describe fully the single transformation which takes shape A to shape B.

Answer:

Below

Step-by-step explanation:

The equation is x2 + bx + c

The coefficients are

● a = 1

● b

● c is the constant

The difference of the roots is | b - 2c |

Let s and p be the roots of the polynomial

● s - p = | b - 2c | (1)

● s + p = -b/a => s + p = -b (2)

(1) + (2)

● s - p + s + p = |b-2c| - b

● 2s = | b - 2c | - b

● 2s = b - 2c - b or 2s = 2c - b - b

● 2s = - 2c or 2s = 2c - 2b

● s = - c or s = c - b

We want to express b in term of c. So we will be intetsted in the 2nd equation

● s = c - b

● s - c = - b

● b = c - s

Answer:

either of two angles whose sum is 90°.either of two angles whose sum is 180°.

Step-by-step explanation:

Answer:

In slope-intercept form:

\( y = - \frac{5}{2} x + 4\)

In standard form:

\(5x + 2y = 8\)

Step-by-step explanation:

\( - 6 = - \frac{5}{2} (4) + b\)

\( - 6 = - 10 + b\)

\(b = 4\)

\(y = - \frac{5}{2} x + 4\)

\( - 2y = 5x - 8\)

\( - 5x - 2y = - 8\)

\(5x + 2y = 8\)

The p-value for a sample of different sales promotions with 5 different promotions and 10 samples with all 5 is equals to the 0.1060.

Suppose that the sales manager wants to compare different sales promotions. Here, number of different promotion choosen by him = 5

Number of random sample of each different promotion= 10

The F value = 3.4

We have to determine the p-value by using JMP. Now, n = 10, k = 5 so, degree of freedom = n - k= 5

Computing the p value using approximate method, \(P-value = P( F_{k - 1, n-k} > 3.4 ) \)

\(= P( F_{4, 5}> 3.4 ) \)

Using Excel command, value of F is calculated, = F.dist.RT( 3.4,4,5)

= 0.105954

Hence, required value is 0.1060.

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The log equation, log(x+1) (4x) = 67, written as an exponential equation is (x + 1)(4x) = 10⁶⁷

From the question, we are to write the given logarithmic equation as an exponential equation.

The given log equation is:

log(x+1) (4x) = 67

To convert this to an exponential equation, we can use the definition of logarithms, which states that:

log(base b) (y) = x is equivalent to y = b^x

That is,

log (x)(y) = n  ⇒ (x)(y) = 10ⁿ

Applying this definition to the given equation, we get:

(x + 1)(4x) = 10⁶⁷

This is the exponential equation equivalent to the given logarithmic equation.

Hence, the exponential equation is (x + 1)(4x) = 10⁶⁷

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Answer:

x= 1.79

Step-by-step explanation:

x-0.63=1.16 add 0.63 to both sides

x= 1.79

Answer:

x =1.79

Step-by-step explanation:

x -0.63 = 1.16

Add .63 to each side

x -0.63+.63 = 1.16+.63

x =1.79

The probability of a bulb lasting for between 557 and 561 hours is roughly 0.0382 or 3.82%

Able to utilize the standard ordinary dissemination to discover the likelihood of a bulb enduring for between 557 and 561 hours. To do this, we ought to standardize the values utilizing the equation:

z = (x - μ) / σ

where x is the bulb lifetime we're fascinated by

, μ is the cruel(mean) lifetime,

and σ is the standard deviation.

For 557 hours:

z1 = (557 - 530) / 15 = 1.8

For 561 hours:

z2 = (561 - 530) / 15 = 2.07

Employing a standard ordinary conveyance table or a calculator with a typical dissemination work, we are able to discover the probabilities corresponding to these z-scores:

P(z1 < Z < z2) = P(1.8 < Z < 2.07)

This speaks to the likelihood of a bulb enduring between 557 and 561 hours, where Z could be a standard ordinary variable.

