Given the following function, find f(-2), f(0), and f(4).
f(x) = x² +1

f(-2)=
f(0)=
f(4)=

Answer:

x=7

Step-by-step explanation:

(160+3x)=(195-2x)

(a) The probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4.

(B) The chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

(a) If we assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4, since there is a 1 in 4 chance that the nucleotide chosen from the first region will be the same as the nucleotide chosen from the second region.

(b) If we again assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability of choosing a particular three-nucleotide sequence is (1/4)³ = 1/64.

The probability of choosing the same three-nucleotide sequence from both regions is the product of the probabilities of choosing that sequence from each region, or (1/64) x (1/64) = 1/4096. Therefore, the chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

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a) If the function f(x) = 0.42x + 50 represents the cost (in dollars) of a one-day truck rental when the truck is driven x miles, the truck rental cost when you drive 85 miles is $85.70.

b) When you drive the truck and pay $65.96, the total distance the truck is driven is 38 miles.

A mathematical function is an equation representing the relationship between the independent and dependent variables.

An equation is two or more mathematical expressions equated using the equal symbol (=).

f(x) = 0.42x + 50

a) The number of miles the truck is driven = 85 miles

= 0.42(85) + 50

= 85.7

= $85.70

b) The total cost for x miles = $65.96

f(x) = 0.42x + 50

65.96 = 0.42x + 50

0.42x = 15.96

x = 38 miles

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Answer:

Choice B.

Explanation:

The side length is the distance between the vertices of the triangle given.

By the sandwich's theorem,

the limit of the function f(x) at x→2 is 1.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

The functions;

g(x) = 1/{x²-4x + 5},

and h(x) = {2x²-8x +10}/{x²-4x+6}

If f is a function that satisfies g(x) ≤ f(x) ≤ h(x) for 0 < x < 5.

To find the limit at x→2.

\(\lim_{x \to \2} g(x) =\) 1/{2²-4(2) + 5} = 1

\(\lim_{x \to \2} h(x) =\) {2(2)²-8(2) +10}/{(2)²-4(2)+6} = 1

By the sandwich's theorem,

the limit of the function f(x) at x→2 is 1.

Therefore, 1 is the limit.

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The cumulative distribution function of x is 0.60.

Here X has discrete probability distribution.

\($$\begin{aligned}&\mathrm{P}(\mathrm{X}=1)=0.30 \\&P(X=3)=F(3)-F(1)=0.40-0.30=0.10 \\&P(X=4)=F(4)-F(3)=0.45-0.40=0.05 \\&P(X=6)=F(6)-F(4)=0.60-0.45=0.15 \\&P(X=12)=F(12)-F(6)=1-0.60=0.40\end{aligned}$$\)

Following table shows the pmf:

X P(X=x)

1 0.3

3 0.1

4 0.05

6 0.15

12 0.4

Following is the graph of CDF is [SEE in attachement]

\($P(3 \leq X \leq 6)=F(6)-F(1)=0.60-0.30=0.30$$P(X \geq 4)=1-F(3)=1-0.40=0.60$\)

The probability function that X will have a value less than or equal to x is known as the Cumulative Distribution Function (CDF) of a real-valued random variable X, evaluated at x. It is employed to describe a table's random variables' probability distribution.

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The statement which holds true for the given function as required to be determined is; f (-2) = 1.

It follows from the task content that the statement which holds true for the given function is to be determined.

Since the given function in the task content is; f(x) = x² - 3.

By checking for the value of the function instance; f (-2) we. have that;

f (-2) = (-2)² - 3

f (-2) = 4 - 3

f (-2) = 1.

Consequently, the statement which holds true as required is; f (-2) = 1.

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Answer:

3/4

Step-by-step explanation:

Let's say that r is the radius of the large circle or the diameter of the small circle.

Area of the big circle is \(\pi r^{2}\) .

Area of the small circle is \(\pi \frac{r}{2} ^{2} = \pi \frac{r^{2}}{4}\).

The ratio of these 2 circles is 1/4 (calculation in the comments).

So the shaded part represent 1 - 1/4 = 3/4.

The hotel owner needs approximately 2,248 square feet of fabric to make a pool covering for the winter for their regular hexagonal pool with a side-to-side length of 30 feet.

To calculate the area of the pool, we first need to find the apothem (the distance from the center of the hexagon to the midpoint of any side). For a regular hexagon, the apothem is equal to the side length times the square root of 3 divided by 2. So, the apothem of this hexagonal pool is:

apothem = 30 × √3/2 = 25.980762

The area of a regular hexagon is given by the formula:

area = 3 × √3/2 × apothem^2

Substituting the value of the apothem, we get:

area = 3 × √3/2 × 25.980762^2 = 2247.72

Rounding this to the nearest square foot, the hotel owner will need approximately 2,248 square feet of fabric to construct the cover for the pool.

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Answer:

1/2 + 2/3 + 5/4 = 29/12 = 2 5/12  ≅ 2.4166667

Step-by-step explanation:

Answer:

85

Step-by-step explanation:

Answer:

(2b-a)x(2b-3)x(2b+3)

Step-by-step explanation:

Answer:

41.90

Step-by-step explanation:

FORMULA 1/3×πr×r×h

Solution

Step1

The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.

