Georgia joined the the big race. Her race can be modeled with the equation y=3x+4 where x is seconds and y is distance. How much of a head start did georgia get? How can you tell from the equation?

The expression - 1/5× ( 3 - 12 × (1/3)² is simplified to -1/3

A fraction can be described as the part of a whole element, number or variable.

The types of fractions are;

From the information given, we have that;

- 1/5× ( 3 - 12 × (1/3)²

find the square

- 1/5 × ( 3- 12 × 1/9)

multiply the values

-1/5 × ( 3 - 4/3)

expand the bracket

- 1/5 × (9 -4 /3)

- 1/5 × 5/3

-5/15

- 1/3

Hence, the value is -1/3

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The probability that the number 75 ends up in the 45th position in the resulting permutation is 0.01.

To calculate this probability, we can use the concept of permutation. In a permutation of n distinct elements, the probability of any particular element ending up in a specific position is (1/n).

In this case, we have 100 distinct elements, and we want to find the probability that the number 75 ends up in the 45th position. So, the probability is (1/100) or 0.01.

Another way to think about it is that there are 100! (100 factorial) total possible permutations of the numbers 1 to 100. In order for 75 to be in the 45th position, the other 99 numbers can be arranged in 99! ways. Therefore, the probability of 75 being in the 45th position is (1/100!) * (99!) = 1/100 = 0.01.

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Suppose  x₁, x₂, ..., xₙ are iid random variables with uniform distribution between 0 and 1. The probability that its sum is less than 1 is 1/n!

Let x₁, x₂, ..., xₙ be independent identically distributed random variables with uniform distribution in the interval [0, 1].

Let's define the sum of those random variables as

Sₙ = x₁ + x₂ + ... + xₙ

For 0 ≤ t ≤ 1, the probability that the sum is less than t is:

P(Sₙ < t) = tⁿ/n!

Where:

n! = factorial of n

In the given problem, t = 1. Therefore,

P(Sₙ < 1) = 1ⁿ/n!

For example, if n = 4,

S = x₁ + x₂ + x3 + x₄

P(S < 1) = 1/4!

P(S < 1) = 1/(4×3×2) = 1/24

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So, the person's blood-alcohol level is estimated to be 40 mg/dL after 4 hours.

An exponential model for the person's blood-alcohol level can be represented by the function f(t) = A * e^(-kt) where A is the initial blood-alcohol level, k is the decay constant and t is the time in hours.

To find the decay constant k, we can use the known information that after 2 hours, 112.5 mg/dL remains. We can substitute the known values into the exponential function, and solve for k:

f(2) = A * e^(-2k) = 112.5

A = 200 mg/dL

200 mg/dL = 112.5 * e^(-2k)

k = ln(200/112.5)/(-2)

Using this value of k, we can now find the blood-alcohol level after 4 hours:

f(4) = A * e^(-kt) = 200 * e^(-k*4)

f(4) = 200 * e^(-1.6) = 200 * 0.20 = 40 mg/dL

Therefore, the person's blood-alcohol level is estimated to be 40 mg/dL after 4 hours.

It's worth noting that this model is based on the assumption that the blood-alcohol level decays exponentially, and many other factors like body weight, gender, metabolism, and the amount of alcohol consumed can affect the actual blood-alcohol level.

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Using a system of linear equation, the cost of each shirt and pant is $9 and $11 respectively.

A system of linear equations is a collection of one or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system.

A linear equation is an equation that can be written in the form of ax+by=c, where x and y are variables, and a, b, and c are coefficients.

In this problem, we need to define our variables and the solve the equations.

Let;

x + 2y = 31 ...eq(i)

3x + y = 38 ...eq(ii)

Solving both equations

x = 9, y = 11

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Answer:

-8/3 is the slope of these two points.

Step-by-step explanation:

Answer:

The distance between the two points can be found using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) = (-4, 8) and (x2, y2) = (4, 5)

So, d = √((4 - (-4))² + (5 - 8)²) = √((8)² + (-3)²) = √(64 + 9) = √73

Rounding to the nearest tenth, d = √73 ≈ 8.6

The sales tax paid 1.15=3y/23

What is Sales tax?

Government-imposed consumption taxes on the purchase of goods and services are known as sales taxes. Typically, a sales tax is assessed at the point of sale, paid to the store, and then forwarded to the government. A company is responsible for paying sales taxes in a specific jurisdiction if it has a nexus there. Depending on the local rules, this could be a physical location, a worker, an affiliate, or some other kind of presence.

Step by step Explaination:

Sales tax: 15%

Converting 15%=15/100

                         =0.15

To show sales tax paid is 3y/23

0.15=3y/23

Multiply both side by 23

23*0.15=3y

3.45=3y

Divide both sode by 3

3.45/3=y

y=1.15

The sales tax paid 1.15=3y/23(as the purchase price includes sales tax).