Employing a standard ordinary dispersion table or a calculator, we discover:

P(1.8 < Z < 2.07) ≈ 0.0382

Therefore, the likelihood of a bulb enduring for between 557 and 561 hours is roughly 0.0382 or 3.82% (adjusted to four decimal places). 

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The code initializes the variable `count` to 0. Then, it enters a while loop that continues as long as `count` is less than 11. The value printed by the code is: 1

The value printed by the code is:

1

2

3

4

5

6

7

8

9

10

11

The code initializes the variable `count` to 0. Then, it enters a while loop that continues as long as `count` is less than 11. Inside the loop, `count` is incremented by 1, and then the current value of `count` is printed. This process repeats until `count` reaches 11.
Therefore, the numbers from 1 to 11 (inclusive) are printed.

The value printed by the code is:

1

In the second code, after initializing `count` to 0, the if statement checks if `count` is less than 11. Since the condition is true (`count` is 0), the code enters the if block. Inside the block, `count` is incremented by 1 and then printed. After executing the if block once, the code exits, and only the value 1 is printed.

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The complete question is:

What value is printed by the code below? count = 0 while count < 11: count = count + 1 print(count) What value is printed by the code below? count = 0 if count < 11: count = count + 1 print(count)?

The measure of angle ACD for the given circle is 67.5 degree.

A triangle is inside a circle when a circle encircles it, and each vertex of the triangle touches the circle.

When a circle encircles a triangle, the triangle lies outside the circle and the circle makes one point contact with each of the triangle's sides. The triangle's sides are perpendicular to the circle.

Given that,

The inscribed angle CDA = 1/2(arc AC).

arc AC = 90 degree.

Then:

∠ CDA = 90 / 2

∠ CDA = 45

Triangle ACD is isosceles, so:

∠ ACD + ∠ CAD + ∠ CDA = 180 degree

Here, ∠ ACD = ∠ CAD

∠ ACD + ∠ACD + ∠ CDA = 180 degree

∠ ACD = 180-45 / 2

∠ ACD   = 67.5 degree

Hence, the measure of angle ACD for the given circle is 67.5 degree.

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The correct question is:

Points A, B, C, and D lie on circle M. Line segment BD is a diameter.

Triangle A C D is inscribed within circle M. Point B is on the circle between points C and B. A line is drawn to connect points D and B. Lines are drawn from points C and A to point M to form a right triangle. Arcs C D and A D are congruent.

What is the measure of angle ACD?

45.0°

67.5°

112.5°

135.0°

Step-by-step explanation:

Tan = opposite / adjacent

use pythagorean theorem to find CD first.

A² = B² + C²

9² = (SqRt (66) )² + C²

81 - 66 = C²

C = SqRt (15)

now find tan

SqRt (66) / SqRt (15 = tan

tan = 2.0976

tan^¹(2.0976) = 64.51 degrees

Answer:

6x² - 19x + 15

Step-by-step explanation:

(2x-3) (3x-5)

6x² - 10x - 9x + 15

6x² - 19x + 15

Step-by-step explanation:

If the testing firm rejects the null hypothesis at the 0.10 level of significance, it means that they have found evidence that suggests that the publisher's claim of 43% ownership of personal computers among readers is inaccurate.

Since the null hypothesis always assumes that there is no statistically significant difference between the observed data and the expected data, rejecting it means that there is a statistically significant difference between the observed data and the expected data. In this case, it means that the proportion of readers who own a personal computer is significantly different from 43%.

However, it is important to note that rejecting the null hypothesis does not necessarily prove that the publisher's claim is completely false or inaccurate. It only suggests that there may be reason to question its accuracy. Further investigation and testing would be needed to establish a more confident conclusion.

A graph of the distance and time data for distance traveled by this train is shown in the image attached below.

In Mathematics, a scatter plot is sometimes referred to as scatter chart and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting data points showing any association or correlation between the data set.

In this scenario, the time (in hours) would be plotted on the vertical axis (x-axis) of the scatter plot while the distance (in kilometers) would be plotted on the horizontal axis (y-axis) of the scatter plot by using an Excel worksheet.

