Find the equation, (f(x) = a(x-h)2+ k), for a parabola containing point (-1,0) and having (-3, 4) as a vertex. What is the standard form of the equation?

30 pounds is available to fill the suitcase with other items.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

An airline requires carry on luggage to weigh at most 40 pounds.

The Suitcase presently carry 10 pounds.

Let  p be the pound available to fill your suitcase with other items.

So, p= 40- 10

p = 30 pounds

Hence, 30 pounds is available to fill the suitcase with other items.

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a) The cell corresponding to a positive diagnosis when the person has antibodies present as well as the cell for a negative diagnosis when the person has no antibodies present are the cells representing a CORRECT diagnosis.

The cell corresponding to a negative diagnosis when you actually have antibodies present is called a FALSE NEGATIVE and is considered as a TYPE II error.

The cell corresponding to a positive diagnosis when you actually don't have antibodies present is called a FALSE POSITIVE and is considered as a TYPE I error.

For the tree diagram for the questions below, refer to the picture attached.

b) To know the probability that a person without HIV will be diagnosed positive (false positive), we just trace the tree diagram from population to "antibodies not present" to "positive". The tree diagram will give us a value of 0.00588.

ANSWER: The probability of a false positive is 0.00588 or 0.588%.

c) We do the same thing as the previous subproblem to determine the probability that a person with HIV will be diagnosed as negative. We trace the tree diagram from population to "antibodies present" to "negative". The tree diagram will give us a value of 0.003.

ANSWER: The probability of a false negative is 0.003 or 0.3%.

d) Same thing for this subproblem. We trace the tree diagram from population to "antibodies present" to "positive" to know that the value is 0.01997.

ANSWER: The probability that a person with HIV will be diagnosed as positive is 0.01997 or 1.997%.

Answer:

1-given

2-if lines are parallel, then corresponding angles are equal

3-Substitution

4-if alternate interior angles are equal then lines are parallel.

Step-by-step explanation:

Given j is parallel to k,[tex]m\angle3 =m\angle 1[/tex]

We have to prove that line l is parallel to m

We  have to match reason with its correct statement in given proof.

1.j is parallel to k,[tex] m\angle 3=m\angle 1[/tex]

Reason:given

2.[tex]m\angle 1=m\angle 2[/tex]

Reason:if the lines are parallel , then corresponding angles are equal.

3.[tex]m\angle 2=m\angle 3[/tex]

Reason: substitution

4.line l is parallel to m

Reason: If alternate interior angles are equal ,then lines are parallel.

Final answer:

To calculate the new mean after adding a score of 12 to the original 6 scores with a mean of 5, determine the total sum of the original scores, add 12, and divide by the new number of scores. The new mean for the 7 scores is 6.

Explanation:

To find the new mean when one person with a score of x = 12 is added to a sample of n = 6 scores with a current mean of m = 5, first calculate the total sum of the scores before the new score is added. This can be done by multiplying the mean by the number of scores. Then add the new score to this total and divide by the new number of scores.

So, the mean for the new set of scores is 6.

The relationship where y varies directly as x and inversely as the square root of w can be represented by the equation y = k * (x / sqrt(w)). Here, k is a constant of proportionality.

From the statement given, we can deduce an equation representing a direct proportionality to x and an inverse proportionality to the square root of w.

In mathematics, direct and inverse proportionality relationships are commonly depicted as y = kx and y = k/x respectively, where k is a constant. For direct proportionality, as x increases, y also increases. Contrastingly, for inverse proportionality, as x increases, y decreases.

Given the statement, we can represent the relationship as follows: y = k * (x / sqrt(w)).

Here, y varies directly as x and inversely as the square root of w. The constant k is the constant of proportionality which can be determined based on specific values of x, y and w.

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Answer:

The required equation is [tex]g(x)=\frac{3}{x-4}-5[/tex].

Step-by-step explanation:

The given function is

[tex]y=\frac{3}{x}[/tex]

It can be written as

[tex]f(x)=\frac{3}{x}[/tex]

The transformation of a function is defined as

[tex]g(x)=f(x+a)+b[/tex]

Where, a represents the horizontal shift and b represents the vertical shift.

If a>0, then the function f(x) shifts a units left and a<0, then the function f(x) shifts a units right.

If b>0, then the function f(x) shifts b units up and b<0, then the function f(x) shifts b units down.

Since the function translated 4 units to the right and 5 units down, therefore the value of a is -4 and bis -5.

[tex]g(x)=f(x-4)-5[/tex]

[tex]g(x)=\frac{3}{x-4}-5[/tex]                         [tex][\because f(x)=\frac{3}{x}][/tex]

Therefore the required equation is [tex]g(x)=\frac{3}{x-4}-5[/tex].

Answer:

c!

