John worked 18 hours last week. He earned $216. What was his hourly rate?

Answer:

Slope [tex]\frac{-2}{5}[/tex]

Step-by-step explanation:

2x + 5y = 21  Subtract 2x from both sides of the equation

5y = -2x + 21  divide all the way through by 5

y = [tex]\frac{-2}{5}[/tex] x + [tex]\frac{21}{5}[/tex]  The slope is the coeffience of the variable (the number before the x)

The required amount of 25% saline solution is 8 liters.

In mathematics, the equation that used to find an Unknow quantity is known as Linear Equation. Here we use different types of variables to represent the unknown value like x, y, z or a, b, c.. etc.

Here we have

4 liters of a 40% saline  

we need to make it a 30% of saline solution by adding a mount of 25% saline solution

Let us assume that we added x L of 25% of saline solution  

After adding x L of 25% saline into 4 liters of 40% saline to get 30% saline solution then the resultant solution is “x+4” liters of 30% saline.

The mathematical representation for the above line will be

⇒ x litres 25% saline + 4 litres 40% saline = (x+4) litres 30% saline

⇒ x(25%) + 4(40%) = (x+4)(30%)

⇒ 25x/100 + 4(40/100) = (x+ 4)30/100  

⇒ 25x + 160 = (x +4)30  

⇒ 25x + 160 = 30x + 120

⇒ 30x - 25x = 160 - 120

⇒  5x = 40

⇒ x = 8

Therefore

The required amount of 25% saline solution is 8 liters

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Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.

[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]

[tex] \sf x = 4 :: 8 : 2[/tex]

Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:

[tex]\boxed{\: x = \frac{4 \times8}{2} = \frac{32}{2} = 16 }[/tex]Therefore, the resulting geometric proportion would be:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{16 : 4 :: 8 : 2}[/tex]

The inequality that represents the graph is y < 4

The graph is shown in the figure

The graph is the pictorial representation of the collection of data. It has 2 axis . The x axis and y axis

Consider the each block of the graph as 1 units

At y = 4 there is dotted line parallel to the x axis of the graph

The dotted line represents the inequality symbol less than, Therefore the value of y is less than 4

From the graph, the entire region of the graph that y less than 4 are shaded therefore for all the value of x the value of y is less than 4

The inequality will be

y < 4

Hence, the inequality that represents the graph is y < 4

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As per the unitary concept,

a) There are 5/8 cups of flour would you need for half the recipe

b) There are 6 1/4 cups of flour would you need for 5 dozen cookies.

Unitary method:

The method by which first we find the value of single unit and then the value of the required number of units is known as the Unitary Method.

Given,

Here we have given that,  A recipe that makes 3 dozen chocolate chip cookies calls for 2 and 2/5 cups of flour.

So, here we need to find the following:

a) Exactly how much flour would you need for half the recipe?

b) Exactly how much flour would you need to make 5 dozen cookies?

In order to find these value, we have to calculate the amount of flour need for 1 dozen.

In order to calculate that, one we need to divide the total amount by the cups of flour need.

Then we get,

=> 3/ (2 2/5)

=> 3/ (12/5)

=> 15/12

=> 1.25

So, for half dozen cookies, we need

=> 1.25/2

=> 0.625

Which is in the fraction form of,

=> 5/8

And for 5 dozen of cookie we need.

=> 5 x 1.25

=> 6.25

The fraction equivalent is

=> 6 1/4 cups.

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Solve for y by simplifying both sides of the inequality, then isolating the variable.

Inequality Form:

y<−10 or 1<y<6

Interval Notation:

(−∞,−10)∪(1,6)

Step-by-step explanation:

I assume this means that both purchase one item every day.

so, their number of purchases are the same (x).

80 - 4.5x >= 60 - 2.5x

20 - 4.5x >= -2.5x

20 >= 2x

10 >= x

our

x <= 10

after 10 purchased drinks their balances will be equal.

before that, Ashley's card balance will be greater than Aaron's.

after that, Aaron's card balance will be greater than Ashley's.

so, for up to 10 purchased drinks Ashley's card balance will be greater or equal to Aaron's.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

C(x) = 11.99 + 7

The slope of the function is 11.99.

The y-intercept of the function is 7.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

C(m) = 11.99m + 7

The equation is in the form of y = mx + c

So,

m = 11.99

c = 7

The slope of the function is 11.99.

The y-intercept of the function is 7.

Thus,

The slope of the function is 11.99.

The y-intercept of the function is 7.

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The mean number of students per Faculty is 326.

Mean simply means the average of a set of numbers.