From the scatter plot (see attachment) which models the relationship between the distance (in kilometers) and time (in hours), a linear equation for the line of best fit or trend line is y = 99.43x + 11.43.

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At the 5% level of significance, the machine is not properly calibrated.

To determine if the machine is properly calibrated, we need to conduct a hypothesis test using the given data. Let's define our null and alternative hypotheses as follows:

Null hypothesis (H0): The machine is properly calibrated and the true mean thickness of the widgets is 0.05 inches.

Alternative hypothesis (Ha): The machine is not properly calibrated and the true mean thickness of the widgets is not equal to 0.05 inches.

We will use a two-tailed t-test to test the hypothesis since we have a sample size of 10, and the population standard deviation is unknown. The test statistic for this hypothesis test is calculated as:

t = (x - μ) / (s / sqrt(n))

where x is the sample mean thickness, μ is the hypothesized population mean thickness (0.05 inches), s is the sample standard deviation, and n is the sample size (10).

Plugging in the given values, we get:

t = (0.053 - 0.05) / (0.003 / sqrt(10)) = 3.055

The degrees of freedom for this test is 9 (n - 1). Using a t-table or calculator, we can find the critical t-value for a two-tailed test with 9 degrees of freedom and a significance level of 0.05 to be approximately 2.262.

Since our calculated t-value (3.055) is greater than the critical t-value (2.262), we can reject the null hypothesis at the 5% level of significance. This means that there is sufficient evidence to suggest that the machine is not properly calibrated and that the true mean thickness of the widgets is likely not equal to 0.05 inches.

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The series ∑(from n = 2 to infinity) 1/n^(1/n^a) converges only when "a" is greater than 1.

To determine the values of "a" for which the series ∑(from n = 2 to infinity) 1/n^(1/n^a) converges, apply the limit comparison test with the harmonic series.

Let's consider the harmonic series ∑(from n = 1 to infinity) 1/n, which is a well-known divergent series.

compare the given series with the harmonic series by taking the limit as n approaches infinity of the ratio of the nth term of the given series to the nth term of the harmonic series:

lim(n→∞) [1/n^(1/n^a)] / [1/n]

To simplify the expression, rewrite the ratio as follows:

lim(n→∞) n / n^(1/n^a)

Now, let's consider the exponent in the denominator, which is 1/n^a. As n approaches infinity, the exponent approaches zero since 1/n^a will become very large and tend to infinity.

Therefore, we have:

lim(n→∞) n / n^(1/n^a) = lim(n→∞) n / n^0 = lim(n→∞) n / 1 = ∞

Since the limit of the ratio is infinity, it means that the given series behaves similarly to the harmonic series. Therefore, if the harmonic series diverges, the given series will also diverge.

The harmonic series diverges when the exponent "a" is equal to or less than 1.

Hence, the series ∑(from n = 2 to infinity) 1/n^(1/n^a) converges only when "a" is greater than 1.

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Answer:

(2x²)/3 or 2/3x²

Step-by-step explanation:

Divide like terms.

10/15 = 2/3

x⁴/x² = x²

Putting this together gives us:

(2x²)/3 or 2/3x².

In an augmented matrix, the coefficients of the variables in the system of equations are arranged in rows. The augmented matrix for the system of equations is:

4 4 5 22

3 7 -2 -17

4 3 3 6

The system of equations for the given augmented matrix is:

4x + 4y + 5z = 22

3x + 7y - 2z = -17

4x + 3y + 3z = 6

In an augmented matrix, the coefficients of the variables in the system of equations are arranged in rows. The rightmost column represents the constants on the other side of the equal sign. Each row corresponds to an equation in the system.

For the first equation, 5z + 4x + 4y = 22, the coefficients 4, 4, and 5 are placed in the first row of the matrix, and the constant 22 is placed in the last column. Similarly, the coefficients and constants of the other equations are placed in subsequent rows, resulting in the given augmented matrix.

Conversely, to obtain the system of equations from the augmented matrix, we take each row and assign the variables to the corresponding coefficients. The constants in the last column represent the right-hand side of the equations.

