write the area A of a square as a function of its perimeter P. ...?

Answer:   4) 0.0062097

Step-by-step explanation:

Given : The length of a social media interaction is normally distributed with a mean of [tex]\mu=3[/tex] minutes and a standard deviation of [tex]\sigma=0[/tex] minutes.

Using the formula , [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponding to x=4 will be :-

[tex]z=\dfrac{4-3}{0.4}=2.5[/tex]

Using the standard normal distribution table for z-value , the  probability that an interaction lasts longer than 4 minutes will be :-

[tex]P(z>2.5)=1-P(z\leq2.5)=1-0.9937903=0.0062097[/tex]

Hence, the probability that an interaction lasts longer than 4 minutes = 0.0062097

f(-4) = 20 when evaluated in the given function f(n) = n^2 - n. This result was obtained through substitution in the function followed by simplification.

In this problem, you are given a function f(n) = n^2 - n. To find the value of f(-4), you simply need to substitute -4 in place of n in the function and compute.

So,

f(-4) = (-4)^2 - (-4)

= 16 - (-4)

= 16 + 4 = 20

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Answer: [tex]c=12x+3[/tex], where c is the total cost of x pizzas.

The cost of 5 pizzas = $63

Step-by-step explanation:

Given : Cost of each pizza = $9.00

Cost of each topping =  $1.50

⇒ Cost of 2 toppings =  2 x $1.50 = $3.00

Then, the cost of each pizza having 2 toppings =  $9.00+  $3.00=  $12.00

Let x be the number of pizzas .

Then , the cost of x pizzas = 12x

Since , Delivery charge =  $3.00

Then, the total cost of ordering x pizzas( in dollars) =  Cost of x pizzas+ Delivery charge = 12x+3

Function rule to show the total cost of the pizzas if the pizza ordered has 2 toppings : [tex]c=12x+3[/tex] , where c is the total cost.

Put x= 5

[tex]c=12(5)+3=60+3=63[/tex]

Hence, the cost of 5 pizzas = $63

Answer:

the answer should be 4, you left the - off of the 61

Step-by-step explanation:

Answer:

It is $787.50.

Answer:

The answer to this question is

As speed increases the height Increases

Step-by-step explanation:

Because increases mean going up so when the speed is going up the height of the speed also increases so that's why when the speed increases also the height increases

I hope this works

YW!

The correct explanation of the graph will be;

''As speed increases, height is decreases.''

Option D is true.

What is an mathematical expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph is shown in figure for the relation of height and speed.

Since, The graph is shows when the speed of any object increase, then its height will also be increase.

Thus,  

The correct explanation of the graph will be;

''As speed increases, height is decreases.''

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By setting up an equation and solving for the number of students in each club, we find there are 48 students in the science club.

To solve the problem, we can set up an equation based on the information given. Let the number of students in the robotics club be represented by x.

According to the problem, the science club has 12 more students than the robotics club, so the science club has x + 12 students. We also know that there are a total of 84 students in both clubs combined. Therefore, we can set up the following equation:

x + (x + 12) = 84

Combining like terms, we have:

2x + 12 = 84

Subtracting 12 from both sides gives us:

2x = 72

Dividing both sides by 2 gives us:

x = 36

So, there are 36 students in the robotics club. To find the number of students in the science club, we add 12 to the number of students in the robotics club:

36 + 12 = 48

Therefore, there are 48 students in the science club.

Answer:

[tex]144.9\leq x\leq 145.5[/tex]

Step-by-step explanation:

Let x represent actual weight of object.

We have been that the weight of an object on a particular scale is 145.2 lbs. The measured weight may vary from the actual weight by at most 0.3 lbs.

[tex]|\text{Actual}-\text{Ideal}|\leq \text{Tolerance}[/tex].

