a spinner has 20 equally sized sections, 16 of which are yellow and 4 of which are blue. the spinner spun and at the same time and fair coun is tossed what is the probability that the spinner lands on blue and the coin toss is tails

Systems of equation that have the same solution are called equivalent systems.

Given a system of two equations, we can produce an equivalent system by replacing one equation by the sum of the two equations, or by replacing an equation by a multiple of itself.

In contrast, we can be sure that two systems of equations are not equivalent if we know that a solution of the one is not a solution of the other.

Note: This idea of equivalent systems of equations pops up again in linear algebra. However, the examples and explanations in this article are geared to a high school algebra 1 class.

Example 1

We're given two systems of equations and asked if they're equivalent.

System A

−12x+9y=7

9x−12y=6

​

system B

−12x+9y=7

3x−4y=2

​

If we multiply the second equation in System B by 3, we get:

3x−4y=2

3(3x−4y)= 3(2)

9x−12y=6

​

Replacing the second equation of System B with this new equation, we get an equivalent system:

−12x+9y=7

9x−12y=6

​

Whoa! Look at that! This system is the same as System A, which means system A is equivalent to System B

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Answer:

2,220,000 mlg

Step-by-step explanation:

This question can be solved by a simple conversion calculation. Thankfully we're converting between two units of measurement with the same base!

So First, let's convert 222 decagrams to grams, and then convert grams to milligrams.

The conversion rates we need are:

1 decagram = 10 grams

1 gram = 1000 milligrams

Now for the math!

[tex]222 dg *\frac{10g}{1dg} =2220g\\then...2220g * \frac{1000mlg}/1g\\\\\\=2,220,000 mlg[/tex]

Answer: I would say 1 gallon

Step-by-step explanation: 1 gallon because 1 gallon would be closer then a shower or a cup

For the two triangles to be congruent by the side angle side (SAS) criterion, then the angle in between the two marked sides must be congruent.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are also equal. Therefore, their corresponding angles would also be congruent.

For the two triangles to be congruent by the side angle side (SAS) criterion, then the angle in between the two marked sides must be congruent.

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Answer:

as shown on the screen shot

Answer:

The range = 14

Step-by-step explanation:

Definition: (range of a data set)

the range of a data set is the difference between the greatest and smallest  value.

In a box plot :

We should notice the maximum (generally located at the top right) and the minimum value (generally located at the top left)

Then we make the difference.

97.

In our case :

Max value = 24

Min value = 10

Therefore

The range = 24 - 10 = 14

The perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.

We are given the vertices:

A(-4,4), B(2,-2), and C(-4,-2).

We need to find the perimeter of ABC.

AB = √ ( 2 + 4)² + (-2 - 4)²

AB = √ 6² + 6²

AB = √72

AB = 6 √2 units

BC = √ (-4 - 2)² + ( -2 + 2)²

BC = √ 6²

BC = 6 units

AC = √ ( -4 + 4)² + (-2 - 4)²

AC = √ 6²

AC = 6 units.

Perimeter = AB + BC + AC

Perimeter = 6 √2 + 6 + 6 units

Perimeter = 12 + 6 √2 units.

Perimeter = 12 + 6(1.414) units

Perimeter = 12 + 8.848 units

Perimeter = 20.848 units

Therefore, the perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.

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Using a system of equations, the numbers of each machine made are given as follows:

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

The factory needs to make 54 tables each day, hence:

x + y + z = 54.

The number of dining tables made per day should equal the number of coffee tables, hence:

x = y.

Then, on the first equation:

2y + z = 54.

The number of coffee tables should be three more than the number of end tables, hence:

y = z + 3.

Replacing in the equation 2y + z = 54:

2(z + 3) + z = 54

3z = 48

z = 16.

Then:

The numbers of each machine made are given as follows:

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Answer:

Step-by-step explanation:

height of the building

The G.C.F of the given algebraic expression is; ⁴⁹/₆a xy

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

We are given the algebraic expression;

(3 x y * 4x²y * ¹/₁ * 5x³y ^ z * 4)7a * 1/1 * 7*6

Expanding this further gives;

⁴⁹/₆a((3xy * 4x²y * 20x³y ^ z )

Now, the GCF of the terms inside the bracket would be x y. Thus, expanding the GCF  we have;

⁴⁹/₆a xy((3 * 4x * 20x²y^(z - 1))

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The length of the rectangle is 8 feet, width 1 is 7 feet and width 2 is 3.

A rectangle of area 80 square feet is broken and forms two square rectangles of area 56 square feet and 24 square feet, which has a common length.

Area of the rectangle = length × width

Now suppose the length is x feet, and let width 1 be a and width 2 be b.

Therefore we get that

            rectangle first is of area = x a

            rectangle second is of area = x b

Therefore original rectangle area = area of first rectangle + area of the second rectangle

80= x a + x b

80  = x( a + b)

As it is given that the length is common and is greater than both the width of the rectangle

56 = 8 × 7

24 = 8 × 3

So we will take x = 8 and a =7, b= 3

Now put these numbers in the equation to see if they fulfill the criteria

80 = 8( 7 + 3)

80 = 80

Therefore we get a length is 8, a width of 1 is 7, and a width of 2 is 3.

