Julieta recorded the grade-level and instrument of everyone in the middle school School of Rock below. Seventh Grade Students Instrument # of Students Guitar 12 Bass 3 Drums 10 Keyboard 5 Eighth Grade Students Instrument # of Students Guitar 4 Bass 3 Drums 6 Keyboard 2 Based on these results, express the probability that a student chosen at random will play an instrument other than guitar as a fraction in simplest form.

The solution of the given system of equations is (-2, -2).

What is addition method?

Using the Addition Method to Solve Systems of Equations in Two Variables. The addition method, also known as the elimination method, is a third strategy for resolving linear equation systems. With this approach, we add two terms that share the same variable but have opposing coefficients, resulting in a sum of zero.

Consider, the given system of equations

-5x - 9y = 28             ..(1)

-4x + 5y = -2              ..(2)

Multiply equation (1) by 5 and multiply equation (2) by 9.

-25x - 45y = 140         ..(3)

-36x + 45y = -18          ..(4)

Adding equation (3) and (4), we get

     -25x - 45y = 140

+   -36x + 45y = -18

______________________

     -61x + 0  = 122

-61x = 122

   x = -2

Plug x = 2 in equation (1)

-5(-2) - 9y = 28

    10 - 9y = 28

           9y = -18

             y = -2

Hence, the solution of the given system of equations is (-2, -2).

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Question 17

Opposite angles of a parallelogram are congruent, so [tex]3y+2=62 \implies y=20[/tex].

Adjacent angles of a parallelogram are supplementary, so [tex]62+5x+3=180 \implies x=23[/tex].

Question 18

Diagonals of a parallelogram bisect each other.

[tex]3y+9=2y+16 \implies y=7\\\\10x-24=5x-4 \implies x=4[/tex]

Answer:

The slope is 1/2

Step-by-step explanation:

To find the slope of the line, put the equation in slope intercept form.

y= mx+b where m is the slope and b is the y intercept

4y -2x = -30

Add 2x to each side

4y -2x+2x = 2x-30

4y = 2x-30

Divide by 4

4y/4 = 2x/4 -30/4

y = 1/2x -15/2

The slope is 1/2

Answer:

0.5

Step-by-step explanation:

To find the slope of the line you have write this in slope intercept form.

That is,

Here,

m - Slope

c - y intercept

Now, to write this expression in slope intercept form, you have to make y the subject of this expression.

[tex] 4y - 2x = - 30[/tex]

Add 2x to both sides.

4y = 2x - 30

Now divide both sides by 4.

y = 2/4x - 30/4

Accordingly,

[tex]y = 0.5x - 7.5[/tex]

Slope of the line (m) = 0.5

Equation of the tangent to the curve at point (-1,1) is: y=2x+3

Given,

x=cos(t)+cos(2t)

y=sin(t)+sin(2t)

P(-1,1)

For the point(-1,1), the value of t satisfy the equations x=cos(t)+cos(2t) and y=sin(t)+sin(2t) is pi/2.

To find an equation of the tangent to the curve at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2, we need to first find the slope of the tangent line at this point. To do this, we need to take the derivative of the x and y functions with respect to t:

dx/dt = -sin(t) + 2sin(2t)

dy/dt = cos(t) - 2cos(2t)

Now we can use this information to find the slope of the tangent line at the given point (x,y) where x=cos(t)+cos(2t) and y=sin(t)+sin(2t) and t= pi/2:

slope = dy/dx = (cos(t) - 2cos(2t)) / (-sin(t) + 2sin(2t)) evaluated at t = pi/2

slope = (cos(pi/2) - 2cos(2pi/2))/(-sin(pi/2) + 2sin(2pi/2)) = 0 - (-2)/0 + 0 = 2

Now, we can use this slope to find the equation of tangent using:

(y-y1)= m(x-x1)

=> y-1=2(x+1)

=>y=2x+3

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Answer:

x = [-3, 1]

Step-by-step explanation:

I wrote it in interval notation but if x can be any whole number between those two it can literally be -3, -2, 1, 0 or 1. Unless there are further restrictions or some sort of equation, there is no one number answer. Pick your poison, write it like x = {-3, -2, 1, 0, 1} if you'd like or the way I wrote it.

The people that developed pneumonia will be 78 people.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

According to the CDC, 6% of people who contract measles also develop pneumonia. If there were 1,296 cases of the measles in the United States in 2019, the people that developed pneumonia will be:

= 6% × 1296

= 78 people.

The second question can't be solved as the information isn't given.