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Answer:

length = 15x + 6

Step-by-step explanation:

given the length is 3 times the width, then

length = 3(5x + 2) ← distribute parenthesis by 3

          = 15x + 6

Answer:

To find the percent of increase in the cost of season tickets, we can use the following formula:

(New cost - Old cost) / Old cost x 100 = % increase

Using the given information:

(1,441 - 1,310) / 1,310 x 100 = 10.06%

So, the percent of increase in the cost of season tickets is 10.06%.

Answer: 2/3, or 0.6666666667

Step-by-step explanation:

Answer:

The simplest form of 6/9 is 2/3.

Step-by-step explanation:

1) Divide both the numerator and denominator by three(does not apply to all situations).

2) Outcome should be 2/3 or .666

The endpoints of the line segment after translation will be (−5, 2) and (−3, −2). Then the correct option is A.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The translation does not change the shape and size of the geometry. But changes the location.

The endpoints of the line segment are (−2, 7) and (0, 3).

Translate the points 5 units down and 3 units left. Then the points are given as,

(−2 − 3, 7 − 5) and (0 − 3, 3 − 5)

(−5, 2) and (−3, −2)

The endpoints of the line segment after translation will be (−5, 2) and (−3, −2). Then the correct option is A.

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The slope of y = -2x is -2.

The slope of a linear equation is a measure of how steep the line is. In other words, it represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

In the equation y = -2x, the coefficient of the x term is -2, which means that for every unit increase in x, the value of y will decrease by 2 units. So the slope of this line is -2.

The slope can also be thought of as the tangent of the angle the line makes with the x-axis. In this case, the slope being -2, means the angle of the line with the x-axis is negative, which means the line is going downward and to the left.

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Answer:

The appropriate form for this equation is B. 6x - 30 = 84. This equation can be used to calculate the number of t-shirts Lashanda sold. By solving the equation, we can determine that she sold 14 t-shirts.

Step-by-step explanation:

The difference between the y-intercepts of the lines y = 5x + 3 and

y = (17/2)x - 19 is  22 units.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

The given equation of the line in slope intercept form is y = 5x + 3.

The slope of the line given in the table is,

m = (32 - 15)/(6 - 4).

m = 17/2.

Now, 15 = (17/2)×4 + b.

15 = 34 + b.

b = - 19.

So, The required equation of the line is y = (17/2)x - 19.

The difference between the y-intercepts of the lines y = 5x + 3 and

y = (17/2)x - 19 is 3 - (- 19) = 22 units.

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The height of the house is 48 foot and it cast a 24 foot shadow

An equation shows the relationship between numbers and variables in an expression.

Two shapes are said to be similar if the ratio of their corresponding sides are in same proportion.

The garden shadow and house shadow are similar. An 6ft tall garden shed a 3-foot shadow and a house cast a 24-foot shadow.

Let x represent the height of the house, then:

6/3 = x/24

x = 6 * 24/3 = 48 ft

The height of the house is 48 foot

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Algebraic expressions can be written by using the key words to write an operation.

Algebraic Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

In order to write an algebraic expression from a written statement, we have to understand the key words and their translation to mathematical operation.

Some of the keywords are :

Addition : sum, added to more than, increased by, .......

Subtraction : Difference of, difference between, less than, decreased by, ..........

Multiplication : product, times, multiplied by, ......

Division : ratio of, quotient of, .......

So for example, sum of 6 and a number which is 2 times x can be written as 6 + 2x.

Hence in order to write the expressions, know the key words.

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Answer:

Depth after 9 minutes is -253 feet

Step-by-step explanation:

Since we can find the submarine's depth as a function of time, m (in minutes), lets use the function to calculate the answer.

We are given the equation for depth: Depth(m) = -370+13m

Depth(x) means that the equation will tell us the submarine's depth after m minutes. The equation is missing the units, but we know from the statement that the initial depth is -370 feet and the rate of ascention is +13 feet/min. So we can enhance the equation by rewriting it with the units.

Depth(m) = -370ft+13(feet/minute)*m [m is minutes]

The sub's depth after 9 minutes is:

Depth(9) = -370ft+13(feet/minute)*(9 minutes)

Depth(9) = -370ft + 13*(9)

Depth(9) = -370+117

Depth(9) = -253 feet

Answer:

The misplaced modifier in the sentence is "sitting in the back of the fridge."

Step-by-step explanation:

It implies that Fabiola Torres is stale and sitting in the back of the fridge, rather than the Skittles.

The correct sentence would be: "Fabiola Torres found some stale Skittles in the back of the fridge."

An acute triangle is a sort of triangle in which all three internal angles of the triangle are less than 90°. Acute triangles are also named acute-angled triangles.

A triangle is a fundamental polygon with three sides and three vertices. Since the triangle has three sides, it also has three interior angles. An angle which measures between 0° to 90° is called an acute angle. An acute triangle is a kind of triangle in which all three internal angles of the triangle are less than 90°.

