Which of the following is a perfect square trinomial?

(A) 4x2 - 4x + 1

(B) 4x2 - 2x + 2

(C) 4x2 - 4x + 2

(D) 4x2 - 8x + 16

(E) 4x2 - 12x + 16

Answer:

Graph attached as a screenshot. Hope this helps!

The difference quotient for the function is 8.

The function is given by:

f ( x ) = 8 x − 9, where h ≠ 0

To find f(a), substitute a for x in the function. So we have:

f ( a ) = 8 a − 9

To find f(a + h), substitute a + h for x in the function. So we have:

f ( a + h ) = 8 ( a + h ) − 9

The difference quotient can be found using the formula:

(f(a + h) - f(a))/h

Substituting the values found above, we have:

(8 ( a + h ) − 9 - (8 a − 9))/h

Expanding the brackets and simplifying, we have:

((8a + 8h) - 9 - 8a + 9)/h

= 8h/h

= 8

Therefore, the difference quotient for the function is 8.

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The formula (p∧ ¬q) → (p∧q) is true whenever ¬p is true. The formula holds true regardless of the truth value of q when p is false.

To determine the truth value of the formula (p∧ ¬q) → (p∧q) when ¬p is true, we need to construct a truth table.

Let's consider the variables p and q and their respective truth values. Since ¬p is true, p must be false.

p q ¬q p∧ ¬q p∧q (p∧ ¬q) → (p∧q)

F T F F F T

F F T F F T

In the truth table above, we evaluate the truth values of the individual components of the formula and then determine the truth value of the entire formula. As we can see, regardless of the value of q, the formula evaluates to true. Thus, the formula (p∧ ¬q) → (p∧q) is true when ¬p is true.

Based on the truth table, we can conclude that the formula (p∧ ¬q) → (p∧q) is true whenever ¬p is true. The formula holds true regardless of the truth value of q when p is false.

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The introduction of imaginary numbers similar to the introduction of negative numbers through the determination of square root of a negative number.

Complex numbers are square root of a negative number. Since a square root of a negative number  cannot be determined, it is always represented with "i"

Given the rational number √-4 for instance, this will result in complex number or imaginary number since it is a negative number.

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Answer: The model of the Cape Hatteras Lighthouse is 7 feet tall, as it follows a scale of 8 inches = 30 feet. The actual lighthouse is 210 feet, so to calculate the height of the model, you would divide the actual lighthouse's height by the scale that is used. 210 feet divided by 30 equals 7 feet, which is the height of the model. This is why models are made to a specific scale, as it allows us to calculate the size of the model accurately, without having to measure every single dimension.

Answer:

1 kg

Step-by-step explanation:

Number of chickadees = 100

Quantity of seed eaten = 100 kg

Number of days = 100

Quantity of seeds each chickadee eats per day =Number of chickadees ÷ Quantity of seed eaten ÷ Number of days

= 100 ÷ 100 ÷ 100

= 1 ÷ 100

= 0.01 kg of seed

How many kg of seeds can 10 chickadees eat in 10 days?

= Quantity of seeds each chickadee eats per day × number of chickadee × number of days

= 0.01 kg × 10 × 10

= 1 kg

10 chickadees eat 1 kg of seeds in 10 days

(a) To satisfy (*) with X ~ N(0, 1) and Z ~ N(0, 2), we can rearrange the equation as follows: Y = Z - X. Since X and Z are normally distributed, their linear combination Y = Z - X is also normally distributed.

The mean of Y is the difference of the means of Z and X, which is 0 - 0 = 0. The variance of Y is the sum of the variances of Z and X, which is 2 + 1 = 3. Therefore, Y ~ N(0, 3). The joint distribution of X, Y, and Z is multivariate normal with means (0, 0, 0) and covariance matrix:

```

   [ 1  -1  0 ]

   [-1   3 -1 ]

   [ 0  -1  2 ]

```

(b) i. To show that X and Y are dependent, we need to demonstrate that their covariance is not zero. Since Y = aX, the covariance Cov(X, Y) = Cov(X, aX) = a * Var(X) = a * 2 ≠ 0, where Var(X) = 2 is the variance of X. Therefore, X and Y are dependent.

ii. For Y = aX to hold, we require a ≠ 0. If a = 0, Y would always be zero regardless of the value of X. The variance of Y can be obtained by substituting Y = aX into the formula for the variance of a random variable:

Var(Y) = Var(aX) = a^2 * Var(X) = a^2 * 2

iii. The smallest variance that Y can have is 2, which is achieved when a = ±√2. This occurs when Y = ±√2X.

iv. To find the joint distribution of X, Y, and Z such that Y assumes the variance bound of 2, we can substitute Y = √2X into the covariance matrix from part (a). The resulting covariance matrix is:

```

   [ 1   -√2   0 ]

   [-√2   2   -√2]

   [ 0   -√2   2 ]

```

The determinant of this covariance matrix is -1. Therefore, the determinant of the covariance matrix of the random vector (X, Y, Z) is -1.