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The dog moves quickly through 250-meter passes

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

dog run =11 metres per second

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Answer:

follow me if this helped you

Step-by-step explanation:

The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Answer:

20

Step-by-step explanation:

Answer: cubic inches

Step-by-step explanation: volume is cubed since it is 3 dimensions and it is in inches which are the units given

Answer: 61 cm.

Step-by-step explanation: The perimeter of any shape is the total distance of the exterior. This means that the sum of all side lengths of a shape is the perimeter. For a rectangle, the sum of both lengths and widths is the perimeter.

You can use the formula 2L+2W=P to solve this problem. 308 is P or the perimeter and 93 is L or the length. We can substitute these values and we get 2(93)+2(w)=308. We then subtract 2(93) or 186 from both sides to get 2W= 122. We then divide by two to get W or the width is equal to 61 cm.

With the amount of silk she has, she can create 48 garments.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

She possesses 144 yards of silk cloth.

Each dress needs 3 yards of silk for the skirt and 1 yard for the bodice.

According to the data given, the calculation is as follows:

144/3

48

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Answer:

x= 18,0

Step-by-step explanation:

Refer to the images attached. Please let me know if you have any questions regarding how I did things or why.

Answer:

14

Step-by-step explanation:

35% of 40

= [tex]\frac{35}{100}[/tex] × 40

= 0.35 × 40

= 14

Answer:

[tex]l = \frac{P}{2} - w[/tex]

Step-by-step explanation:

[tex]P= 2(l+w)[/tex]

[tex]\frac{P}{2} = l +w[/tex]

[tex]l = \frac{P}{2} - w[/tex]

Answer:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\dfrac12} 0& 30\\\cline{1-2} \vphantom{\dfrac12} 1& 20\\\cline{1-2} \vphantom{\dfrac12} 2& 10\\\cline{1-2} \vphantom{\dfrac12} 3& 0\\\cline{1-2} \end{array}[/tex]

See attachment for the graph of the inequality.

Step-by-step explanation:

Given information:

The inequality to represent the given information is:

To complete the given table, input p from 0 through 3 into the inequality and solve for d.

[tex]\begin{aligned}p=0 \implies 10(0) + d & \leq 30\\d & \leq 30\end{aligned}[/tex]

[tex]\begin{aligned}p=1 \implies 10(1) + d & \leq 30\\10+d & \leq 30\\d & \leq 20\end{aligned}[/tex]

[tex]\begin{aligned}p=2 \implies 10(2) + d & \leq 30\\20+d & \leq 30\\d & \leq 10\end{aligned}[/tex]

[tex]\begin{aligned}p=3 \implies 10(3) + d & \leq 30\\30+d & \leq 30\\d & \leq 0\end{aligned}[/tex]

Completed table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \sf Pizza & \sf Drinks\\\cline{1-2} \vphantom{\dfrac12} 0& 30\\\cline{1-2} \vphantom{\dfrac12} 1& 20\\\cline{1-2} \vphantom{\dfrac12} 2& 10\\\cline{1-2} \vphantom{\dfrac12} 3& 0\\\cline{1-2} \end{array}[/tex]

To graph the inequality:

Answer:

Okay so, if he is getting a console for $17.50, then you first want to do is subtract that from the total amount that he has which is $49.

49 - 17.50 = $31.50

Now each game costs $5.25

You can either just keep adding 5.25 by itself until you get to 31.50, or you can just divide 31.50 by 5.25, but I am going to just multiply then by certain numbers until I get the result.

5.25 * 5 = 26.25 so we know he can buy more than 5.

5.25 * 6 = 31.50

He can buy 6 games!

Step-by-step explanation:

Hope it helps! =D

The area of the hexagon is approximate, Area = (150 √3) m².

What is a formula of a hexagon?

A Regular hexagon has six sides and angles that are congruent and is made up of six equilateral triangles. The formula to find out the area of a regular hexagon is as given:

Area = (3√3 s²)/ 2

where 's' represents the length of a side of the regular hexagon.

A hexagon is a six-sided polygon. The area of a hexagon can be calculated using the formula:

Area = (3 * √3 * (side length)^2) / 2

In this case, the hexagon is 10m by 5m, so the side length of the hexagon is 10m. Plugging this into the formula, we get:

Area = (3 * √3 * (10m)^2) / 2

Area = (3 * √3 * 100m^2) / 2

Hence, the area of the hexagon is approximate:

Area = (150 √3) m².

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a) In fractions the probability that a teenager selected at random is female and their favorite hobby is watching films is given as: 1/4, while

b) if  the teenager from the question above rejoins the group and another teenager is picked at random, the probability that the teenager picked at random is male and their favorite hobby is playing video games is 1/6.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

With regard to problem (a),

There is a total of 32 teenagers.

