The right triangle ABC shown below is inscribed inside a parabola. Point B is also the maximum point of the parabola (vertex) and point C is the x intercept of the parabola. If the equation of the parabola is given by y = -x2 + 4x + C, find C so that the area of the triangle ABC is equal to 32 square units.

The value of n for the given circle with chords is; n = 14

To find the length of the given side with length "n", we must know the relationship between the different sections when the chords cross one another.

Now, the relationship we require is that when we multiply the 2 parts of both chords together, it will be equal to the product of the two sides in the other chord. Thus;

7(8) = 4(n)

56 = 4n

14 = n

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This answer explains how to calculate the probability of having exactly five girls in ten births using the binomial probability formula.

Probability of Exactly Five Girls in Ten Births:

Answer:

$0.40

Step-by-step explanation:

Did the test, K12

Answer:

3) [tex]x=1\\ y=5[/tex]

4) [tex]x=-2\\ y=6[/tex]

Step-by-step explanation:

3) For this system of equation you already has one variable in the second equation. Therefore, you only need to solve for [tex]y[/tex] in the second one and substitute its value into the first equation to calculate [tex]x[/tex]:

[tex]\left \{ {{7x + 3y= 22} \atop {4y=20}} \right. \\[/tex]

[tex]y=\frac{20}{4} \\ y=5[/tex]

[tex]7x + 3(5)= 22\\ 7x=7\\x=1[/tex]

4) You must add both equations to cancel the variable [tex]y[/tex] and solve for [tex]x[/tex]. Then, susbstiute the value of this variable into one of the original equations to calculate [tex]y[/tex]:

[tex]\left \{ {{-2x+y=10} \atop {4x-y=-14}} \right.[/tex]

[tex]2x=-4\\ x=-2[/tex]

[tex]-2(-2)+y=10\\ y=6[/tex]

An arithmetic sequence is a sequence with a constant

 increase or decrease also known as the constant difference

In the sequence 10, 40, 70, 100, ….

The constant difference between the terms is 30

A recursive formula for a sequence would be:

a1= first term in the sequence

an = term you are trying to find

an-1 = previous term in the sequence

d = constant difference

Explicit Formulas: 

A formula that allows you to find the nth term of the sequence by substituting known values in the expression.

Formula : an = a1 + d( n - 1)

a1= first term in the sequence

an = current term in the sequence

d = constant difference

n = term number

Solution: 

Write the explicit formula of the sequence 4, 7, 10, 13, 16 ….

Formula for explicit term:

an = ___ + ___( n - 1)

Simplify: an = ___ + ___n

In the sequence 4, 7, 10, 13, ….

To find the 11th term explicitly, I plug in the into the formula I just made: 

an = 1 + 3n

a11 = 1 + 3(11)   

a11 = 34 

Find the 15th term of the sequence using the formula: an = 1 + 3n

Write the recursive formula of the sequence 4, 7, 10, 13, ….

Recursive formula:

a1 =

an = a  n  - 1

In the sequence 4, 7, 10, 13, 16 ….

To find the 5th term recursively, I plug it into the formula I just made: 

  an = an-1 + 3

a5 = a5-1 + 3   in words: 5th  term equals the 4th term plus 3

a5 = 13 + 3 

a5 = 16  

Recursive and Explicit Formulas for Arithmetic (Linear) Sequences

Answer:

The graph of the function is the last graph.

Step-by-step explanation:

To know which graph represents the function [tex]g(x)=3.5^{x-1}[/tex] you should give values to x and compare it with the values on the graphs, as follows:

When x=-3

[tex]g(-3)=3.5^{-3-1}[/tex]

[tex]g(-3)=3.5^{-4}[/tex]

[tex]g(-3)=0.007[/tex]

So, the first point is (-3, 0.007)

When x=-2

[tex]g(-2)=3.5^{-2-1}[/tex]

[tex]g(-2)=3.5^{-3}[/tex]

[tex]g(-2)=0.02[/tex]

So, the second point is (-2, 0.02)

When x=-1

[tex]g(-1)=3.5^{-1-1}[/tex]

[tex]g(-1)=3.5^{-2}[/tex]

[tex]g(-1)=0.08[/tex]

So, the third point is (-1, 0.08)

When x=0

[tex]g(0)=3.5^{0-1}[/tex]

[tex]g(0)=3.5^{-1}[/tex]

[tex]g(0)=0.29[/tex]

So, the fourth point is (0, 0.29)

When x=1

[tex]g(1)=3.5^{1-1}[/tex]

[tex]g(1)=3.5^{0}[/tex]

[tex]g(1)=1[/tex]

So, the fifth point is (1, 1)

When x=2

[tex]g(2)=3.5^{2-1}[/tex]

[tex]g(2)=3.5^{1}[/tex]

[tex]g(2)=3.5[/tex]

So, the fourth point is (2, 3.5)

If you compares all the points, the graph of the function is the last graph.

