The scores on a psychology exam were normally distributed with a mean of 57
and a standard deviation of 4. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing​ score? Approximately what percentage of the students​ failed?

Step 1: Line up the equations so that the variables are lined up vertically.

Step 2:  Choose the easiest variable to eliminate and multiply both equations by different numbers so that the coefficients of that variable are the same.

Step 3:  Subtract the two equations.

Step 4:  Solve the one variable system.

Step 5:  Put that value back into either equation to find the other equation.

Step 6:  Reread the question and plug your answers back in to check.

Final answer:

To solve systems of equations, one can use methods like graphing, substitution, or elimination, and check the solution by substituting it back into the original equations. For inequalities, graph the lines, decide where to shade by testing a point, and find the overlap of the shaded regions for the solution.

Explanation:

Steps to Solving Systems of Equations and Inequalities

The process of solving systems of equations and inequalities involves several steps. To solve a system of equations, you can use methods such as graphing, substitution, or elimination. When solving inequalities, additional considerations such as shading the solution region are necessary. Here's a step-by-step approach for both equations and inequalities:

For Equations:

Choose a suitable method (graphing, substitution, elimination).

Apply the selected method to find the point of intersection, which represents the solution to the system.

Check your solution by substituting it back into the original equations.

For Inequalities:

Graph the lines or curves that represent the inequalities, using dashed or solid lines.

Determine where to shade the region by testing a point not on the line.

Find the overlap of the shaded regions if there is more than one inequality.

It's important to practice these steps with different systems to become proficient in solving them. Remember to pay close attention to the signs of the inequalities when graphing and shading the solution regions.

Let x and y be the two numbers.  

x = y - 4  

2y = 5x - 10  

solve the system of equations:  

2y = 5(y - 4) - 10  

2y = 5y - 20 - 10  

-3y = -30  

y = 10  

x = 10 - 4 = 6

I will try my best...

Let x and y be the two numbers.  

x = y - 4  

2y = 5x - 10  

Now, we solve the system of equations:  

2y = 5(y - 4) - 10  

2y = 5y - 20 - 10  

-3y = -30  

So...

y = 10  

x = 10 - 4 = 6

the answer is B. hope i helped!

Answer:

She did not get the correct answer because she did not put the decimal in the correct spot. The correct answer should be 428.206.

Step-by-step explanation:

17.06×25.1=428.206

Answer:

D.)  (12 + 11 + 20) ÷ 3

Step-by-step explanation:

If the point (a, b) is in Quadrant IV of a coordinate plane, then the x-coordinate of (a, b) will be positive and the y-coordinate will be negative.

EX: (5, -5)

Final answer:

The point (a,b) is in Quadrant IV, where 'a' is positive and 'b' is negative. Switching the coordinates to (b,a) places it in Quadrant II, where 'b' is now the x-coordinate (negative), and 'a' is the y-coordinate (positive).

Explanation:

Given that the point (a,b) is in Quadrant IV of a coordinate plane, where 'a' is the x-coordinate, and 'b' is the y-coordinate. In Quadrant IV, x-coordinates (a) are positive, and y-coordinates (b) are negative, hence a > 0 and b < 0. When we consider the point with coordinates (b,a), we switch the positions of 'a' and 'b'. Since 'a' is positive and 'b' is negative, the point (b,a) would then be in Quadrant II, where x-coordinates are negative and y-coordinates are positive. To recap, in the Cartesian coordinate system, a point's location is determined by the signs of its x and y values, which change across different quadrants, affecting the point's location accordingly.

Answer:

Hypotenuse, AB = 7.61 cm

Step-by-step explanation:

In the given figure it is given that, ABC is a right angled triangle with base length BC = 3 cm and perpendicular distance AC = 7 cm. We have to find the length of hypotenuse i.e. AB

The length of hypotenuse is solved using Pythagoras theorem. The mathematical expression for the Pythagoras theorem can be written as :

[tex]AB^2=AC^2+BC^2[/tex]

[tex]AB^2=7^2+3^2[/tex]

[tex]AB^2=58[/tex]

AB = 7.61 cm

So, the length of the hypotenuse of the triangle is equal to 7.61 cm    

we have

[tex]\frac{3}{5}x+ \frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex]

Combine like terms in both sides

[tex](\frac{3}{5}x+ x)+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]

we know that

[tex](\frac{3}{5}x+ x)=(\frac{3}{5}x+ \frac{5}{5}x)=\frac{8}{5}x[/tex]

substitute in the expression above

[tex]\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]-----> equation A        

Multiply equation A by [tex]5*3*2=30[/tex] both sides

[tex]30*(\frac{8}{5}x+\frac{2}{3})=30*(\frac{1}{2}-\frac{1}{5}x)[/tex]

[tex]48x+20=15-6x[/tex] ---------> equation B

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]48x+6x=15-20[/tex]

[tex]54x=-5[/tex] ---------> equation C

Solve for x

[tex]x=-\frac{5}{54} =-0.09[/tex]

We are going to proceed to verify each case to determine the solution.

