Consider the function y = 9 - x2, where x ≥ 3. What is the inverse of the function? What is the domain of the inverse? Show all of your work for full credit.

Answer: There is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.

Step-by-step explanation:

Let E₁ be the event that members prefer swimming on weekends.

Let E₂ be the event that members prefer swimming on weekdays.

Let A be the event that the members are female.

Probability that members prefer swimming on weekends P(E₁) = 25%

Probability that members prefer swimming on weekdays P(E₂)= 75%

Probability that members prefer swimming on weekends and are female PA∩E₁)= 10%

Probability that members prefer swimming on weekdays and are female P(A∩E₂) = 55%

Using Conditional theorem, we will find the probability that a member is female given that the the person prefers swimming on weekends.

[tex]P(A\mid E_1)=\dfrac{P(A\cap E_1)}{P(E_1)}\\\\P(A\mid E_1)=\dfrac{10}{25}\\\\P(A\mid E_1)=0.4\\\\P(A\mid E_1)=0.4\times 100\%=40\%[/tex]

Hence, there is a probability that a club member picked randomly is female, given that the person prefers swimming on weekends is 40%.

1 cup of fruit juice is equivalent to 1 cup of fresh fruit.​

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1 cup of fresh juice.

Fresh juice and 1 cup of fresh fruit are the same.

So,

Fresh juice = 1 cup

Thus,

1 cup of fruit juice is equivalent to 1 cup of fresh fruit.​

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The minimum number of dots and/or dashes needed to represent any letter in the English alphabet in Morse code is one. The letters 'E' and 'T' each use one symbol, dot and dash respectively.

In International Morse code, each letter in the English alphabet is represented by a unique combination of dots and dashes. In regards to your question - the minimum number of dots and/or dashes needed to represent any letter in the English alphabet is one. The English letters 'E' and 'T' are represented by the single symbols "." (dot for 'E') and "-" (dash for 'T') respectively. Hence, this is the minimum for symbolizing any letter.

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Answer:

it is 80 and 75

Step-by-step explanation:

I go to RSM and when I answered this answer it said that it was correct

Answer:

Therefore, Tamar is thinking of the number 0.89.

Step-by-step explanation:

Let x be the number Tamar is thinking of.

0.8 < x < 0.9

Since the greatest digits in the hundreths is greater digit, and there's an "8" in the tenths, the number can described as:

0.88< x < 0.9

There is only a single number in the hundredths that would fit the expression above, and that is 0.89.

Therefore, Tamar is thinking of the number 0.89.

Answer:

Let the be the number Tamar is thinking of. So from the above question,

0.8 < t < 0.9

Note that the greatest digits in the hundreths is greater digit, and there's an "8" in the tenths, the number can described as:

0.88< x < 0.9

There is only a number in the hundredths that would fit and that is 0.89.

Therefore, t = 0.89.

Step-by-step explanation:

Answer:

198.44 feet

Step-by-step explanation:

The common difference of the arithmetic sequence is:

                                       4

We kn ow that if the first term of an arithmetic sequence is a and d is the common difference of the sequence then the nth term of the sequence is given by the formula:

[tex]a_n=a+(n-1)d[/tex]

Here we are given:

[tex]a=-3[/tex]

and

[tex]a_15=53\\\\i.e.\\\\a+(15-1)d=53\\\\i.e.\\\\a+14d=53[/tex]

Now using the value of a we have:

[tex]-3+14d=53\\\\i.e.\\\\14d=56\\\\i.e.\\\\d=4[/tex]

Answer: 1554

It is correct from the math answer keys

Tonya run 1,554 meters.

"Distance is the total path travelled by an object without considering the direction. "

Value used

1kilometer = 1000meters

According to the question,

Let x represents distance run by Tonya

Natasha ran = 3.1 kilometers

                    = 3100 meters

Therefore,

    x = (3100 / 2) + 4

⇒  x = 1554 meters  

Hence, Tonya run 1,554 meters.

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Answer:

First Part: 0.9769

Second Part: Some Americans may have traveled by other means

Step-by-step explanation:

First Part: You add 9.6 to 88.09 and put it in decimal form.

Second Part: Some Americans may have traveled by other means.

The speed of the train is 40 km/h, and the speed of the plane is 180 km/h.

To solve the word problem regarding the speeds of a train and a plane, we first let the speed of the train be x km/h. According to the problem, the plane's speed is 20 km/h less than 5 times the speed of the train, which can be expressed as 5x - 20 km/h. Since they both travel the same amount of time, we can set up an equation based on their speeds and distances traveled:

Time taken by the train = Distance / Speed of the train = 160 / x

Time taken by the plane = Distance / Speed of the plane = 720 / (5x - 20)

Since the time is the same for both:

160 / x = 720 / (5x - 20)

Cross-multiply to solve for x:

160(5x - 20) = 720x

800x - 3200 = 720x

80x = 3200

x = 40

Answer: the answer is B

Step-by-step explanation:

Answer:

The answer would be B

Step-by-step explanation:

Plato users i am 100% percent right trust me.