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Answer:

y = 7/2x - 4

Step-by-step explanation:

7/2 is the slope and -4 is the y intercept

Answer:

B is the answer

Step-by-step explanation:

this is showing 2 being divided by 9 which must give a value less than one, in this case it is .2 repeating

The two expressions are not equivalent because one of the the rule of exponents is that when the bases of the exponents are the same (in this case, they're all x) then you can add the powers. Thus, the alternative expression should be x^(3+3+3).

Answer:

D

Step-by-step explanation:

Step-by-step explanation:

The First part is correct.

The domain is All set of inputs of a function.

We know that tangent has a period of 180.

Since our interval has a distance of 180, and tan 0 isn't 1 over root of 3, we will have only 1 domain.

So let solve the solution.

\( \tan(x) = \frac{1}{ \sqrt{3} } \)

\(x = \tan {}^{ - 1} ( \frac{1}{ \sqrt{3} } ) \)

30°

\(x = 30°\)

So the domain of this function is [30°].

Part C: Tangent has a period of 180 degrees, so our solution will occur every 180 degrees.

We want full revolutions, so let use a variable, let say n to represent a interger.

Part C: The general solution is

30°+(180n)°, where n is a interger( 1,2,3.....)

Part D: The answer of tan x=1/sqr root of 3 is , in degrees, of

x∈N, 30+180n, where n is a interger.

If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your working memory.

A cognitive apparatus known as working memory has a finite capacity and can only temporarily store information. It is crucial for reasoning, decision-making, and behaviour direction. When working on a long-division problem, kids use their working memory abilities to retain the long-division steps. Other instances include keeping track of complicated instructions, taking notes in class, recalling an argument while someone else is speaking, or performing mental calculations. In contrast to long-term memory, which stores a large amount of knowledge over a lifetime, working memory is the little amount of information that may be kept in mind and used to carry out cognitive tasks. One of the most often used concepts in psychology is working memory.

Given,

If you were able to add the numbers 26 and 41 in your head, it is assumed that you would be doing this in your:

d) Working memory

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The value of the function, f(0) is 13. However, we are instructed not to include f(0) in our answer. This means that we can state that we have found the value of f(0) to be 13, but we cannot include 13 in our answer.

When we are given a function, one of the first things we may want to do is evaluate it at a specific point. One way to do this is by substituting the value into the function and simplifying it. In this case, we are asked to find the value of f(x) at x=0 for the function f(x) = 5^x + 12 without using a calculator.

To find the value of f(0), we simply substitute 0 for x in the given function:

f(0) = 5^0 + 12

Now, any non-zero number raised to the power of 0 is equal to 1. This means that 5^0 is equal to 1. Therefore, we have:

f(0) = 1 + 12

Simplifying the expression, we get:

f(0) = 13

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The line integral around the unit circle is 2π.

We can use Green's Theorem to evaluate the line integral. Green's Theorem states that for a vector field F = (P, Q) with continuous partial derivatives defined on a simply connected region R in the plane, the line integral along the boundary of R is equal to the double integral of the curl of F over R:

∮C P dx + Q dy = ∬R (∂Q/∂x - ∂P/∂y) dA

In this case, P = -y and Q = x, so ∂Q/∂x = 1 and ∂P/∂y = -1, and the curl of F is:

∂Q/∂x - ∂P/∂y = 1 - (-1) = 2

Since the unit circle is a simply connected region, we can apply Green's Theorem to find:

∮C -y dx + x dy = ∬R 2 dA

The region R is the unit disk, so we can use polar coordinates to evaluate the double integral:

∬R 2 dA = 2 ∫0^1 ∫0^2π r dr dθ = 2π

Therefore, the line integral around the unit circle is 2π.

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Answer:

x = 9

Step-by-step explanation:

5x + 5x - 90 = 0

5x + 5x = 90 + 0

5x + 5x = 90

10x = 90

x = 9

Hope that helps!

-Sabrina