Case a) [tex]\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]

the case a) is equal to the equation A

so

the case a) have the same solution that the given equation

Case b) [tex]18x+20+30x=15-6x[/tex]

Combine like terms in left side

[tex](18x+30x)+20=15-6x[/tex]

[tex](48x)+20=15-6x[/tex]

the case b) is equal to the equation B

so

the case b) have the same solution that the given equation

Case c) [tex]18x+20+x=15-6x[/tex]

Combine like terms in left side

[tex](18x+x)+20=15-6x[/tex]

[tex](19x)+20=15-6x[/tex]

[tex]19x+6x=15-20\\25x=-5\\x=-0.20[/tex]

[tex]-0.20\neq -0.09[/tex]

therefore

the case c) not have the same solution that the given equation

Case d) [tex]24x+30x=-5[/tex]

Combine like terms in left side

[tex]54x=-5[/tex]

the case d) is equal to the equation C

so

the case d) have the same solution that the given equation

Case e) [tex]12x+30x=-5[/tex]

Combine like terms in left side

[tex]42x=-5[/tex]

[tex]x=-5/42=-0.12[/tex]

[tex]-0.12\neq -0.09[/tex]

therefore

the case e) not have the same solution that the given equation

therefore

the answer is

case a) [tex]\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]

case b) [tex]18x+20+30x=15-6x[/tex]

case d) [tex]24x+30x=-5[/tex]

Answer:

Option (a) , (b) and ( d) are equivalent to given expression [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]

Step-by-step explanation:

 Given equation :  [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]

We have to use  properties to rewrite the given equation and check which are correct from thee given options,

Consider the given equation,

[tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]

Applying commutative property of addition , [tex]a+b=b+ a[/tex]

Equation becomes,

[tex]\frac{3}{5}x+x+\frac{2}{3}= \frac{1}{2}- \frac{1}{5}x[/tex]

Now adding x terms on right side , we get,

[tex]\frac{3+5}{5}x+\frac{2}{3}= \frac{1}{2}- \frac{1}{5}x[/tex]

[tex]\Rightarrow \frac{8}{5}x+\frac{2}{3}= \frac{1}{2}- \frac{1}{5}x[/tex]

Thus, obtained option (a).

Again consider given equation ,

[tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]

Taking LCM both sides, we get,

[tex]\frac{9x+10+15x}{15}= \frac{5-2x}{10}[/tex]

Solving , we get,

[tex]\frac{9x+10+15x}{3}= \frac{5-2x}{2}[/tex]

Cross multiply, we get,

[tex]2\times (9x+10+15x)=3\times(5-2x)[/tex]

[tex]18x+20+30x=15-6x[/tex]

Thus, obtained option (b).

Taking like terms together,

[tex]18x+6x+30x=15-20[/tex]

[tex]\Rightarrow 24x+30x=-5[/tex]

Thus, obtained option (d).

Thus, Option (a) , (b) and ( d) are equivalent to given expression [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]

it could be 460-490 to round to 500

Answer:

450-549

Step-by-step explanation:

you can round up or down

The answer is about 4 times as many people live in China then in the United States

There are 4.4 times more people living in china than united states as the definition of ratio says "the quantitative relation between two amounts showing the number of times one value contains or is contained within the other".

The indicated quotient of two mathematical expressions is referred to as a ratio. A/B stands for an ordered pair of numbers where B does not equal 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Here,

To find that how many times as many people live in China then in the United States, we need to divide the population of china by the population of united states.

let x be the value of how many times as many people live in China then in the United States,

so, the population of china=1.325 billions

the population of united states=0.304 billions

x=1.325/0.304

x=4.356

x≈4.4 times

As stated in the definition of ratio, "the quantitative relation between two amounts showing the number of times one value contains or is contained within the other," there are 4.4 times as many people living in China as there are in the United States.