Upon substituting our given values, we will get:

[tex]|x-145.2|\leq 0.3[/tex]

Applying absolute value rule [tex]|u|\leq a=-a\leq u\leq a[/tex], we will get:

[tex]-0.3\leq x-145.2\leq 0.3[/tex]

Add 145.2 on each side:

[tex]-0.3+145.2\leq x-145.2+145.2\leq 0.3+145.2[/tex]

[tex]144.9\leq x\leq 145.5[/tex]

Therefore, our required range will be [tex]144.9\leq x\leq 145.5[/tex].

The weight of Stephen's dog such that Stephen has a dog that weighs 5 times as much as Ian's dog will be 60 pounds.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's assume the weight of Stephen's dog is "s" while Ion's dog is "i".

As per the given,

Stephen has a dog that weighs 5 times as much as Ian's dog.

s = 5i

Total weight, s + i = 72

Substitute, i = 72 - s into s = 5i

s = 5(72 - s)

s = 360 - 5s

s + 5s = 360

6s = 360

s = 60 pounds.

Hence "The weight of Stephen's dog such that Stephen has a dog that weighs 5 times as much as Ian's dog will be 60 pounds".

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Final answer:

Using the compound interest formula, the total amount after three years for $50 invested at 6% compounded monthly is approximately $59.70.

Explanation:

To calculate the future value of $50 invested at 6% compounded monthly after a period of three years, we use the formula for compound interest:

FV = P × (1 + (r/n))³⁼ ×⁴

where:

FV is the future value of the investment,

P is the principal amount ($50),

r is the annual nominal interest rate (6% or 0.06),

n is the number of times the interest is compounded per year (12, for monthly compounding),

t is the time the money is invested for, in years (3 years).

Using these values, we calculate as follows:

FV = $50 × (1 + (0.06/12))³·×´ = $50 × (1 + 0.005)·¹·´

Now we calculate this raised to the power of 36 (3 years times 12 months):

FV = $50 × (1.005)³···¶ = $50 × 1.194052

Thus, FV ≈ $59.70

The total amount after three years would be approximately $59.70, assuming the interest is compounded monthly at a rate of 6%.

Answer:

343

Step-by-step explanation:

7*7*7=343

The factor of the 343 will be 7, 7, and 7. Then the number 343 is a perfect cube of 7.

The integers that are the threefold multiplication with the same number are known as perfect cubes.

To put it another way, a perfect cube is the combination of complex times multiplying a whole integer by itself.

A perfect cube is a quantity that may be stated as the composition of three different numbers.

A. The factor of the 21 will be 3 and 7. It can not be a perfect cube.

B. The factor of the 49 will be 7 and 7. It can not be a perfect cube.

C. The factor of the 343 will be 7, 7, and 7. It is a perfect cube.

D. The factor of the 600 will be 2, 2, 2, 3, 5, and 5. It can not be a perfect cube.

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The statement "Five quarters are added to the bowl every week" is a correct option (A) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The function q(w)=3+5(w−1) represents the number of quarters in a bowl on week w.

q(w) = 3 + 5(w−1)

q(w) = 5w - 5 + 3

q(w) = 5w - 2

y = mx + c

m = 5

Here 5 means five quarters are added to the bowl every week.

Thus, the statement "Five quarters are added to the bowl every week" is a correct option (A) is correct.

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The function [tex]\( f(x) = \frac{5x}{x-x^2} \)[/tex] has a removable discontinuity at ( x = 0 ) after canceling the common factor [tex]\( x \).[/tex]

A removable discontinuity occurs at a point where a function is not defined due to a factor in the denominator that could be canceled out with a factor in the numerator.

Let's analyze each function to determine if any of them have a removable discontinuity.

[tex]a. \( g(x) = \frac{2x-1}{x} \)[/tex]

- The denominator ( x ) is zero at ( x = 0 ).

- The numerator ( 2x-1 ) is non-zero at ( x = 0 ).

- Since there is no common factor in the numerator and denominator that could cancel out, the discontinuity at ( x = 0 ) is not removable.