Answer:

93,600.16

Step-by-step explanation:

Final answer:

The function in question involves simplifying the base 4^3 multiplied by the square root of 4. Through understanding exponent rules and square root operations, this simplifies to 128, demonstrating the importance of algebraic fundamentals.

Explanation:

Understanding the Simplified Base of 4^3 \sqrt{4}

The question asks which function has a simplified base of 4^3 \sqrt{4}. Simplifying this expression requires understanding of exponent rules and square roots. The cube of 4, or 4^3, equals 64. The square root of 4 is 2, hence \(\sqrt{4}\) simplifies to 2. Combining these, we see that 4^3 multiplied by \(\sqrt{4}\) equals 64 * 2 = 128.

To put this into perspective, we would express the original operation as 4 raised to the power of 3 and then multiplied by the square root of 4, which can also be depicted as 4^3 * 2 since \(\sqrt{4} = 2\). Thus, the simplified base is not a direct function but rather an arithmetic operation resulting in 128.

It's crucial to note that while operations like these involve basic principles of exponents and roots, each step must be carefully followed to ensure accuracy. The concept behind these operations is grounded in the mathematical principles of handling integers, powers, and roots, highlighting the importance of solid fundamentals in algebra.

Final answer:

The flabby expression is found in the sentence 'In the future, we should be more careful about scheduling calls,' which can be more concisely stated as 'In the future, we should schedule calls more carefully.'

Explanation:

The sentence that contains a flabby expression is: "In the future, we should be more careful about scheduling calls."

Flabby expressions are phrases or sentences that are wordy and can be expressed more concisely without losing their meaning. The sentence could be more directly stated as "In the future, we should schedule calls more carefully." By removing unnecessary words, the sentence becomes clearer and more to the point. Flabby expressions are usually considered poor writing style because they can make sentences needlessly long and obscure the main point.

We have been given that

[tex]I = $54, P = $900, t = 18 \text{ months

}[/tex]

We know the formula,

[tex]I=Prt[/tex]

On substituting the given values, we get

[tex]54=900\cdot r\cdot \frac{18}{12}\\\\r=\frac{54\cdot 12}{900\cdot 18}\\\\r=\frac{1}{25}\\\\r=0.04\\\\r=4\%[/tex]

The annual rate interest is 4%

Answer:

the answer is -1/4

Step-by-step explanation:

Final answer:

The actual root of the polynomial f(x) = 60x²– 57x – 18 among the given options is -6/5.

Explanation:

According to the Rational Root Theorem, possible roots of the polynomial equation f(x) = 60x² − 57x − 18 are the factors of the constant term (−18) divided by the factors of the leading coefficient (60). The roots could be ±1/60, ±1/30, ±1/20, ±1/15, ±1/12, ±1/10, ±1/6, ±1/5, ±1/4, ±1/3, ±1/2, ±1, ±2/5, ±3/5, ±6/5, ±9/5, ±18/5, ±2, ±3, ±6, ±9, ±18.

To determine which of the given options are actual roots of the polynomial, we substitute each value into the polynomial and check if it returns a value of zero:

Substituting x = 3 into f(x) gives 60(3)² − 57(3) − 18 = 540 − 171 − 18 = 351, which is not zero.

Substituting x = 6 into f(x) gives 60(6)² − 57(6) − 18 = 2160 − 342 − 18 = 1800, which is not zero.

Substituting x = −1/4 into f(x) gives 60(−1/4)² − 57(−1/4) − 18 = 15 − −14.25 − 18 = 11.25, which is not zero.

Substituting x = −6/5 into f(x) gives 60(−6/5)² − 57(−6/5) − 18 = 86.4 − −68.4 − 18 = 0, which is zero. Therefore, −6/5 is an actual root of the equation.

Thus, the actual root among the given options is −6/5.

The factors of x^2 + 3x – 4 are (x + 4) and (x - 1), found by determining the factors of -4 that add up to 3.

The factors of x2 + 3x – 4 can be found using the method of factoring quadratics. To factor this quadratic expression, we look for two numbers that multiply to give the constant term (-4) and add to give the coefficient of the middle term (3). Those numbers are 4 and -1, as 4 × -1 = -4 and 4 + (-1) = 3. Therefore, the expression can be factored into (x + 4)(x - 1).

Visualizing with algebra tiles or drawing on the concepts of geometric representation of polynomials, we can understand that this factoring corresponds to breaking down the area of a rectangle (represented by x2 + 3x – 4) into two smaller rectangles whose dimensions give the factors (x + 4) and (x - 1).

Hence, the number of party favors you can buy is $[tex]45[/tex].

What is inequality?

An inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Here given that,

Party favors are on sale for $[tex]2.40[/tex] each. You have $[tex]380[/tex] to spend on the decorations and gifts, and you have already spent $[tex]270[/tex] on decorating.

So,

[tex]380-270=[/tex] $[tex]110[/tex]

To find the number of party favors you can buy, we divide $[tex]110[/tex] by the favors that are on sale for $[tex]2.40[/tex] is

[tex]\frac{110}{2.40}[/tex] = $[tex]45[/tex]

Hence, the number of party favors we can buy is $[tex]45[/tex].

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