For the following word problems, create a system of equations and solve by using the substitution method.

A probability is the number of outcomes divided by the number of total outcomes.

An odd is given by a:b, in which a is the number of successes and b is the number of failures.

From the question, the probability of 5 cars will pass over a small bridge is 0.16

That means the total outcomes is 100 and the outcomes of successes are 16

Then to find the failures subtract 16 from 100

The failures = 100 - 16 = 84

Successes = 16

a = 16

Failures = 84

b = 84

Odds = a: b

Odds = 16: 84

Divide each term by 4 to simplify

Odds = (16/4): (84/4)

Odds = 4: 21

The answer is 4: 21

Based on the given situation, if x is number of kilograms of lobster, you can write the following expressions:

51 + 5x cost in the first restaurant

33 + 8x cost in the second restaurant

In order to determine the value of x which makes the cost the same in both restaurants, equal the previous expressions and solve for x:

51 + 5x = 33 + 8x subtract 33 both sides and 5x subtract both sides

51 - 33 = 8x - 5x simplify

18 = 3x divide by 3 both sides

18/3 = x

6 = x

x = 6

Hence, the weight of the lobster is 6 kg.

The cost of the dinner is:

51 + 5(6) = 51 + 30 = 81

Hence, the cost of the dinner is $81

Answer: y = 2x - 8

Step-by-step explanation:

When x = 0, y = -8. This is the y-intercept.

As x increases by 1, y increases by 2. This makes 2 the slope.

The equation for the linear relationship given, in slope-intercept form is y = 2x-8

The slope-intercept form of a linear equation is where one side contains just "y". So, it will look like: y = mx + b where "m" and "b" are numbers.

Given that, coordinates representing a linear relationship.

x → 0, 1, 3, 4

y → -8, -6, -2, 0

We need to find an equation for the given linear relationship in slope-intercept form,  

Considering points, (0, -8) and (4, 0)

We know that, the equation of a line passing through, two points is given by,

y-y₁ = (y₂-y₁) / (x₂-x₁) (x-x₁)

Here, y₁ = -8, y₂ = 0, x₁ = 0, x₂ = 4

Therefore, the equation is =

y+8 = 8/4(x-0)

y+8 = 2x

y = 2x-8

Hence, the equation for the linear relationship given, in slope-intercept form is y = 2x-8

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Answer:

4.5

Step-by-step explanation:

4.5 + 4.5 + 4.5 + 4.5 = 18

You write it like this in the number line:

4.5, 9, 13.5, 18

Answer:

See below

Step-by-step explanation:

Point (4,-8)  slope form would be

( y - -8) = -2 ( x -4)          

y+8 = -2x + 8       re-arrange to y = mx + b form

y = - 2x        

We define the following variables:

• x = age (in years) of the eldest,

• y = age (in years) of the second,

• z = age (in years) of the youngest.

From the statement, we know that:

0. the eldest is 7 years older than the second → , x = 7 + y,,

1. the second is 2 older than the youngest → ,y = 2 + z,,

2. the sum of the ages 12 years from now will be 56 → x + y + z + 12 = 56 → ,x + y + z = 56 - 12 = 44,.

We have the following system of equations:

i) Replacing the second equation in the first one, we have:

ii) Summing the ages of the three daughters, we have:

iii) Equalling the last equation with the third one, we have:

Replacing the value of z in the equation of x and y, we get:

Answer

The ages of the daughters are 20, 13 and 11.

seems hard very xd oihfoidhfoidshfodjsklfdsfdsfsdfdsf

Answer:

[tex]260 \: {cm}^{2} [/tex]

Step-by-step explanation:

hope it helped, have a nice day!: )

The volume of a cylinder is given by:

solve for h:

divide the height by 12:

The thickness of each cookie is 0.499992681in or approximately 0.5in

For 3 yards, it costs, 1.50.

So for one yard,

Therefore for 5 yards,

Question 1

[tex]-14=-4(9x-1)\\\\-14=-36x+4\\\\-18=-36x\\\\x=\frac{1}{2}[/tex]

Question 2

Multiplying both sides by 12,

[tex]4x-7x=8\\\\-3x=8\\\\x=-\frac{8}{3}[/tex]

ANSWER

EXPLANATION

The Principal is $5200;

Increase rate is; 6.5%

The increase in dollar is;

Hence, the amount in the account at the end of the year;

Therefore, the increase in dollar is $338 while the amount in the account at the end of the year is $5538

A triangular prism have two possible cross sections: A triangle and a rectangle

Answer:

y=0.75x+2

Step-by-step explanation: Slope as k and constant as b two points that showed by the graph: (0,2) (4,5)

so we can get 2=0*k+b b=2

5=4k+b

4k=5-2

4k=3

k=3/4

k=.75

Answer:

=82

Step-by-step explanation:

the value of

x + y²

putting x=1,y=9

we get,

1+(9)^²

=1+81

=82

Formula to calculate Principal with clompound interest:

For the given situation:

A= 60,000

r= 7% =7/100= 0.07

n= 12 (as it is compounded monthly and a year has 12 months)

t= 10 years

Then, they must deposit approximately $29,855.75

On (-∞, -2) ∪ (3,∞) f(x) is positive, On (-∞, -0.5) it is negative, On (0.5, ∞) it is increasing, in none of the intervals it is having positive concavity, On (-∞, ∞) it has negative concavity.