Conclusion: In part (a), we found that Y follows a normal distribution with mean 0 and variance 3 when X ~ N(0, 1) and Z ~ N(0, 2). In part (b), we demonstrated that X and Y are dependent. We also determined that Y = aX is possible for any a ≠ 0 and found the corresponding variance of Y to be a^2 * 2. The smallest variance Y can have is 2, achieved when Y = ±√2X. We constructed a joint distribution of X, Y, and Z where Y assumes this minimum variance, resulting in a covariance matrix determinant of -1.

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Option B is true of a probability mass function but not a probability density function.

A probability mass function is used to describe the probability distribution of a discrete random variable. The function maps each possible value of the random variable to the probability of that value occurring. Therefore, a probability mass function takes on only non-negative values and sums to one over its domain.Option A and C are true of both probability mass function and probability density function.

A probability density function, on the other hand, describes the probability distribution of a continuous random variable. The function assigns probabilities to intervals of possible values rather than to specific values. For this reason, the probability that a random variable X is equal to a specific value x is always zero. Therefore, option B is true of a probability mass function but not a probability density function.Option D is true of both probability mass function and probability density function. This is because, for continuous random variables, the probability that a random variable X is between a and b is the area under the function between a and b (integral), while for discrete random variables, it is the sum of the probabilities of all values between a and b.

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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Answer:

C

Step-by-step explanation:

In order to write the equation, you need to identify the slope and y-intercept.

1) the y intercept is what y is when x=0. According to the table, it is -2.

2) the slope is the change in the y values over the change in the x values.  Notice that the y values are increasing by one for every increase in 1 in the x values, so the slope is 1/1 or 1.

3) we can then put those values into slope-intercept form which is y=mx+b where m is the slope and b is the intercept.

4) so the equation is y=(1)x-2 or y=x-2  (they are the same)

Answer:

The answer is y<17

Step-by-step explanation:

First, move the constant to the right.

3y<65-14

Then, subtract 65 and 14

3y<51

Lastly, divide both sides by 3.

y<17

Answer:

Step-by-step explanation:

slope formula: \(\frac{y2-y1}{x2-x1}\)

                       : \(\frac{-2--5}{1--11}\)

                       : \(\frac{1}{4}\) ............this is our slope, m.

using y - y1 = m ( x - x1 )

⇒     y - 2 = \(\frac{1}{4}\) ( x - 1 )

⇒      \(y =\) \(\frac{x}{4}\) + \(\frac{7}{4}\)

Answer:

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

Step-by-step explanation:

\(m= \frac{y2-y1}{x2-x1}\)

So, plug in (-11,-5) and (1,-2),

\(m=\frac{(-2) - (-5)}{1-(-11)}\)

Subtract,

\(m=\frac{3}{12}\)

Divide 3 by 12:

\(m=\frac{3}{12} = .25\) or \(\frac{1}{4}\)

The slope is .25 or \(\frac{1}{4}\)

So, the equation so far is:

\(y=\frac{1}{4} x + b\)

Now, we have to find the y-intercept.

\(y=\frac{1}{4}x+b\)

Substitute the x for 1 and -2 in place of y.

\(-2=\frac{1}{4}(1) +b\)

Now solve.

\(-2=\frac{1}{4}(1) +b\\-2=\frac{1}{4} +b\\-\frac{1}{4} -\frac{1}{4} \\\\-2\frac{1}{4} =b\)

the y-intercept is: \(-2\frac{1}{4}\) or \(-\frac{9}{4}\)

The full equation is : \(y=\frac{1}{4}x - \frac{9}{4}\)

Hope this helps! Brainliest would be much appreciated! Have a great day! :)

We can say that a and b are identical in absolute value if a and b are nonzero integers such that a divides b (a | b) and b divides a (b | a). That is to say, a =± b.

The transitive property of divisibility serves as evidence for this. We know that there are numbers k and l such that b = ak and a = bl exist if a | b and b | a. We obtain a = alk by substituting the expression for b into the second equation. We can divide both sides by a to get l = 1/k because an is not zero. Given that k and l are both integers, they must both either be 1 or -1. B Equals ak if k = 1, else then b = ak = a(1) = a, and if k = -1, then b = ak = a(-1) = -a. In either case, we have shown that a = ±b.

