1+1).

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In the basis step, we need to show that the equation P(1) is true. The equation of the inductive hypothesis (IH) is P(k), where k is any natural number greater than or equal to 1. In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true.

To prove the equation P(n): 11⋅2 + 12⋅3 + ... + 1n⋅(n+1) = n(n+1) using mathematical induction, we follow the two-step process.

1. Basis Step:

We start by showing that the equation is true for the base case, which is n = 1:

P(1): 11⋅2 = 1(1+1)

Simplifying, we get: 2 = 2, which is true.

2. Inductive Step:

Assuming that the equation is true for some arbitrary value k, the inductive hypothesis (IH) is:

P(k): 11⋅2 + 12⋅3 + ... + 1k⋅(k+1) = k(k+1)

In the inductive step, we need to show that if P(k) is true, then P(k+1) is also true:

P(k+1): 11⋅2 + 12⋅3 + ... + 1k⋅(k+1) + 1(k+1)⋅((k+1)+1) = (k+1)((k+1)+1)

By adding the (k+1)th term to the sum on the left side and simplifying the right side, we can demonstrate that P(k+1) is true.

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The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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The maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀ is given as -

Polarization is the property of wave oscillations having a definite direction relative to the wave's propagation direction. Transverse waves that can be polarized are EM waves. The polarization direction is defined as the direction parallel to the EM wave's electric field.

The effect of a polariser on polarised light is described by Malus' law, which states that-

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The correct question is -

What is the maximum resultant intensity in terms of the intensity of the initial unpolarized incoming light I₀.

The probability of getting a return of 200% or more in a single year is approximately 0.0000317 or 0.00317%.

Assuming that the returns from holding small-company stocks are normally distributed, the probability of doubling or tripling your money in a single year can be estimated using the normal distribution formula.

To calculate the probability of doubling your money, you need to find the number of standard deviations away from the mean that represents a return of 100%. If we assume that the average return for small-company stocks is 10% per year with a standard deviation of 20%, we can use the formula:

Z = (100% - 10%) / 20% = 4.5

Using a normal distribution table or calculator, we can find that the probability of getting a return of 100% or more in a single year is approximately 0.0000317 or 0.00317%.

Similarly, to calculate the probability of tripling your money, you need to find the number of standard deviations away from the mean that represents a return of 200%. Using the same formula as above, we get:

Z = (200% - 10%) / 20% = 9.5

Using a normal distribution table or calculator, we can find that the probability of getting a return of 200% or more in a single year is approximately 0.000000002 or 0.0000002%.

It's important to note that these calculations are based on assumptions and estimates, and actual returns may vary significantly. Investing in small-company stocks involves significant risks, and investors should carefully consider their investment goals, risk tolerance, and overall financial situation before making any investment decisions.

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Answer:

y=8x+25

y=5x+12

Step-by-step explanation:

To write a system of equations you must write an equation for both plan A and B. For plan A, the 25 dollars is the constant because it is only paid once. The 8 dollars must be multiplied by the variable x because it is paid each month. These added together will equal the total cost or y. In plan B the 12 dollars is the constant and 5 is being multiplied by the variable.

Answer:

(-2) and 3

Step-by-step explanation:

Answer:

f=-2, f=3, f=-4, they are all smaller than 4!!!

85 is the sample mean of the scores of ten students taken from their test

15/3 is the sample standard deviation of the scores of ten students taken from their test

Sample Standard Deviation: The sample standard deviation (s) is the square root of the sample variance and is also a measure of the spread from the expected values. In its simplest terms, it can be thought of as the average distance of the observed data from the expected values.

given ten students take a test and the scores are 80, 99, 83, 82, 100, 75, 83, 85, 71, 92

Sample mean of 80, 99, 83, 82, 100, 75, 83, 85, 71, 92 is

m= sum of observations/number of observations

sum of observations=80+99+83+82+100+75+83+85+71+92=850

number of observations=10

m=850/10=85 is the sample mean of the scores of ten students taken from their test

sample standard deviation,

s=√(assumed value-mean)²/√(number of observaionts-1)

let Assumed value be 100

s=√(100-85)²/√10-1

s= √(15)²/√9

s=15/3 is the sample standard deviation of the scores of ten students taken from their test

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The sample mean of ten students' test results, considered as a sample, is 85.

The sample standard deviation of 10 students' test scores, as determined by their scores, is 15/3.

What does "Sample Standard Deviation" mean?

Sample Standard Deviation: The sample standard deviation (s) is a measurement of the variation from the expected values and is equal to the square root of the sample variance. It can be conceptualized as the average difference between the observed data and the predicted values.

Ten pupils are given a test, and their results are as follows: 80, 99, 83, 82, 100, 75, 83, 85, 71, and 92

80, 99, 83, 82, 100, 75, 83, 85, 71, and 92 are the sample means.

m = total observations / total observations

80+99+83+82+100+75+83+85+71+92=850 is the total number of observations.

Ten observations were made.

