of the 30 girls who tried out for the lacrosse team at euclid Middle School, 12 were selected. Of the 40 boys who tried out but, 16 were selected. Are the ratios of the numbers of students on the team to the number of students trying out the same for both boys and girls? How do you know?

Answer:

[tex]\( f(x) + g(x) = -4x - 10 \).[/tex]

To find the domain of [tex]\( f(x) + g(x) \)[/tex], we need to consider the values of [tex]\( x \)[/tex] for which the function is defined. Since [tex]\( f(x) \)[/tex]  and [tex]\( g(x) \)[/tex] are both linear functions, their domain is all real numbers.

So, the domain of [tex]\( f(x) + g(x) \)[/tex] is [tex]\( \mathbb{R} \)[/tex] , which means that [tex]\( x \)[/tex] can be any real number.

Explanation:

To find [tex]\( f(x) + g(x) \)[/tex] , we simply add the functions [tex]\( f(x) \) and \( g(x) \)[/tex] together:

[tex]\[ f(x) + g(x) = (2x - 7) + (-6x - 3) \][/tex]

Now, let's simplify:

[tex]\[ f(x) + g(x) = 2x - 7 - 6x - 3 \][/tex]

[tex]\[ f(x) + g(x) = (2x - 6x) + (-7 - 3) \][/tex]

[tex]\[ f(x) + g(x) = -4x - 10 \][/tex]

The solutions to the given quadratic equation are x=1 and x=1.

The given quadratic equation is x²-2x+1=0.

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

Here, a=1, b=-2 and c=1

Now, x = [2 ± √(4 - 4)]/2

x=2±0/2

x=1

With factoring, we get

x²-2x+1=0

x²-x-x+1=0

x(x-1)-1(x-1)=0

(x-1)(x-1)=0

(x-1)=0

x=1

Therefore, the solutions to the given quadratic equation are x=1 and x=1.

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IQ scores follow a bell curve distribution where 100 is the mean. About 50% of people score above 100. Therefore, in a group of 78 students, we would expect about 39 students to have IQ scores above 100.

The question is asking to determine what percent of 78 students in a population have IQ scores above a 100. Given that the IQ scores in large populations are centered at 100 and follow a bell curve, most people fall within the range of 85 to 115. The percentage of people who score above 100 is the same as those who score below it - about 50%.

According to the nature of a bell curve, approximately 34% of people score between 100 and 115, and about 14% score above 115. Therefore, around 50% (34% + 14%) of the people score above 100.

Applying this percentage to the population of the 78 students, we would expect about 50% of this student population to have scores above 100. So, 50% of 78 students amounts to 39 students. Rounded off to one decimal place, the answer would be 39.0 students. However, students can't be divided, so we conclude that about 39 students from the group of 78 have IQ scores above 100.

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divide the two

40.8 / 8 = 5.1 gallons per container

Lev and Jim have a total of 100 in tens, and with Dawn's 9 ones added, they make the number 109.

Lev has 9 tens which is equal to 90 (because 9 times 10 equals 90). Jim has 1 ten which is equal to 10. When they put all their tens together, we add 90 and 10 to get 100. Dawn then adds 9 ones to the tens. To find the final number, we add Dawn's 9 ones to the previously combined tens, which is adding 9 to 100, resulting in 109. Therefore, by pooling together their tens and ones, they made the number 109.

Answer: The manager sold the couch at $163.85.

Step-by-step explanation:

Since we have given that

Wholesale price of the couch = $113.00

If Jessica's Furniture Store marks up all furniture by 45%.

So, Increment in whole sale price is given by

[tex]\frac{45}{100}\times 113\\\\=\frac{5085}{100}\\\\=\$50.85[/tex]

So, the manager sold the couch at the price is given by

[tex]\$113.00+\$50.85\\\\=\$163.85[/tex]

Hence, the manager sold the couch at $163.85.

A sequence can be both arithmetic and geometric, and this is illustrated where terms follow both an arithmetic and geometric progression.

Yes, a sequence can be both arithmetic and geometric. An example of such a sequence is when the terms of the sequence follow both an arithmetic progression, where the difference between consecutive terms is constant, and a geometric progression, where each term after the first is found by multiplying the previous term by a fixed, non-zero number.

Final answer:

The expression –32 + (2 – 6)(10) evaluates to –72, by first calculating the operation within the parentheses, multiplying it by 10, and then adding it to –32.