Step-by-step explanation:

i did the test loll <3

Answer:

Option A. AB || DC

Step-by-step explanation:

In the given picture measurement of angle 2 = measurement of angle A

or m∠2 = m∠A (opposite angles)

This only possible only when m∠A = m∠2 = m∠C (Corresponding angles)

If these angles are equal then two lines AB and DC are parallel and two transverse AB and DC are intersecting them.

Therefore option A. AB || DC is the answer.

24.99 + 39.99 = 64.98

69.53-64.98 = 4.55

4.55/69.53 = 0.0654 = 6.5% sales tax

Final answer:

The bear population will be approximately 1965 bears in 10 years.

Explanation:

To calculate the bear population in 10 years, we can use the formula for exponential growth:

P = P₀(1 + r)ⁿ

Where:

P is the final population

P₀ is the initial population

r is the growth rate as a decimal

n is the number of years

In this case, the initial population (P₀) is 1462, the growth rate (r) is 3% (0.03), and the number of years (n) is 10. Plugging these values into the formula, we get:

P = 1462(1 + 0.03)¹⁰ ≈ 1965.32

Therefore, there will be approximately 1965 bears in 10 years.

Answer:

[tex]6x^3+3x -6[/tex]

Step-by-step explanation:

(4x3 − 2x − 9) + (2x3 + 5x + 3)

[tex](4x^3 - 2x - 9) + (2x^3 + 5x + 3)[/tex]

To add two polynomials, we remove the parenthesis

[tex]4x^3 - 2x - 9+2x^3 + 5x + 3[/tex]

To add it , we combine like terms. we add the like terms

[tex]4x^3+2x^3- 2x+ 5x - 9+ 3[/tex]

[tex]6x^3+3x -6[/tex]

To write an equation for a line that is parallel to a given line and passes through a given point, use the point-slope form of the linear equation. The slope of the parallel line is equal to the slope of the given line. Plug in the values and simplify to get the equation.

To find an equation for a line that is parallel to the given line and passes through the given point, we need to use the fact that parallel lines have the same slope. The slope of the given line is 3/4, so the slope of the parallel line will also be 3/4. Using the point-slope form of a linear equation, we can write the equation:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope. Plugging in the values, we get:

y - (-18) = 3/4(x - (-8))

Simplifying the equation gives:

y + 18 = 3/4(x + 8)

Next, we can distribute the 3/4 to both terms in the parentheses:

y + 18 = 3/4x + 6

To isolate y, we subtract 18 from both sides:

y = 3/4x - 12

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The logarithmic equation is equivalent to the exponential equation is [tex]log_4[/tex] 256 = c

The correct option is (D).

Logarithms are useful for solving exponential equations and investigating the properties of exponential functions. They will also be incredibly useful in calculus, where they will be used to compute the slope of various functions and the area circumscribed by various curves.

Given:

[tex]4^c[/tex] = 256

Now, writing into Logarithmic Function we can write it as

[tex]log_4[/tex] 256 = c

If we further solve it we get

256 = [tex]4^c[/tex] (log become exponential we move from either side of Equal Sign.)

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Final answer:

To find when the pebble hits the ground, solve for time using the quadratic equation from the given height function, resulting in around 6 seconds.

Explanation:

To find how long the pebble takes to hit the ground, we need to find the time t when its height h becomes 0. This means we need to solve the equation for t when h = 0:

-16t² + 12t + 900 = 0

This is a quadratic equation, and we can solve it using various methods like factoring, the quadratic formula, or completing the square. Here, we'll use the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

where a = -16, b = 12, and c = 900:

t = (-12 ± √(12² - 4 × -16 × 900)) / (2 × -16)

t = (-12 ± √(614400)) / -32

t ≈ (-12 ± 247.88) / -32

There are two possible solutions:

t1 ≈ 25.50 seconds

t2 ≈ -5.50 seconds (we can discard this since time cannot be negative)

The pebble will hit the ground approximately 6 seconds after it is thrown.

The rectangle has a width of approximately 4.18ft and a length of approximately 7.55ft. These are obtained by setting up and solving a system of equations based on the given information.

Let's start by setting up equations based on the problem statement. Let's denote the width of the rectangle as

w and the length as l. From the problem, we know two things: one is that the length is 5 feet less than three times the width, which can be written as  l = 3w - 5. The second thing we know is that the area of the rectangle, which is obtained by multiplying the length by the width, is 28 square feet, written as l*w = 28 . By substituting the first equation into the second, we can solve for w: (3w - 5)*w = 28

. This simplifies to a quadratic equation 3w^2 - 5w - 28 = 0 which can be solved to give w=~4.18 ft and w=-2.02ft. Because the width cannot be negative, we discard the second solution. Substituting w=~4.18ft into l = 3w -5 gives

l=~7.55 ft . Therefore, the dimensions of the rectangle are approximately 4.18ft (width) and 7.55ft (length).

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