So if a and b are nonzero integers such that a divides b and b divides a, then we can conclude that a and b have the same absolute value, but possibly opposite signs.

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Let A = (xa,ya) and B = (xb,yb) be any two given points

The general formula for the coordinates of the midpoint of AB is: x = (xa + xb)/2 and y = (ya + yb)/2

I

Answer:

see below

Step-by-step explanation:

Identify the graph shown as linear or non linear.  - nonlinear since it is not a linear

Then estimate and interpret the intercepts of the graph,

y intercept -  ( 0,-6)  where it crosses the y axis

x intercepts ( -12,0)  and ( 12,0)

any symmetry,  symmetric across the y axis

where the function is positive, or above zero  (-∞, -12) and (12,∞)

negative, or below zero ( -12,12)

increasing,  growing ( 0, ∞)

and decreasing, getting smaller (-∞, 0)

the x-coordinate of any relative extrema,  the minimum is (0,-6)

and the behavior of the graph. As x goes to -∞ y goes to ∞  and s x goes to ∞ y goes to ∞

The statement "If a function f '(x) exists and is nonzero for all x, then f(8) ≠ f(0)" is not necessarily true.

If f(x) is an increasing or decreasing function on the Interval [0, 8], then it is possible that f(8) = f(0).

For example, consider the function f(x) = x, which is increasing on the interval [0, 8] and satisfies f '(x) = 1 for all x in [0, 8]. Then f(8) = 8 and f(0) = 0, so f(8) = f(0).

However, if we assume that f(x) is strictly increasing or strictly decreasing on the interval [0, 8], then the statement would be true.

This is because if f(x) is strictly increasing or decreasing, then it cannot have any repeated values in its range, and so f(8) ≠ f(0).

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Answer:

no perpendicular

Step-by-step explanation:

Answer:

Grounded beef

Step-by-step explanation:

Answer:

4/5 or 0.8

Step-by-step explanation:

this problem description is not very precise. it leaves out the definition what corners or sides of JKLM correspond to corners and sides of ABCD.

I assume J and K correlate to A and B, and JK is a long side of JKLM.

so, we are going from JKLM to ABCD.

that means we are going from larger to smaller (as JK = 15 and therefore larger than AB = 12).

what is the scale factor to go from 15 to 12 ?

15 × x = 12

x = 12/15 = 4/5 or 0.8

Answer:

AB and BC are the sides of a parallelogram, ABCD. AB = 5 cm, BC = 7 cm and ABC = 60 degrees. Draw the lines AD and CD to complete the parallelogram.

Step-by-step explanation:

Using the subtraction between two amounts, it is found that:

The difference between the longest and shortest measurement is of 33 cm.

The measurements are given as follows:

To find the difference between difference between the longest and shortest measurement, we have to subtracted the longest measurement by the shortest measures.

From the measurements given, we have that:

Hence, the subtraction is given as follows:

41 cm - 8 cm = 33 cm.

The difference between the longest and shortest measurement is of 33 cm.

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Answer:

Is there a picture or something?

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

you know it

I hope this helps! :)

5 is a rational number!

Pls mark as BRAINLIEST

5 is a rational number because it can be written as a fraction; \(\frac{5}{1}\)

♡ Hope this helps! ♡

❀ 0ranges ❀

The triangle that is similar to the triangle ΔABC is the triangle ΔJKL, the correct option is therefore;

B. ΔJKL, in which m∠J = 15° and m∠L = 45°

Triangles are similar if they have the same measure of two of their interior angles, and therefore, have the same shape, but they may have different size.

The specified known angles of the triangle indicates that the known angles are;

m∠A = 15°, m∠B = 120°

Therefore, the third angle of the triangle is; 180 - (15 + 120) = 45

The third angle of the is 45 degrees

Therefore, the triangle that is similar to the specified triangle has an angle interior angle of either; 15°, or 120°, or 45°

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Answer:

20x⁵ + 20x⁴

Step-by-step explanation:

Use distributive rule: a*(b +c) =a*b + a*c

5x⁴(4x + 5) = 5x⁴ * 4x + 5x⁴ * 5

                  = 20x⁵ + 20x⁴

Hint: 5x⁴ * 4x multiply the coefficient and then the variables. For multiplying variable, if they two have same base, then add the powers

5*4 * x⁴ * x = 20x⁵

Answer:

ravi's is 440 and malcolm's is 520 i think

Step-by-step explanation:

Answer: The correct answer is b

Step-by-step explanation:

25% off $30 is 22.50 and then when you add 7%ax it turns out to be 24.08