The sample mean of ten students' test scores, calculated as m=850/10=85, is given.

sample standard deviation,

s=√(assumed value-mean)²/√(number of observaionts-1)

let Assumed value be 100

s=√(100-85)²/√10-1

s= √(15)²/√9

s=15/3 is the sample standard deviation of the scores of ten students taken from their test.

Answer:

(3x+1)(x+5)

Step-by-step explanation:

Sorry for my handwriting lol hope this makes sense

Answer:

B) -2t^2+3t+5

and

C) 4t-7

Answer:

V= 226.19

:)

Step-by-step explanation:

Answer:

226.19 cm

Step-by-step explanation:

The point is on second quadrant.

P(x, y) is on the unit circle

radius of the circle must be 1

The equation x² + y² = r²

\(y=\frac{2}{3}\), r =1

\(x^{2} (\frac{2}{3}) ^{2}= 1^{2}\)

\(x^{2} +\frac{4}{9} =1\)

\(x^{2} =1-\frac{4}{9}\)

\(x^{2} =\frac{5}{9}\)

\(x=\sqrt{\frac{5}{9} }\)

x = ±\(\sqrt{\frac{5}{9} }\)

x- c00rdinate is negative = - \(\sqrt{\frac{5}{9} }\)

P(x, y) = \((-\sqrt{\frac{5}{9} }, \frac{2}{3})\)

Therefore, the point is on second quadrant.

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Answer:

yo si apenas me lo descargue

We can say with 90% confidence that the true mean level of polyunsaturated fatty acid in this brand of diet margarine is between 16.95 and 17.23. The answer is 90%.

Using the t-distribution with 5 degrees of freedom (n-1), we can calculate the t-value for a 90% confidence interval. We use a one-tailed test because we want to find the confidence interval for values greater than 16.65:

t-value = t(0.90,5) = 1.476

Now we can calculate the margin of error (E) for a 90% confidence interval:

E = t-value * (s / √n) = 1.476 * (0.31 / √6) = 0.28

Finally, we can calculate the confidence interval:

16.95 + E = 16.95 + 0.28 = 17.23

Therefore, we can say with 90% confidence that the true mean level of polyunsaturated fatty acid in this brand of diet margarine is between 16.95 and 17.23. Since the range of values between 16.65 and 17.32 falls within this confidence interval, we can also say that we are 90% confident that the true mean level of polyunsaturated fatty acid falls within this range.

So, the answer is 90%.

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We use the quadratic formula to find the roots of the quadratic equation.

The quadratic equation is given below:

f(x) = a\(x^{2}\) + bx + c = 0 where a, b, c

The system of equations used to find roots of equation is y = 12\(x^{3}\)-5x and y=2\(x^{2}\)+x+6.The given equation will be,12\(x^{3}\)-5x=2\(x^{2}\) + x + 6.

Now we take the root of equation into two parts:

1. Left-hand side

2. Right-hand side

Equation no.1 : 12\(x^{3}\)-5x=0

Equation no.2: 2\(x^{2}\)+x+6=0

Now we contains system of equation 0 with y.

So, the equation will be:

12\(x^{3}\)-5x=y

2\(x^{2}\)+x+6=y

However,system of equations can be used to find the roots of the equation 12\(x^{3}\)-5x=2\(x^{2}\)+x+6 is:
y = 12\(x^{3}\)-5x and y = 2\(x^{2}\)+x+6

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Answer:

x=1

Step-by-step explanation:

The value of x is 1. So, the correct answer is d. x = 1.

To find the value of x, we can use the fact that the corresponding sides of congruent triangles are equal.

In triangle ABC, side AB is labeled 4x - 1, side BC is labeled 4, and side AC is labeled 5.

In triangle CDE, side CD is labeled 5, side DE is labeled x + 2, and side CE is labeled 4.

Since triangle ABC is congruent to triangle CDE, we can set up the following equations:

4x - 1 = 5
4 = x + 2

Simplifying these equations, we get:

4x = 6
x = 1

Therefore, the value of x is 1. So, the correct answer is d. x = 1.

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Answer54: A, 55: G, 56: D

Step-by-step explanation:

Answer:

54. 2cm

55. between 6 and 7

56. two irrational numbers

Step-by-step explanation:

Answer:

They are both correct.

Step-by-step explanation:

As we can see, it does not matter whether you plug in x or y in a system of equatins. One thing somebody might be skeptical about in this equation is that one of the equations does not contain a variable. BUT, if reading closer, one can see that both x and y have to be in one of the equations to make the other true.

Hope this helped!

We will see that both Jared and Nicole are correct.

So we know that Jared found an equation:

y = x + 10, then he substituted y for (x + 10) on the other equation, this would be the substitution method, and Jared is correct so far.

We also know that Nicole found the equation:

x = y - 10

And she replaced x by y - 10 on the other equation, she is also correct.

Each one just substituted a different variable, that is why they have different approaches, but in both cases the substitutions are correct.

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