Explanation:

To evaluate the expression –32 + (2 – 6)(10), we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Firstly, we calculate the value inside the parentheses (2 – 6), which equals –4. Then we multiply this value by 10 to get –40. Finally, we add the result to –32 which gives us –32 + (–40) = –32 – 40 = –72.

Final answer:

The expression –32 + (2 – 6)(10) evaluates to –372 after performing the operations inside the parentheses and then multiplying and adding as per the order of operations.

Explanation:

To evaluate the expression –32 + (2 – 6)(10), we start by performing the operation inside the parentheses first. We subtract 6 from 2, getting –34. Then we multiply this result by 10 to get –340.

Next, we add this result to –32: –32 + (–340) = –372. So the final answer to the expression is –372.

Answer:

[tex]\frac{60}{100}[/tex]

Step-by-step explanation:

Here, the given expression,

18 cm per sec

That is, measure in 1 sec = 18 cm

∵ 1 minute = 60 seconds,

⇒ 1 second = [tex]\frac{1}{60}[/tex] minutes,

Also, 1 meters ( m ) = 100 centimeters ( cm ),

⇒ 1 cm = [tex]\frac{1}{100}[/tex] m,

So, the measure in [tex]\frac{1}{60}[/tex] minutes = 18× [tex]\frac{1}{100}[/tex] cm,

Thus, the measure in 1 minute = [tex]18\times \frac{60}{100}[/tex] cm

Hence, the conversion factors are used to multiply to 18 cm/s to get meters per minute is [tex]\frac{60}{100}[/tex]

Answer:

3.    

Step-by-step explanation:

The compound inequality will be:  [tex]9\leq x\leq 16[/tex], where [tex]x[/tex] is the mass of a single pencil and each pencil can have a mass of 10.5 grams.

Explanation

Suppose, the mass of a single pencil in the pack is  [tex]x[/tex] gram.

So, the total mass of 5 pencils will be:  [tex]5x[/tex] grams.

Each package has a mass of 15 grams. So, the total weight of the pack of 5 pencils [tex]=(5x+15)[/tex] grams.

To be within the weight specifications, a pack of 5 pencils should weigh between 60 grams and 95 grams. So, the compound inequality will be..........

[tex]60\leq 5x+15\leq 95\\ \\ 60-15\leq 5x+15-15\leq 95-15\\ \\ 45\leq 5x\leq 80\\ \\ \frac{45}{5}\leq \frac{5x}{5}\leq \frac{80}{5}\\ \\ 9\leq x\leq 16[/tex]

So, the compound inequality to represent the mass of a single pencil in a pack will be:  [tex]9\leq x\leq 16[/tex], where [tex]x[/tex] is the mass of a single pencil.

Final answer:

To determine the first time Carly and Matt will have a soccer game on the same day, we find the least common multiple (LCM) of 4 and 5, which is 20. Thus, they will both have a game on the 20th day.

Explanation:

The question is asking when Carly, who has a soccer game every 4th day, and Matt, who has a soccer game every 5th day, will both have a game on the same day. This is a problem that can be solved using the concept of the least common multiple (LCM). The LCM of two numbers is the smallest number that is a multiple of both numbers. To find when Carly and Matt will have a soccer game on the same day, we need to find the LCM of 4 and 5.

List the multiples of 4 (4, 8, 12, 16, 20, ...) and 5 (5, 10, 15, 20, ...).

Identify the smallest multiple that is common to both lists, which would be 20.

Therefore, the first day Carly and Matt will have a game on the same day is the 20th day.

Answer:

1st 6 is 1/10 of 2nd 6 and 2nd 6 is 10 times the 2nd 6.

Step-by-step explanation:

We are asked to find the relationship between the 6s in 660,472.

Upon looking at our given number, we can see that 1st see is in 10 thousands place and 2nd 6 is in hundred thousands place.

Place value of 1st 6: 60,000

Place value of 2nd 6: 600,000

Let us compare our both numbers as:

We can see that 600,000 is 10 times greater than 60,000, therefore, 1st 6 is 1/10 of 2nd 6 and 2nd 6 is 10 times the 2nd 6.

The solution of the given inequality is z ≥ 3.1

The Graph of the solution of the inequality z - 4.7 ≥ -1.6 is attached below.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Given that the inequality;

z - 4.7  ≥  -1.6

Solving;

z ≥ 1.6 + 4.7

z ≥ 3.1

Therefore, The solution of the given inequality is z ≥ 3.1

The Graph of the solution of the inequality z - 4.7 ≥ -1.6 is attached below.

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