Step2

Two pairs angles are equal, hence they are similar

Answer

Are similar by AA

1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799  participants were successful.

The successful  participants  can be calculate by solving a linear equation as follows

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.

Linear equations are those with one degree.

In this case, a linear equation must be resolved.

1945 for the men's total

Women are present in 2849.

Participants in total: 1945 + 2849 = 4794

Let x be the proportion of participants that were successful.

Men who failed were 5 times as numerous.

Participants in total: 5x + x = 6x

Due to the issue,

The linear formula is

6x = 4794

x = 4794/6

x = 799

799 of the participants had success.

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Answer:

280x + 37

Step-by-step explanation:

Answer:

Multiply 5 to both sides to get

(x+3)^2 = 100

Step-by-step explanation:

Please refer to the picture above.

Simplify the equation by aiming to eliminate the fraction in the right hand side of the equation by multiplying the denominator to both sides of the equation in step 2

Answer:

\((x + 3)^{2}\) = 100

Step-by-step explanation:

Answer:

Explanation:

Given the expression;

simplifying;

we have;

Therefore;

==========================================================

Explanation:

We simply multiply the two values given to us

600*(1/12) = 600/12 = 50

We expect about 50 bulbs to be defective.

Note how if we had 50 bad bulbs, then 50/600 = (1*50)/(12*50) = 1/12 of the batch of 600 bulbs is defective.

Answer:

The number, x = { -5 < x < 14}

This means x is any integer between -5 and 14

Step-by-step explanation:

From the statement, let the number be x

3 + x = y; y = { -2 < y < 17}

This means that y is any integer between -2 and 17

Therefore, x = y - 3

Subtract 3 from the limits of y

i.e. -2 - 3 = -5 and 17 - 3 = 14

Hence, x = { -5 < x < 14}

Answer:

the sides are congruent.

Answer:

4x^2+15

Step-by-step explanation:

1. multiply whole parenthesis by power of 2

2. gets you 4(x^2+4)-1

3.Multply and it gets you 4x^2+16-1 so it would be 4x^2+15 for your answer

4. throw that into your calculator and make sure its not on radian mode and then press graph

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.

Given that,

From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.

Whether the claim is true or false must be determined.

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.

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It will take 12 seconds until Hudson and Knox have run the same number of feet.

Let's denote the time it takes until Hudson and Knox have run the same number of feet as "t" (in seconds).

The distance Hudson runs can be calculated by multiplying his speed (8.8 feet/second) by the time "t". Thus, the distance Hudson covers is 8.8t feet.

Knox, on the other hand, had a head start of 30 feet. So the distance Knox covers can be calculated by multiplying his speed (6.3 feet/second) by the time "t" and adding the head start of 30 feet. Thus, the distance Knox covers is 6.3t + 30 feet.

To find the time when both runners have covered the same distance, we set their distances equal to each other:

8.8t = 6.3t + 30

Simplifying the equation:

2.5t = 30

Dividing both sides by 2.5:

t = 30 / 2.5

t = 12

Therefore, it will take 12 seconds until Hudson and Knox have run the same number of feet.

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Answer: The probability that the teacher randomly selects 3 female students is 0.0556.

Explanation :Given ,In an algebra class there are 18 male students and 12 female students. Each day, the teacher randomly selects 3 students from the class to present their work on a problem, If no one student can be selected twice To find :The probability that the teacher randomly selects 3 female students

Formula used: Probability of event =  \(\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}\)Number of total students = 18 + 12 = 30Number of ways to select 3 students from 30 students =  \(_{30}C_3 = \frac{30!}{3!(30-3)!} = \frac{30!}{3!27!} = \frac{30*29*28}{3*2*1} = 4060\)Number of ways to select 3 female students out of 12 female students = \(_{12}C_3 = \frac{12!}{3!(12-3)!} = \frac{12!}{3!9!} = \frac{12*11*10}{3*2*1} = 220\)Therefore, the probability that the teacher randomly selects 3 female students is \(\frac{220}{4060}\) = 0.0556.

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Answer: No

Step-by-step explanation:

2.7 + 3.5 is not greater than 9.8.

Answer:

no It cant

Step-by-step explanation:

2.7 + 3.5 is not greater than 9.8.

Answer:

1. 8 pounds= 128 ounces ---> 3 pounds = 48 ounces

2. There are 207 calories in 3 pounds of ice cream

Step-by-step explanation:

For the first question, for the ounces, I'm pretty sure that they will want you to just multiply 8x16 to get the number of ounces of the total equation

For the next step, you will need to divide 552 by 8 to find how many calories per pound, and you will get 69. Next you will want to multiply this by 3 to find the answer

Answer:

The answer is 48 ounces in 3lbs. and there is 3312 calories in three pounds.

Step-by-step explanation: You multiply 16 times 3 for the number of ounces in 3 lbs. Then u divide the answer by 8 which is 6 then you multiply that by 552 for the number of calories.

The area is 250.5 in^2