To know more about ratio,

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Charges per load = $5.25

Total money = $31.50

As the situation says that charges are 5.25 and one has a total money of 31.50 so lets suppose the total load one has be 'w'

so equation becomes:

[tex]5.25w\leq31.50[/tex]

solving it we get, [tex]w\leq6[/tex]

So, option C is the correct answer.

Answer:

Step-by-step explanation:

The lines can be related in following three ways

Now three real life examples of above three scenarios are described below:

Answer:

1. KI

2. HI and DF

3. 8

4. 4 and 7

Step-by-step explanation:

Answer,

42

Explanation,

18/3 = 6

6 x 7 = 42

Hope this helps :-)

So if you let x and y be the two numbers...

the sum of the two means you add them together... so you get:

x+y=56 : the difference means you subtract them.. so

x-y = 16

now you have two equations and two unknowns... which you can solve with a variety of methods... you can use elimination, substitution, or trial and error.

x+y=56

x-y = 16

I will use the elimination method: Because there is a plus y and a negative you cancel that out and you add the 2x's. Therefore:

2x=72

x=36

Now, you can plug in 36 into one of your original equation:

36+y=56

y=20

Those are your two numbers!

The product of the numbers is 720.

Simplify fractions by cancelling all the common factors from both the numerator and the denominator and writing the fraction in its lowest/simplest form.

Given that, the sum of two numbers is 56. the difference of the 2 numbers is 16.

Let the numbers be x and y,

x+y = 56

x-y = 16

On solving, we get,

x = 36 and y = 20

x*y = 36*20 = 720

Hence, The product of the numbers is 720.

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Answer:

i realy need help with this one

Step-by-step explanation:

ANSWER

ANSWER TO QUESTION 1.

If you give [tex]x[/tex] surfing lessons, then you will earn $ [tex]25x[/tex]

If you are charged $200 for using the place, then your profit will reduce by $200.

The profit function is given by

[tex]P(x)=25x-200[/tex] dollars.

The y-intercept is  [tex]-200[/tex]. It is negative because it is a cost which is a liability. So it does not add to your profit.

ANSWER TO QUESTION 2.

The slope is [tex]25[/tex]. It is positive because as the number of hours increases, the profit earned also increases. In other words there is a direct relation between the number of hours worked and the profit earned.

ANSWER TO QUESTION 3.

The slope intercept form is when an equation is written in the form;

[tex]y=mx+c[/tex],

where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept. The profit function in slope intercept form is

[tex]P(x)=25x-200[/tex]

ANSWER TO QUESTION 4.

If you break even, then the difference between the revenue and cost is zero. So we equate the profit function to zero.

[tex]25x-200=0[/tex]

[tex]25x=200[/tex]

[tex]x=8[/tex]

Therefore you need to give 8 different lessons to break even.

ANSWER TO QUESTION 5.

If you give 20 lessons, the [tex]x=20[/tex]. We need to substitute

[tex]x=20[/tex] in to the profit function to calculate the profit made after 20 lessons.

[tex]P(20)=25(20)-200[/tex]

[tex]P(20)=500-200[/tex]

[tex]P(20)=300[/tex].

ANSWER TO QUESTION 6.

If the new price is $75, then the new profit function becomes

[tex]P(x)=75x-200[/tex]

ANSWER TO QUESTION 7.

To find the number of lessons that lets you break even, we equate the new profit function to zero.

[tex]75x-200=0[/tex]

We solve for x by adding 200 to both sides of the equation.

[tex]\Rightarrow 75x=200[/tex]

We now divide through by 75

[tex]\Rightarrow x=\frac{200}{75}[/tex]

[tex]\Rightarrow x=2\frac{2}{3}[/tex]

Therefore you would have to 2\frac{2}{3} lessons to break even. That is approximately 3 lessons.

ANSWER TO QUESTION 8.

If you give 20 lessons and we want to find the profit you made with this new profit function, then we have to plug in [tex]x=20[/tex] in to [tex]P(x)=75x-200[/tex].

That is,

[tex]P(20)=75(20)-200[/tex]

[tex]P(20)=1500-200[/tex]

[tex]P(20)=1300[/tex] dollars

The question is about simplifying an algebraic expression, specifically 3x - 1/2y + 2 2/3y - 5/6x. This can be achieved by first consolidating like terms and performing multiplication and addition/subtraction to get the simplified expression 2 1/6x + 2 1/6y.

This question appears to be about simplifying algebraic expressions. The expression at hand is 3x-1/2y +2 2/3y -5/6x. To simplify this, you should first consolidate your like terms. The 'like terms' in this case, are the X terms (3x and -5/6x) and the Y terms (-1/2y and +2 2/3y).