Of those, 8 are female with a favorite hobby of watching films.

Thus,

Related Probability = 8/32; divide both numerator and denominator by 8 to get;

= 1/4

With regard to problem (b), the probability that the teenager picked at random is male and their favorite hobby is playing video games is:

P = (14/32) x  (2/14)

P = 2/32; thus

P = 1/16.

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Full Question:

A group of teenagers are asked about their favourite hobbies. The results are shown in the following table: Sports Playing video games Watching films Total

Male 9 2 3 14

Female 7 3 8 18

Total 16 5 11 32

Q6a. In fractions, what is the probability that a teenager selected at random is female and their favorite hobby is watching films? You can simplify this fraction if you wish.

Q6b. the teenager from the question above rejoins the group and another teenager is picked at random what is the probability that the teenager picked at random is male and their favourite hobby is playing video games? you can simplify this fraction if you wish

Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

Thus, all angles are equivalent to 60 degrees.

So, for a triangle, we know that Interior angle + neighbouring outside angle = 180°, 60° + x = 180°, and x = 180° - 60° = 120°.

Thus, a triangle's x value is 120°.

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Answer:

Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.

Step-by-step explanation:

The equation of the square coop is 4x = 20 and the length is 5yd .

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

20yd of fencing to build the walls of a square coop.

Therefore, the perimeter of the square coop is 20 yd .

Then the equation of the perimeter of the square coop is 4x = 20.

Solving the equation,

4x = 20

We get,

x = 5yd

The equation of the square coop is 4x = 20 and the length is 5yd .

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Whenever you want to add clarification, explanation, or a side remark to a statement, you should use parentheses ().

3(0.4h+5)=4(0.2h+7)

When adding extraneous information or an aside to a sentence, parentheses, a pair of punctuation marks, are most frequently utilized.

Two curving vertical lines can be seen in parentheses: ( ). Parenthesis refers to a single instance of this punctuation.

To the left, we reposition every term:

3(0.4h+5)-(4(0.2h+7))=0

Parentheses are increased.

0h-(4(0.2h+7))+15=0

-(4(0.2h+7)), which we calculate as follows:

4(0.2h+7)

Parentheses are increased.

0h+28

In addition, we add up all the numbers and variables.

h+28

Resuming the equation

-(h+28)

In addition, we add up all the numbers and variables.

h-(h+28)+15=0

Parentheses are removed.

h-h-28+15=0

In addition, we add up all the numbers and variables.

-13!=0

For this equation, there is no answer.

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Answer:  -2 1/2

Step-by-step explanation

if the equation is + but a number is negative, remember that +- = - which means 5/12 + (-2 11/12) = 5/12 - 2 11/12

2 11/12 is bigger than 5/12, so we'll switch it around and it'll become

2 11/12 - 5/12

2 11/12 - 5/12 = 2 6/12

Because 2 11/12 is originally a negative number, +- = -

which means the answer will be negative, so it is  -2 6/12.

but we're not done yet, we need to simplify it by dividing it with 6

so the final answer is -2 1/2

if it didn't make any sense at all heres an equation version :

5/12 + (-2 11/12)

= 5/12 - 2 11/12

= 2 11/12 - 5/12

= 2 6/12 (2 11/12 is originally negative so the ans will be negative)

= - 2 6/12 (divide by 6 to simplify)

= - 2 1/2

Answer:

The answer is 6x²+x+7

Step-by-step explanation:

(3x²+3) + (3x²+x+4)

3x²+3 + 3x²+x+4

COLLECT LIKE TERMS

3x²+3x²+x+3+4

ADD UP LIKE TERMS

6x²+x+7

Answer:

533

Step-by-step explanation:

Ends in an odd number

Answer:

the first one: 0533

Step-by-step explanation:

1,3,5,7,9 are basic odd numbers

2,4,6,8 are basic prime numbers

see what the last digit is aka the ones place

see if it ends in an odd or even

the only one that has the last digit as an odd number is the first one 0533, therefore it is the answer.

Answer:

20%

Step-by-step explanation:

The probability that the first unbelted driver is in the 6th car stopped is
(1 - 0.20)^5 * 0.20,
where 0.20 is the probability that a driver does not wear their seatbelt (20%),
and (1 - 0.20)^5 is the probability that the first 5 cars stopped all have drivers who wear their seatbelts.

This simplifies to (0.8)^5 * 0.2 = 0.32768 * 0.2 = 0.065536.