Christian is rewriting an expression of the form y = ax2 + bx + c in the form y = a(x – h)2 + k. Which of the following must be true?
h and k cannot both equal zero
k and c have the same value
the value of a remains the same
h is equal to one half –b

The expression  -10 × X × 5 when X = -1 is equal to 50.

To evaluate -10 × X × 5 when X = -1, we substitute -1 for X in the expression:

-10 × (-1) × 5

Following the order of operations, we first perform the multiplication:

-10 × (-1) × 5 = 10 × 5

-10 × (-1) × 5 = 50

using the above as a guide, we have the following:

-10 × X × 5 when X = -1 is equal to 50.

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Answer:

(2a − 5)(a + 2)

Step-by-step explanation:

Answer:

So basically it’s D

Step-by-step explanation:

:)

Answer:

2nd Option is correct.

Step-by-step explanation:

We are given with four statements which describes a graph of a function.

We need to find the graph which represents the linear function.

Linear Function:

Linear functions are the functions whose graph are straight lines.

A linear function has the following form

y = f(x) = a + bx

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

So, In graphs of 1st , 3rd and 4th Options are curves not a straight line.

Only 2nd Option has graph which is straight as mentioned in it that a line passing through two points.

Therefore, 2nd Option is correct.

The positive solution to the equation is a rational number between one and two.

The positive solution to the equation is a rational number. It is greater than one but less than two. To find the solution, we would need to see the equation itself. However, based on the given options, the only option that fits the criteria of being between one and two and being a rational number is 'The solution is greater than one but less than two.'

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The original bill amount that Isabella owed before the late fee was $19,500.

We need to understand the relationship between the late fee and the original bill amount.

Isabella was charged a late fee of 4% of the original bill amount, and this late fee was $780.

Let's use the variable x to represent the original bill amount. Since the late fee is 4% of the original bill, we can write the equation:

[tex]0.04x = 780[/tex]

To find x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.04:

[tex]x = \frac{780}{0.04}[/tex]

Now, we can calculate this value:

[tex]x = 19500[/tex]

To calculate the balance, add the outstanding deposits to the ending balance and subtract the outstanding checks.

To calculate the balance, we need to start with the ending balance and make adjustments for outstanding deposits and outstanding checks. First, add the outstanding deposits to the ending balance: 59.75 + 175.46 = 235.21. Next, subtract the outstanding checks from the previous result: 235.21 - 231.69 = 3.52. Therefore, the balance is $3.52.

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To estimate the probability of getting fewer than 4 successes in a binomial distribution, we can use the normal distribution as an approximation based on the conditions np > 5 and nq > 5. By calculating the mean and standard deviation of the normal distribution, we can use a z-score to find the estimated probability. In this case, the estimated probability is approximately 0.1709.

The given question requires us to estimate the probability of getting fewer than 4 successes in a binomial distribution. To determine if we can use the normal distribution as an approximation, we need to check if both np and nq are greater than 5. In this case, np = 13 * 0.4 = 5.2 and nq = 13 * 0.6 = 7.8, so both conditions are satisfied. Thus, we can use the normal distribution as an approximation. Let's estimate P(fewer than 4) using the normal distribution.

The mean of the normal distribution is given by μ = np = 13 * 0.4 = 5.2. The standard deviation is calculated using the formula σ = √(npq), where q = 1 - p. So, q = 1 - 0.4 = 0.6. Plugging in the values, we get σ ≈ √(13 * 0.4 * 0.6) ≈ 1.789. Now, we can use the normal distribution to estimate the probability.

Using the z-score formula z = (x - μ) / σ, where x is the number of successes we want to estimate the probability for, we can find the z-score for 3.5 (less than 4). z = (3.5 - 5.2) / 1.789 ≈ -0.951. Now, we can use a standard normal distribution table or calculator to find the cumulative probability for this z-score. P(fewer than 4) = P(z < -0.951) ≈ 0.1709 (approximately). Therefore, the estimated probability of getting fewer than 4 successes in the given binomial distribution is approximately 0.1709.

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Firstly, we would have to evaluate whether a normal approximation would be useful to use. However, given our conditions where `n` is 13, `p` is 0.4, `q` (the complement of `p`) is 1 - 0.4 or 0.6, we can clearly use the normal approximation to the binomial distribution because both `np` (13 * 0.4 = 5.2) and `nq` (13 * 0.6 = 7.8) are greater than 5.

For the normal approximation, we begin by calculating the mean (µ) and standard deviation (σ) of the binomial distribution. The mean of a binomial distribution is calculated as `np` hence in our case, `np` is 13 * 0.4 which is equal to 5.2. To find the standard deviation, we use the formula `sqrt(npq)`, so in our case, we have`sqrt(13 * 0.4 * 0.6)`, which is approximately 1.76635.