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Linear equation: a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0)

then ax + by + cz = r is called a linear equation in three variables. (The

“three variables” are the x, the y, and the z.)

The numbers a, b, and c are called the coefficient of the equation. The

number r is called the constant of the equation

y(a-b)=c(y+a)

ya-yb=cy+ca

ya-yb-cy=ca

y(a-b-c)=ca

[tex]y=\frac{ca}{a-b-c}[/tex]

case 1:

if either C and a are zero the y is zero,

case 2:

if

[tex]c\neq 0 \\a\neq 0\\y\neq 0[/tex]

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Answer:

Step-by-step explanation:

no solution

The target of achieving 88% votes from people is not achieved

Given that the golden party got 12598 votes, the pink party got 9112 votes, the brown party got 20059 votes and the purple party got 4466 votes. and 52,852 people can vote

The total number of people participated in voting=12598 + 9112 + 20059 + 4466

The total number of people who participated in voting=46,235

Percentage of people who participated in voting= [tex]\frac{46235}{52852}[/tex]×100

The percentage of  people who participated in voting=87.5%

The target is 88%, 88%>87.5% i.e. lesser than the actual voting percentage

Therefore, The target of achieving 88% votes from people is not achieved

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Answer: 18

Step-by-step explanation:

18

If Yasmin is the youngest of three siblings who ages are consecutive integers then Yasmin's age is 18, option B is correct.

Let's assume Yasmin's age is represented by the variable "Y".

Yasmin is the youngest, so her age is the smallest integer among the three siblings' ages.

Since their ages are consecutive integers, we can represent the ages of the three siblings as Y, Y+1, and Y+2.

According to the given information, the sum of their ages is 57.

So we can write the equation:

Y + (Y+1) + (Y+2) = 57

Now, let's solve for Y:

3Y + 3 = 57

Subtract 3 from both sides:

3Y = 54

Divide both sides by 3:

Y = 18

So, Yasmin's age (Y) is 18 years old. Option B is correct.

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She make 5 apple pie and 2 peach pie.

In the given statement is:

Bonnie made 7 pies. there were 6 slices in each apple pie and 7 slices in each peach pie. if Bonnie made 44 slices of pie in total.

To find the how many of each pie did she make

Now, According to the question :

Let start the solution

Total number of slices made by Bonnie is 44

Let Number of apple pies be x

and, number of peach pies is (7 - x) ............(1)

Pieces of an apple pie is 6x

Pieces of peach pie = 7 (7 - x)

Calculation

6x + 7(7 - x) = 44

6x + 49 -7x = 44

-x = 44 - 49

-x = -5

x = 5

Put the value of x in equation (1)

7 - x = 7 - 5 = 2

She make 5 apple pie and 2 peach pie.

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Answer:

2

Step-by-step explanation:

A continuous variable does allow fractional amounts. a discrete variable  does not allow fractional amounts.

Which variables require boundaries, also known as real limits, in their measurement scales?

A researcher must utilize genuine limits, which are boundaries that are exactly halfway between adjacent categories, to specify the units for a continuous variable.

What distinguishes a ratio scale from an ordinal scale?

For continuous data, what kind of data would you use?

Line graphs, skews, and other data analysis techniques are used to measure continuous data. One of the most popular kinds of continuous data analysis is regression analysis.

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Answer:

4.5%

Step-by-step explanation:

I = prt

234 = 2600 × r × 2

r = 234/5200

r = 0.045

r = 4.5%

Answer:

4.5%

Step-by-step explanation:

$234 is interest for 2 years

interest for 1 year will be 234/2 = 117

117/2600 = 0.045 which is 4.5%

Answer:

The correct pair matching each type of letter to its correct description would be as follows:

send it to favorably influence employers’ decision on hiring you - thank you letter

state how you meet the job requirements - cover letter

send 3-5 days after submitting your application or résumé - follow-up letter

express your desire to work for a particular company - letter of interest

A 'thank you' letter is a letter written to admit gratefulness for a favor that has been done.  It can also be written in anticipation of a favor to be done. Hence, writing it to a potential employer after an interview is a way of trying to influence the employer's decision on hiring you.

A cover letter, as it relates to job application, is a letter written to express how one meets the requirement for a job. In it, a job seeker would state their qualifications, skills, and experience as it relates to the job they are applying for.

A follow-up letter is usually written to follow up with a situation that one expects that a response should have been given or written just to further emphasize one's interest in something. Writing a follow-up letter after submitting an application for  a job is a way of reminding potential employers of one's desire to take up a job in their firm.

A letter of interest is written to show a desire to work in a particular organization or company irrespective of whether they have got a vacancy.

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the polynomial function f(x)=(x+1)(x+3)9x-4) is rewritten in standard form, the degree would be  3  and the constant term would be 12 .