Sampling is the choosing of a group of individuals from within a statistical population to estimate attributes of the entire population. Options C & D are right.

Sampling is the choosing of a group of individuals from within a statistical population to estimate attributes of the entire population in statistics, quality assurance, and survey methods.

The following options are right;

C. The manager selects 20 boards at random each day for 5 days and examines them.

Reason;

This method, which involves sampling 30 boards in a row an hour after manufacturing begins, does not yield a significant sample size.

Furthermore, if a component of the equipment fails later in the day, the statistics will be deceptive. Similarly, statistics will be deceptive if the gear is only defective until it "warms up."

D. The manager sends an email to 20 customers who buy lumber from the mill, asking each how many of the boards they bought the past week was defective. Results from the first 5 customers to respond are tallied.

Reason;

These  technique, a voluntary survey, is likely to elicit replies solely from those who have strong feelings about their product.

Hence Options C & D are right.

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Methods B and D are biased for determining defective boards, while methods A and C minimize bias. Random sampling across different times and responses reduces bias in data.

The goal is to determine which sampling methods are likely to be biased when finding the percentage of defective boards produced by a sawmill.

In summary, method B and method D are likely to introduce bias in sampling. Methods A and C are designed to minimize bias and provide a more accurate representation of defective boards.

Answer:

what they r trying to say is n is 3 so 3+11=14

Answer:

(g o f) (x) = 2x + 16

Step-by-step explanation:

" (g o f) (x) )" is called "the composition of f and g."

Evaluating this involves substituting the function f(x) = 2x + 1 for x in g(x) = x+14:

(g o f) (x) = 2(x+1) + 14, or

(g o f) (x) = 2x + 2 + 14, or

(g o f) (x) = 2x + 16

Answer:

2x+29

Step-by-step explanation:

a p e x

Answer:

[tex]AREA = x^{2} +20\cdot x + 96[/tex] square inches

Step-by-step explanation:

If dimension of signs are increased then new sides will be x+8 and x+12

It will change fom square into a rectangle So, its area will be given by :

AREA (y) = (x+8)(x+12)

[tex]AREA = x^{2} +20\cdot x + 96[/tex] square inches

Answer:

[tex]3[/tex] (Square root of [tex]2[/tex]) units

Step-by-step explanation:

we know that

The larger triangle is an isosceles right triangle

so

Applying the Pythagoras Theorem

[tex]6^{2} =x^{2} +x^{2} \\ 36=2x^{2} \\18=x^{2}\\x=\sqrt{18}\ units \\x=3\sqrt{2}\ units[/tex]

Final answer:

The circumference of the lid is approximately 132 millimeters, Thus, option D is correct.

Explanation:

To find the circumference [tex](\( C \))[/tex] of the lid, we use the formula for the circumference of a circle:

[tex]\[ C = \pi \times d \][/tex]

Where [tex]\( d \)[/tex] is the diameter of the circle.

Given that the diameter (\( d \)) of the lid is 42 millimeters and using the value of [tex]\( \pi \)[/tex] as [tex]\( \frac{22}{7} \)[/tex], we can calculate the circumference as follows:

[tex]\[ C = \frac{22}{7} \times 42 \][/tex]

[tex]\[ C = \frac{22 \times 42}{7} \][/tex]

[tex]\[ C = \frac{924}{7} \][/tex]

[tex]\[ C \approx 132 \, \text{mm} \][/tex]

Therefore, the circumference of the lid is approximately 132 millimeters, which corresponds to option D.

A ray in geometric optics represents the path of light as a straight line originating from a point, while a line segment is a part of a line with two endpoints and a measurable length. The properties mentioned can be used to determine if they define a ray or a line segment.

A ray in geometric optics is a straight line that originates at some point. In the context of light, a ray represents the path of light as it travels. When light encounters objects or changes media, it may change direction but it continues to travel in a straight line or as a ray. We can think of a ray of light as a straight line or a laser ray.

A line segment, on the other hand, is a part of a line with two endpoints. It has a definite length and can be measured. In the context of light, a line segment would indicate a finite path of light.

Given the properties mentioned, we can determine if they define a ray or a line segment. If the properties describe a straight line with no defined endpoints, it is a ray. If the properties suggest a line with two endpoints and a measurable length, it is a line segment.

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