In this case, the number of students in nine faculties of a university are given as 168, 285, 397, 331, 383, 359, 366, 280 and 369. The mean will be:

= Total values / 9

= (168 + 285 + 397 + 331 + 383 + 359 + 366 + 280 + 369) / 9

= 2938 / 9

= 326.44

The mean is 326.

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Answer:

see below

Step-by-step explanation:

To graph this equation, start at the origin (0,0) since there is not y-intercept.

Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.

Because the rise (up and down, numerator) is 1, we know that we will go up one unit.

The run (side to side, denominator) is 4, so we will go to the right 4 units.

This makes the first point (4, 1).

Continue doing this until you get an idea of the line and connect the points to get the graph

Answer:

Info down in Explaination

Step-by-step explanation:

To graph this equation, start at the origin (0,0) since there is not y-intercept.

Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.

Because the rise (up and down, numerator) is 1, we know that we will go up one unit.

The run (side to side, denominator) is 4, so we will go to the right 4 units.

This makes the first point (4, 1).

Continue doing this until you get an idea of the line and connect the points to get the graph

Answer:

0.5867  (or 58.7%)

Step-by-step explanation:

The probability that a randomly selected student has a score between 350 and 550 is  59%.

Standard score or z score in statistics is defined as the number of standard deviations by which that the value of a score is above or below the mean value.

Given that,

The scores of the students on a standardized test are normally distributed.

Mean, μ = 500

Standard deviation, σ = 110

z score = (x - μ) / σ

For x = 350,

z = (350 - 500) / 110 = -1.36

Probability = 1 - 0.9131 = 0.0869

For x = 550,

z = (550 - 500) / 110 = 0.45

Probability = 0.6736

Probability that a randomly selected student has a score between 350 and 550 is,

P = 0.6736 - 0.0869 = 0.5867 ≈ 59%

Hence the required probability is 0.5867 or 58.67%.

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Answer:  median = 61

Reason:

A normal distribution is perfectly symmetric. Such distributions have mean = median = mode.

The variable X has a binomial distribution, as:

There are three requirements for the binomial distribution to represent a variable, as follows:

In the context of the variable X, these requirements are respected as follows:

Hence yes, the variable X has a binomial distribution.

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Answer:

Step-by-step explanation:

Perpendicular lines have opposite-reciprocal slopes.

It means the product of the slopes is - 1.

Let's find the slopes of the two lines and their product.

Find the product of slopes:

This is not  - 1, therefore the lines are NOT perpendicular.

The yards of roadside that Ben is cleaning more than Adam is 26 yards. Sheridan is correct.

The first step is to determine the length of Oakley Street. Pythagoras theorem would be used to determine the length.  Oakley Street is the hypotenuse of the right triangle that is formed by the streets.

The Pythagoras theorem: a² + b² = c²

where:

39² + 52² = c²

1,521 +  2704 = c²

c² = 4,225

c = √4225

c = 65 yards

Total yards Ben picked = 39 + 52 = 91 yards

Yards picked by Adam = 65 yards

Difference in the yards of litters picked = 91 - 65 = 26 yards

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The cost of 1 slice of cheese pizza and 3 sodas cost will be;

⇒ $5.25

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.

And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.

Now,

Let the cost of 1 slices of cheese pizza = x

And, The cost of 1 slices of soda = y

Since, Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.

Hence, We get;

⇒ 3x + 2y = $8.75  ..(i)

And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.

So, We get;

⇒ 2x + 4y = $8.50  ..(ii)

Multiply by 2 with (ii);

⇒ 2 (3x + 2y) = 2 × $8.75

⇒ 6x + 4y = $17.5  

Subtract from (ii), we get;

⇒ 6x + 4y - 2x - 4y = $17.5 - $8.50

⇒ 4x = $9

⇒ x = $2.25

And, ⇒ 2x + 4y = $8.50

⇒ 2 × $2.25 + 4y = $8.50

⇒ $4.5 + 4y = $8.50

⇒ 4y = $8.50 - $4.5

⇒ 4y = $4

⇒ y = $1

Thus, The cost of 1 slice of cheese pizza and 3 sodas cost will be;

⇒ $2.25 + 3 × $1

⇒ $2.25 + $3

⇒ $5.25

Therefore, The cost of 1 slice of cheese pizza and 3 sodas cost will be;

⇒ $5.25

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Answer:

graph 1

symmetry about the x and y axes

graph 2

symmetry about the y axis

graph 3

symmetry about the y axis

Step-by-step explanation:

try to imagine that you folded the graph by the x axis or y axis. If the to side of the graph are overlapping, the graph is symmetry across the axis you folded.

