A conjecture and a portion of the flowchart proof used to prove the conjecture are shown.



Which equation best represents the information that should be in the box labeled 1?

3x = 9

3x = 26

3x = 27

3x = 30

The permutations formula is applied to determine the number of different 5-digit combinations where successive digits must be different, resulting in a total of 30,240 combinations.

Permutations are used when the order of elements matters. In this case, the number of different 5-digit combinations where successive digits must be different can be calculated using the permutations formula.

From linear pair postulate, if two angles are in linear pair, then they are supplementary.

Also, the definition of supplementary angles states that the sum of the angles is 180 degrees.

Hence, the correct option is Definition of supplementary angles.

option C: (6, 2).

The student has asked for the possible dimensions of a rectangle given that its perimeter is 16 inches. To find the dimensions that are correct, we need to remember that the perimeter of a rectangle is calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. We must check each pair of dimensions provided and see if they satisfy this equation when the perimeter is 16 inches.

Therefore, the only possible dimensions for the rectangle given the choices provided and where both dimensions are greater than zero is option C: (6, 2).

It would take 20 sessions to break even on what she spends for the snow blower.

The cost of the snow blower is $689, hence:

Cost = $689

Let x represent the number of sessions, Since $35 is paid to clear the driveway, hence:

Revenue = 35x

At breakeven:

Cost = Revenue

35x = 689

x = 20 (to nearest whole number)

Hence it would take 20 sessions to break even on what she spends for the snow blower.

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Answer: There are 220 employees working now.

Step-by-step explanation:

Hi, to answer this question, first, we have to multiply the number of employees by the percentage in decimal form.

So, mathematically speaking:

Finally, we subtract the number obtained to the initial number of employees.

There are 220 employees working now.

Feel free to ask for more if needed or if you did not understand something.

yes:

100/50 = 2

250/5 = 5

Answer:

Local maximum: (0,1)  

Local minimum: [tex](-\pi,-1)\text{ and }(\dfrac{3\pi}{2},-1)[/tex]

Step-by-step explanation:

To estimate the local maximum and local minimum using graph.

Local maximum: It is largest value of function for all other values of function near by.

Local minimum: It is smallest value of function for all other values of function near by.

A function has two extrema maxima or minima.

Please see the attachment for graph.

In graph highest point only 1, Only one local maximum at x=0

Local maximum: (0,1)

In graph two lowest point at [tex]x=-\pi\text{ and }x=\dfrac{3\pi}{2}[/tex]

Local minimum: [tex](-\pi,-1)\text{ and }(\dfrac{3\pi}{2},-1)[/tex]

Hence, Local maximum: (0,1) ; Local minimum: [tex](-\pi,-1)\text{ and }(\dfrac{3\pi}{2},-1)[/tex]

let number of hours = x

1st equation is 15.54+0.11x

2nd equation is 16.14-0.09x

now calulate x so the 2 equations are equal:

15.54+0.11x=16.04-0.09x

mutiply evrything by 100 to get rid of the decimal points andmake the calculations a little easier

1554+11x=1604-9x

add 9 x to both sides:
1554+20x=1604

subtract 1554 from both sides:
20x=50

divide 50 by 20 for x
x=50/20 = 2.5

x = 2.5

 so they were the same after 2.5 hours

The total amount of money spent by Danny is [tex]\fbox{\$12.86}[/tex].

Further explanation:

Given:

Danny spends $5.87 on a photo, $2.49 for balloon and $4.50 on strawberries.

Calculation:

Consider the total money spent as [tex]S[/tex], money spends on photo as [tex]x[/tex], money spends on balloons as [tex]y[/tex] and money spend on strawberries as [tex]z[/tex].

Total money spent [tex]S[/tex] is written as the sum of the money spent on photo [tex]x[/tex], balloons [tex]y[/tex] and strawberries [tex]z[/tex] as follows:

[tex]S=x+y+z[/tex]                                                                        …… (1)

Substitute, 5.87 for [tex]x[/tex], 2.49 for [tex]y[/tex] and 4.50 for [tex]z[/tex] in equation (1) to obtain the total money spent by Danny as follows:

[tex]\begin{aligned}S&=5.87+2.49+4.50\\&=8.36+4.50\\&=12.86\\\end{aligned}[/tex]

Thus, the total amount of money spent by Danny is [tex]\fbox{\$12.86}[/tex].

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1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}  

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2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12  

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3. what are the domain and range of the function f(x) = 3x + 5?  

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Answer Details :

Grade: Middle School

Subject: Mathematics

Chapter: linear equation

Keywords:

Money, Danny, anniversary, photo, balloon, strawberries, dollar, spent, x+y+z, function, substitution, direct substitution, elimination, graph, middle term factorization, scientific notation.

Final answer:

Susan's number is found by solving the equation x/4 - 11 = 11, which after isolating the variable and multiplying both sides by 4 yields the answer x = 88.

Explanation:

If Susan subtracts 11 from one-fourth of her number, she gets 11. To solve this problem, we set up an equation where x represents Susan's number. The one-fourth of her number would be x/4, and subtracting 11 from one-fourth of her number yields: x/4 - 11 = 11.

To find x, we first isolate the variable on one side by adding 11 to both sides of the equation, so we have x/4 = 22. Next, we multiply both sides by 4 to solve for x: x = 22 * 4. Therefore, Susan's number is 88.

Answer:

The correct option is 2.

Step-by-step explanation:

The formula form speed is

[tex]speed=\frac{distance}{time}[/tex]

[tex]time=\frac{distance}{speed}[/tex]

It is given that the school is 16 miles from his home. He averages 40 miles per hour on his way to school. Time taken by Aidan to reach school from the home is

[tex]t_1=\frac{16}{40}[/tex]

Let speed at which Aidan drive home be s. Time taken by Aidan to reach home from the school is

[tex]t_2=\frac{16}{s}[/tex]

It is given that his total trip takes 1 hour.

[tex]\frac{16}{40}+\frac{16}{s}=1[/tex]

[tex]\frac{16s+640}{40s}=1[/tex]

[tex]16s+640=40s[/tex]

[tex]640=40s-16s[/tex]

[tex]640=14s[/tex]

Divide both sides by 14.

[tex]\frac{640}{24}=s[/tex]

[tex]s=26.666667[/tex]

[tex]s\approx 27[/tex]

Aidan return with speed about 27 mph Therefore the correct option is 2.

Answer:

B

Step-by-step explanation:

did it on edg

Answer:

Option: d is the correct answer.

               d. 98

Step-by-step explanation:

The scores of Myra's test are as follows:

               84, 99, 88, 82, 95, 85

Let 'x' be the minimum  score that is obtained by Myra in the last test so that the average is greater than 90 marks.

i.e.

[tex]\dfrac{84+99+88+82+95+85+x}{7}>90\\\\\\i.e.\\\\\\\dfrac{533+x}{7}>90\\\\\\i.e.\\\\\\533+x=90\times 7\\\\\\533+x>630\\\\\\x>630-533\\\\\\x>97[/tex]

Hence, the minimum score has to be 98.

(   Since, the scores are in whole number )

The acceptance rate of the students is 51.1%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a local university accepted 2,300 students out of 4,500 applicants for admission.

The acceptance rate will be calculated as,

Acceptance rate  = ( 2300 x 100 ) /4500

Acceptance rate  =   51.1 %

Therefore, the acceptance rate of the students is 51.1%.

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