What is  polynomial function?

f(x)=(x+1)(x+3)9x-4)

f(x ) = 3x³ + 36x² + 27x - 4x² - 16x - 12

f(x) =  3x³ + 32 x² + 11x - 12

in above function highest degree would be 3 and constant -12 .

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.

Answer:

angle 11 is an obtuse angle

Step-by-step explanation:

93           <        90

⬆️                     ⬆️

obtuse               right

Answer:

5

Step-by-step explanation:

This uses the Pythagorean theorem ([tex]f^2 + g^{2} =h^2[/tex]).  So you would take your values 3 and 4 and plug them into the equation.  [tex]3^2+4^2=h^2[/tex].  This becomes [tex]9+16=h^2[/tex].  Simplify and this becomes [tex]25=h^2[/tex].  If you take the square root of both sides you will end with 5 = h.  Therefore your answer is 5.

Answer:

H=5

Step-by-step explanation:

Since it's a right triangle, you can use the Pythagorean Theorem which is [tex]a^2 + b^2 = c^2[/tex] or in this case: [tex]f^2 + g^2 = h^2[/tex]

Substitute 3 in for f and 4 in for g: [tex]3^2 + 4^2 = h^2[/tex]

Add 9 and 16 together, it's 25 and then find the square root of 25 and the square root of h and the answer is 5

[tex]f^2 + g^2=h^2\\3^2 + 4^2 = h^2\\9 + 16 = h^2\\25 = h^2\\\sqrt25 = \sqrt h^2\\5 = h[/tex]

GOOD LUCK! :)

The coordinate of point c is such that point c is 7/8 of m to j is [ 7/8(x₂ - x₁),  7/8(y₂ - y₁) ].

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.

For example (5,3) here 5 will be for the x and 3 will be for the y.

Another example is (9,0) here 9 is for x and 0 is for y.

Let's say the coordinate of m → (x₁,y₁)

j → (x₂ ,y₂)

Now since point c is proportion with 7/8

So,

It will be 7/8 times of difference between of x and y coordinate of points m and j

So,

x = 7/8(x₂ - x₁) and y = 7/8(y₂ - y₁)

Hence "The coordinate of point c is such that point c is 7/8 of m to j is [ 7/8(x₂ - x₁),  7/8(y₂ - y₁) ]".

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Answer:

Step-by-step explanation:

[tex]\frac{4}{6} + \frac{2}{4} + \frac{3}{5} = \frac{80}{120} + \frac{60}{120} + \frac{72}{120} = \frac{212}{120}[/tex]

simplest form : [tex]\frac{53}{30}[/tex]

Answer:

Step-by-step explanation:

Any 1 of the following transformations will work. There are others that are also possible.

translation up 4 units, followed by rotation CCW by 90°.

rotation CCW by 90°, followed by translation left 4 units.

rotation CCW 90° about the center (-2, -2).

Step-by-step explanation:

The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.

The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is a sequence of transformations involved, so a single rotation is probably not of interest.

If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.

If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.

Of course, rotation 90° CCW in either case is the same as rotation 270° CW.

_____

Answer:

Step-by-step explanation:

The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is a sequence of transformations involved, so a single rotation is probably not of interest.

If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.

Disclaimer:

The equations were not given in the question.

So, take random examples for the functions f(x) and g(x) to simplify.

f(g(x)) denotes the composition function.

Important note:

After computing the composition function we must define the domain of the new function.

Example 1:

f(x) = x² and g(x) = x + 4, here the domain of f and g is the set of all real numbers.

⇒ f(g(x)) = f(x + 4) = (x + 4)²

⇒ f(g(x)) = x² + 8x + 16

This new function is also defined for all the real numbers.

Example 2:

f(x) = 5/x and g(x) = x² - 4, here the domain of g is the set of all real numbers and the domain of f is the set of all real numbers except x=0.

⇒ f(g(x)) = f(x² - 4)

⇒ f(g(x)) = 5/(x² - 4) = 5/((x - 2)(x + 2))

The domain for the new function is the set of all real numbers except x=2 and x=-2.

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Solving a system of equations we can see that we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

Let's define the variables:

We know that we want to make 200ml, then:

x  + y = 200

And the concentration of these 200ml must be of 68%, then the concentrations in the left side and in the rigth side must give the same value, so we can write:

x*0.5 + y*0.8 = 200*0.68

(the concentrations are written in decimal form)

Then we have the system of equations:

x  + y = 200

x*0.5 + y*0.8 = 200*0.68

To solve it we start by isolating x in the first equation:

x = 200 - y

Replacing that in the other equation we get:

(200 - y)*0.5 + y*0.8 = 200*0.68

Now we can solve this for y, we will get:

100 - y*0.5 + y*0.8 = 136

y*0.3 = 136 - 100 = 36

y = 36/0.3 = 120

So we need to use 120 ml of the 80% solution, and the other 80ml are of the 50% solution.

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