Seeing as how f (x) = 0 there. A function’s “positive regions” are those times when it is above the x-axis. Y-values that are positive are where it is (not zero).

The portions of a function that are below the x-axis are known as its negative regions.

You must first take the derivative, then make it equal to 0, and then determine which zero values the function is positive between in order to determine when a function is rising. In order to determine when the function is positive and, thus, rising, test values on all sides of these.

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Answer:

6

Step-by-step explanation:

when you change h[×] to h[-2] , -2x +2 change to -2[-2]+2

Answer:

a) 0.0187

b) 0.0943

c) 0.2959

Step-by-step explanation:

a) 9/31 * 8/30 * 7/29 = 0.0187

b) 10/31 * 9/30 * 8/29 + 12/31 * 11/30 * 10/29 + 9/31 * 8/30 * 7/29 = 0.0943

c) 21/31 * 20/30 * 19/29 = 0.2959

Looking at the inequalities, it involves the 'less than or equal to' symbol. This means that the lines of both inequalities must be solid. In options B, C and D, one or two of the lines is broken. This is an indication that they don't represent the given inequality. We would check option A

Optiona

The percent increase of the students in the cafeteria that bought hot lunches is 17.5%

On Monday 365 students purchased hot lunch

On Friday 429 students purchased hot lunch

The first step is to calculate the percent change

429-365

= 64

The percent increase can be calculated by dividing the percent change by the original value and then multiply by 100

64/365 × 100

= 0.175 × 100

= 17.5

Hence the percentage increase in the students purchasing lunch is 17.5%

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Answer: [tex]\sqrt{13}[/tex]

Step-by-step explanation:

Using the distance formula,

[tex]\sqrt{(-6-(-3))^2 +(5-7)^2}=\sqrt{13}[/tex]

Answer:

SAS= Side, Angle, Side

Step-by-step explanation:

According to the image, GB congruent to XP, and LB congruent to PF. So, it means that both triangle have the same angle since they both have two congruent side.

The required solution of the given equation 6x + 3y = −1 for y would be the value of equation y = -2x - 1/3.

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

The equation is given in the question below as:

6x + 3y = −1

We have to determine the solution of the equation 6x + 3y = −1 for y.

⇒ 6x + 3y = −1

Rearrange the terms of the variable in the above equation,

3y = - 6x - 1

Divided by 3 both sides of the equation to get

y = -2x - 1/3

Hence, the required solution of the given equation 6x + 3y = −1 for y would be the value of equation y = -2x - 1/3.

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If he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33

The percentage decrease in the monthly payment = 30%

The amount of decrease in the bill per month = $25

Consider the current bill amount as x

Then the equation will be

x × (30/100) = $25

Solve the equation

0.3x = $25

x = 25/0.3

x = $83.33

Hence, if he make a change to less expensive option that will result in a 30% decrease in your monthly payment that is $25 per month, then the bill is $83.33

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First,we will find the slope of the line

Using 8x - 6y = 5

we will have to re-arrange the equation above to be in the slope-intercept form.

That is; it should be in the form y = mx + b

8x - 6y = 5

6y = 8x -5

y = 8/6 x - 5/6

slope = 8/6 = 4/3

In a parellel equation the slope are the same, hence the slope of our new equation is 4/3

Next, we find the intercept of the new equation;

Using the point (-9, 1) and slope(m) = 4/3

we will substitute into the equation below and then solve for b, where b is the slope of our new equation

y = mx + b

1 = 4/3 (-9) + b

1 = 4(-3) + b

1 = - 12 + b

add 12 to both-side of the equation

1+ 12 = b

13 = b

b= 13

Substituting m = 4/3 and b = 13 into the formula; y = mx+ b

y = 4/3 x + 13

Answer

i) 4% = 0.04

ii) 76% = 0.76

iii) 120% = 1.20

iv) 100% = 1.00

v) 32.5% = 0.325

Explanation

The key to writing percents as decimals is to divide the percents by 100 to get the decimal equivalent.

i) 4% = (4/100) = 0.04

ii) 76% = (76/100) = 0.76

iii) 120% = (120/100) = 1.20

iv) 100% = (100/100) = 1.00

v) 32.5% = (32.5/100) = 0.325

Hope this Helps!!!

We can give two classifications to that triangle

It's a scalene triangle, because all the sides are different (because all the angles are different). Also, it's a acute triangle because all the angles are less than 90°

Answer:

A

Step-by-step explanation:

Comment

The tricky part is f(4)

Log part

That is defined by log_2 which means that the base used for the log is 2.

We don't have log_2 on our calculators so you have to create it.

Substitute 4 for x

log_2 (4) = log_10(4)/ log_10 (2)     Which your calculator can handle

log_2 (4) = Log(4)/ log(2) = 2

f(x) = 1/2 x^2

x = 2.1

Only answers a and b are correct, but which one is right? 2.1 is between 2 and 4. So you choose f(x) = 1/2 x^2

1/2 2.1^2 = 1/2 4.41 = 2.205

Answer

A

Answer:

  (a)  f(2.1) = 2.205 and f(4) = 2

Step-by-step explanation:

You want to evaluate a piecewise-defined function to find f(2.1) and f(4).

The first step in evaluating a piecewise defined function is to match the argument value with the appropriate domain.

Once you have identified the function you are evaluating, substitute the argument for the variable and carry out the arithmetic in the usual way.

The desired function values are f(2.1) = 2.205 and f(4) = 2.