Secondly, perform the operations necessary for the terms – which involve multiplication and addition/subtraction. Thus, the sum of 3x and -5/6x is 2 1/6x (or 2.167x if we want it in decimal form). Similarly, the sum of -1/2y and +2 2/3y is 2 1/6y (or 2.167y in decimal form).

Finally, to complete the simplification, you should combine these totals. The simplified algebraic expression for 3x - 1/2y + 2 2/3y - 5/6x is therefore 2 1/6x + 2 1/6y.

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1) Divide both sides by 3

3(5x+3)=114

2) Move constant to the right side and change it's side

5x+3=38

3) Subtract the numbers

5x=38-3

4) Divide by sides by 5

5x=35

5) The answer is x=7

Hope I could help! :)

Hey mate !!

Answer

= 5x +3=114/3

Simplify 114/3 to 38

= 5x+3=38

Subtract 3 from both sides

=5x=38-3

Simplify 38-3=35

5x=35

Divide both sides by 5

X= 35/5

Simplify 35/5 to 7

X=7

Answer confirmed = x=7

Hope this helps you!

bi(two)...sector(section).  Bisector cuts the segment into two equal sections.  

BC = CD             definition of perpendicular bisector

BC + CD = BD    segment addition postulate

CD + CD = BD   substitution

2CD = BD          added like terms

2CD = 16           substitution

  CD = 8            division property of equality

CD = y + 3         given per graph

y  + 3 = 8           transitive property

  y = 5               subtraction property

Answer: 5

Answer:

B) Kara's highest speed was between 30 and 35 minutes.

Step-by-step explanation:

A zero slope (horizontal line) means a stopped car with zero speed.

The higher the slope, the steeper the line, the higher the speed.

Let's look at the options.

a) The car was stopped between 10 and 15 minutes, not 20. False.

b) Between 30 and 35 min, the graph shows the steepest slope, so this statement is True.

c) False, since here slope is not steepest.

d) Between 5 and 10 minutes, the graph is a straight line, so speed was constant. False.

If you plug in h, the answer would be 13-9 which is 4.

h(13)=13-9=4,inlocuiesti x cu 13 si calculezi.

There are no graphs shown, but the vertical line test is something you can use to find out if a function works. If you make a vertical line anywhere on one of the graphs, it should only pass through one point. For example, a regular straight line almost always passes the vertical line test. If it's a sideways parabola, it will not.

We know that the perimeter is 72 meters, so we have

[tex] y+2x+(2x+6)=72 \iff y+4x+6=72 \iff y=-4x+66 [/tex]

Now we can use the pythagorean theorem: the sum of the squares of the legs is the square of the hypotenuse:

[tex] (2x)^2+(2x+6)^2 = y^2 \iff (2x)^2+(2x+6)^2 = (-4x+66)^2 [/tex]

Expand the squares to get

[tex] 8 x^2 + 24 x + 36 = 16 x^2 - 528 x + 4356 [/tex]

Bring everything to the right hand side to get

[tex] 8 x^2 - 552 x + 4320 = 0 [/tex]

Divide both sides by 8:

[tex] x^2 - 69x + 540 = 0 [/tex]

This equation has solutions [tex] x=9,\ x=60 [/tex]

This solutions would yield the following side lengths:

[tex] x=9\implies\begin{cases} 2x = 18\\2x+6=24\\-4x+66=30\end{cases}[/tex]

[tex] x=60\implies\begin{cases} 2x = 120\\2x+6=126\\-4x+66=-174\end{cases}[/tex]

Since we can't have negative side lengths, we can only accept the solution x=9.

In fact, you can check that 18,24,30 is a pythagorean triplet, i.e.

[tex] 18^2+24^2=30^2 [/tex]

They wash a car for $5, so 5 represents the cost of washing one car. to find out how much they will earn by washing x cars, we can multiply 5 by any number to find the total cost of the washed cars. For example 5×2=10 which means the cost of washing 2 cars is $10 and 5×3=15 means the cost of washing 3 cars is $15 and also 5×4=20 means the cost of washing 4 cars is $20. Basically the cost of the washed cars will increase by $5 each time the number of cars increase.

Hey there!!

Multiply both the sides with 4/3.

Then we get

x = 5 ^ 4/3

x = 8.5 ( avg. )

Hope it helps!

GCF of 45 and 70 is 5

Answer:

x=-39

Step-by-step explanation:

subtract 23 from both sides

-16 - 23= -39

therefore x=-39