Now, to find the probability of getting fewer than 4, we would calculate a z-score for the value of x = 4. This helps convert the raw scores in a dataset into a standardised form, allowing us to better understand the position of individual scores in relation to the rest of the dataset. The z-score is calculated as `z = (x - µ) / σ` . With x being 4, µ is 5.2, and σ is 1.76635, our z-score will be (4 - 5.2) / 1.76635, which gives us approximately -0.67937.

Now, the last step is to find the cumulative probability associated with this z-score. In essence, the cumulative probability associated with a z-score tells you the probability that a certain observation will occur given a standard normal distribution (which is our case, as we've standardised our dataset using the z-score). Checking a z-table, or by using the cumulative distribution function for a value of z = -0.67937, the associated probability is approximately 0.24845.
So the final probability that we will get fewer than 4 is approximately 0.24845 or 24.85% when we use the normal distribution as an approximation to the binomial distribution.

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Answer:  

$16.80

Step-by-step explanation:

Answer with explanation:

[tex]z=2^{\frac{1}{3}}\\\\z^3=2\\\\z^3=2 \times (1 + 0 i)\\\\z^3=2 \times [\cos 0^{\circ} + i \sin 0^{\circ}]\\\\z^3=2 \times [\cos (2 k\pi+ 0^{\circ}) + i \sin(2 k\pi+0^{\circ})],where,k=0,1,2,\\\\z=[2\times[ (\cos (2 k\pi+ 0^{\circ}) + i \sin(2 k\pi+0^{\circ})]]^{\frac{1}{3}}\\\\z=2^{\frac{1}{3}}\times[\cos \frac{2 k\pi+ 0^{\circ}}{3} + i \sin\frac{(2 k\pi+0^{\circ})}{3}]\\\\Z_{0}=2^{\frac{1}{3}},for, k=0\\\\z_{1}=2^{\frac{1}{3}}\times[\cos \frac{(2\pi)}{3} + i \sin\frac{(2\pi)}{3}][/tex]

[tex]z_{1}=2^{\frac{1}{3}}\times[\cos(120^{\circ})+i\sin(120^{\circ})],\text{Used Demoiver's theorem}[\cos A + i\sin A]^k=\cos Ak + i\sin Ak[/tex]

Option A: →Cube root of 2 [cos (120 degrees) + i sin (120 degrees)]

The linear equation that models the growth of a tree that is 4 feet tall and grows 3 inches per year is y = 3x + 48.

The problem involves writing a linear equation in slope-intercept form to model the growth of a tree. The slope-intercept form is given by the equation y = mx + b, where 'm' represents the slope or the rate of change, and 'b' is the y-intercept or the initial value.

In the context of this problem, the tree's initial height is 4 feet and it grows at a rate of 3 inches per year. However, the units of the initial height and the yearly growth rate are different, so we need to convert 4 feet into inches. As 1 foot is equivalent to 12 inches, the initial height of the tree is 4 * 12 = 48 inches.

Therefore, the slope or rate of change 'm' is 3 inches per year and the y-intercept or initial value 'b' is 48 inches. Substituting these values into y = mx + b gives us the linear equation representing the growth of the tree: y = 3x + 48.

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Answer:

C.) side = z + 9

The approximate value of 'x' in the diagram is 31. 64

Using the formula, tan α = opposite side/ adjacent side

Opposite side = side opposite the angle

Adjacent = the other side

IF  α  = 36°

Opposite = 23

Adjacent = x

tan 36 = 0. 727

Substitute values into the formula

tan 36° = 23/ x

0.727 = 23/ x

Make 'x' subject by cross multiplying

x * 0. 727 = 23

x = 23/ 0. 727

x = 31. 64

Thus, the approximate value of 'x' in the diagram is 31. 64

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The value of b that satisfy the inequality are; B) b> -1 and C) b< 1

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

We have given an inequality;

1/5 (7-3b) > 2

To solve for b;

(7-3b) = 10

-3b = 10 - 7

-3b = 3

b = -3/3

b = -1

Thus, the value of b that satisfy the inequality are; B) b> -1 and C) b< 1

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The correct solution for the given inequality 1/5 (7-3b) > 2 gives us b < -1. Option A is correct.

The given inequality is 1/5 (7-3b) > 2. To find the range of values for b that satisfy this inequality, follow these steps:

Multiply both sides of the inequality by 5 to eliminate the fraction: 7 - 3b > 10.

Subtract 7 from both sides of the inequality: -3b > 3.

Since we are dividing by a negative number, remember to reverse the inequality sign: b < -1.

Therefore, the correct answer is b < -1, which is option A.