[tex]b. \( p(x) = \frac{x+2}{x^2-x-2} \)[/tex]

- The denominator [tex]\( x^2-x-2 \) factors as \( (x-2)(x+1) \).[/tex]

- The function becomes [tex]\( p(x) = \frac{x+2}{(x-2)(x+1)} \).[/tex]

- The denominator is zero at ( x = 2 ) and ( x = -1 ).

- The numerator ( x+2 ) is zero at ( x = -2 ).

- There is no common factor between the numerator and the denominator that could be canceled out. So, the discontinuities at [tex]\( x = 2 \) and \( x = -1 \)[/tex] are not removable.

[tex]c. \( f(x) = \frac{5x}{x-x^2} \)[/tex]

- The denominator [tex]\( x-x^2 \) factors as \( x(1-x) \).[/tex]

- The function becomes [tex]\( f(x) = \frac{5x}{x(1-x)} = \frac{5x}{x-x^2} \).[/tex]

- The denominator is zero at x = 0  and  x = 1 .

- The numerator ( 5x ) is zero at ( x = 0 ).

- There is a common factor of ( x ) in the numerator and denominator which could be canceled out, making the discontinuity at ( x = 0 ) removable.

- After canceling the common factor ( x ), the function becomes [tex]\( \frac{5}{1-x} \),[/tex] which is defined at ( x = 0 ).

[tex]d. \( h(x) = \frac{x^2 - x + 2}{x + 1} \)[/tex]

- The denominator ( x + 1 ) is zero at ( x = -1 ).

- The numerator [tex]\( x^2 - x + 2 \) is not zero at \( x = -1 \).[/tex]

- There is no common factor in the numerator and denominator that could be canceled out, so the discontinuity at ( x = -1 ) is not removable.

Conclusion

The function [tex]\( f(x) = \frac{5x}{x-x^2} \)[/tex] has a removable discontinuity at ( x = 0 ), because the discontinuity can be removed by canceling the common factor ( x ) in the numerator and the denominator.

So, the correct answer is:

[tex]c. \( f(x) = \frac{5x}{x-x^2} \)[/tex]

Answer:

The answer is 2.25 times as fast. I just did this one

Step-by-step explanation:

As per linear equation, the total cost of the computer is $645.00.

"A linear equation is an equation in which the highest power of the variable is always 1."

Given, the cost of computer is $600.00.

The sales tax rate is 7.5%.

Therefore, the total cost of the computer is

= $[tex][600.00 + \frac{(7.5)(600.00)}{100}][/tex]

= $[tex][600.00 + 45.00][/tex]

= $[tex]645.00[/tex]

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Researchers can use b) weighting to counter bias in their sampling, which adjusts sample representation to match a desired population. While convenience sampling offers easy data collection, it lacks generalizability, and weighting is necessary to enhance the validity of findings.

To counter bias in their sampling, researchers can employ a method known as b) weighting. This technique adjusts the representation of samples to match a desired population, countering potential biases that may arise from non-random sampling methods such as convenience sampling. It is important to distinguish between non-random sampling methods that are potentially biased and strategies that are used to ensure data accuracy and representativeness.

Convenience sampling, also referred to as availability sampling or haphazard sampling, is a nonprobability sampling strategy where researchers collect data from individuals or elements that are most easily accessible. This approach is useful in exploratory research or student projects where probability sampling is too costly or difficult but does not offer the rigor needed to make generalizations to larger populations. To overcome these limitations and enhance the validity of their findings, researchers may adjust their data using weighting to better reflect the population being studied.

Answer:

0.5 or half of it (1/2)

The solution set for the inequality - 3 (x - 4) > 6(x - 1) does not include 3 as an element which is inequality is false.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We have been given inequality as:

-3(x-4) > 6(x-1)

To determine the solution set for the inequality.

Substitute x = 3 in the given inequality for each value of x with 3 and simplify both sides.

⇒ -3(x-4) > 6(x-1)

⇒ -3(3-4) > 6(3-1)

⇒ -3(-1) > 6(2)

⇒ 3 > 12

Since inequality 3 > 12 is not true,

So, for x = 3, the given inequality is false. Therefore, 3 is not included in the solution set.

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