Hope this helps.

Answer:  " x = 1 ".

    The answer for this 'system of equations' is:  " [1, 15] ".

_________

Step-by-step explanation:

To solve for x :

Given:
  y = 3x + 18

  y = 15 ;

_________
 We know that:

 3x + 18 = 15 ;  Now, subtract 18 from Each Side of the equation:

  3x + 18 − 18 = 15 − 18 ;

  to get:

  3x = 3 ; Now, divide Each Side of the equation by 3 ;

     to isolate x on one side of the equation;

      and to solve for x :
 

   3x / 3 = 3 / 3 ;

   to get:    x = 1

_________

The answer is: " x = 1 " ;

 The answer for this 'system of equations' is:
   " [1, 15] " <== { written as:  " [x, y] "} ;

                         in which: " y = 15 " ; is given in the problem.

_________
Hope this answer is helpful.
 Best wishes!
_________

Answer:126 children

Step-by-step explanation:

first you want to multiply 18 times 4 (72) then 18 times 3 (54) and then you add 72+54=126

your welcome :)

Answer:

It will take them 3.5 hours to paint the room.

Step-by-step explanation:

Step 1: Add the number of hours it takes them together

    A. 6 + 8

Step 2: Divide the total number of hours by two (since two people are working together)

    B. 12 / 2 = 7 hours

Step 3: Divide by two again since you now have twice the speed

    C. 7 / 2 = 3.5 hours

Answer:

0.3125

Step-by-step explanation:

10 / 2 is 5

5 / 2 is 2.5

2.5 / 2 is 1.25

1.25 / 2 is 0.625

0.625 / 2 is 0.3125

The graph of g(x) = -|x + 2| + 4 is obtained after these following transformations from the parent function f(x) = |x|.

The parent function in this problem is defined as follows:

f(x) = |x|.

The transformed function in this problem is defined as follows:

g(x) = -|x + 2| + 4

The transformations are listed and described as follows:

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Using dilation rules, the dilated triangle whose coordinates of the vertices are as follows: A'(-2 , 2), B'(-1,0), C'(1 , 2).

What is the rule for a dilation?

To dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:

(x, y) -> (ax, ay).

suppose the coordinates of the vertices of ABC are given as follows:

A(-6,6), B(-3,0), C(3,6).

After a dilation with a scale factor of 1/3, the coordinates of the vertices of A'B'C' will be given as follows:

A'(-2 , 2), B'(-1,0), C'(1 , 2).

These coordinates are derived multiplying the coordinates of A, B and C by 1/3.

For the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by 2 to generate the dilated triangle.

The direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.

What are the component of force?

If a force acting at some angle [tex]\theta[/tex] with respect to x axis then the force can be resolved into two perpendicular forces ([tex]Fcos\theta[/tex] and [tex]Fsin\theta[/tex]). These perpendicular forces are known as component of forces.

Consider the following diagram of the sialboat.

The component of force along the heading direction is 480N and the component of force perpendicular to the heading is 650N.

If F is the foce the direction of wind then then component of force in the East direction will be [tex]Fcos\theta[/tex] and the component of force in the heading direction is [tex]Fsin\theta[/tex]. Now, take the ratio of these two compnents to find the angle [tex]\theta[/tex] as follows:

[tex]tan\theta=\frac{Fcos\theta}{Fsin\theta}\\tan\theta=\frac{650N}{480N}\\\\\theta=tan^{-1}(1.354)\\=53.6^0[/tex]

Now, calculate the force exerted by the wind. Equate the force in heading direction to find the force.

[tex]Fsin\theta=480N\\F=\frac{480N}{sin\theta}\\=\frac{480N}{sin53.6^0}\\=596.4N[/tex]

Hence, the direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.

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Considering the two figures the value of x is

The value of x is found by the external angle theorem which states that the sum of the two opposite internal angels of a triangle gives the external angle

The value of x is calculated as below

8)  70 + 5x = 9x + 22

70 - 22 = 9x - 5x

48 = 4x

x = 12

9)  65 + 8x + 11 = 16x + 12

65 + 11 - 12 = 16x - 8x

66 = 8x

x = 8.25

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Answer:

angle LHJ is congruent to angle IKL

Answer:

segment JL is congruent to segment JK

segment HL is congruent to segment KI

Angle LJH is congruent to angle KJI

Step-by-step explanation:

we flip the triangles to look for the corresponding sides

Hopes this helps please mark brainliest