Acute triangles are also called acute-angled triangles. Even though the length of the sides of acute triangles varies, the interior angles are never more than 90°.

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The resulting volume when an isosceles triangle with side lengths 5, 5 and 10 is revolved about one of its longer sides is approximately 40.11 cubic units.

Let's call the height of the triangle "h" and the radius of the circle created by the revolution "r". We know that the hypotenuse of the triangle (the longer side) is 10, so we can use the Pythagorean theorem to find the value of h:

h = [tex]\sqrt{(10^2 - (5/2)^2)}[/tex] = [tex]\sqrt{25 - 6.25}[/tex] = [tex]\sqrt18.75}[/tex] = 4.33

Now we can use the formula for the volume of a revolution solid to find the volume:

V = (1/3) * π * [tex]r^2[/tex] * h

r is half the side length of the triangle, so:

r=5/2

V = (1/3) * π * [tex](5/2)^2[/tex] * 4.33 = (1/3) * π * 6.25 * 4.33 = 20.55 * π = 40.11 (approximately)

So the resulting volume of the revolved isosceles triangle is approximately 40.11 cubic units.

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The perimeter of the pool will be 26.85 in.

The perimeter is defined as the sum of all the sides of the given figures like squares, rectangles, etc.

The circumference of the whole circle of diameter 5 in is C = πd, which here is C = π(5 in), or approximately 5π in.  We take only half of this since the figure shows a semicircle, not a full circle.  Then the half-circumference is (5/2)π.

To find the perimeter:  add up the lengths forming the perimeter:  

7 in + (5/2)π in + 7 in + 5 in, or:

19 in +  (5/2)π ≈ 26.85 in

The perimeter will be 26.85 inches.

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When a mountain is cut off at 4,000 feet, a cone is created that has a radius that is half that of the original mountain.

This is because the radius and height of cones both change in an inverse manner as height increases. As a result, volume changes as the inverse cube of rising height (represented as a proportion of the cone's overall height):

The volume of the cone above water is [tex]1/8$[/tex] the total volume of the cone (mountain). Since these cones are obviously comparable, the little cone's radius and height must equal

V1 × Height³= VN

1/8= Height³

Height=1/2

8000.1/2=4000= A

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The inequality that represents the situation is 15c + 5b ≥ 165.

What is inequality?

Inequality means not equal. Generally, if two values are not equal, we use the “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

We can start the inequality by using the following equation:

15c + 5b ≥ 165

This equation represents the total number of daisies used in the floral arrangements.

The left side of the inequality is the total number of daisies used in centerpieces (15c) plus the total number of daisies used in bouquets (5b), and it must be greater than or equal to 165 (the minimum number of daisies needed for the wedding).

Hence, the inequality that represents the situation is 15c + 5b ≥ 165.

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The number of weeks that he will be able to buy the game will be 6 weeks.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Marcus starts with $5 in his piggy bank. He receives a $10.00 allowance each week. Each week he saves $7.00 of his allowance in his piggy bank. His goal is to save at least $47.00 to buy a game.

Let 'x' be the number of weeks. Then the inequality is given as,

$5 + $7x ≥ $47

Simplify the inequality, then we have

$5 + $7x ≥ $47

$7x ≥ $42

x ≥ 6 weeks

The number of weeks that he will be able to buy the game will be 6 weeks.

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Grace usually does 221 performances each year

last year , she does +10 perfromances

to calculate total number of performances in year Y

we will add ( 221 + 10)= 231

therefore, grace completed 231 performances last year

Answer:231

Step-by-step explanation:

just add 10

The standard form of the equation y - 11 = (-4/3)(x+7) is 3y = -4x + 5.

What is standard form?

The general method of representing any kind of notation is known as the standard form. The equation's standard form, which is also known as the approved form of an equation, is represented by the standard form formula.

The given equation is -

y - 11 = (-4/3)(x+7)

The standard form of the equation is y = mx + b.

Solving the equation -

y - 11 = (-4/3)(x+7)

3(y-11) = -4(x+7)

3y - 33 = -4x - 28

3y = -4x - 28 + 33

3y = -4x + 5

Therefore, the standard form is 3y = -4x + 5.

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The ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594 is 7,140:18.

The greatest common factor (GCF) of 180 and 594 is 18.

The least common multiple (LCM) of 180 and 594 is 7,140.

Therefore, the ratio of the LCM to the GCF is 7,140:18.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 180 and 594, you can use the prime factorization method. First, you need to prime factorize each number.

180 = 2 x 2 x 3 x 3 x 5 and 594 = 2 x 7 x 17.

Then, you need to identify the greatest common factor among the prime factors of each number. The prime factors of 180 and 594 that are common to both are 2 and 2, which means that the GCF of 180 and 594 is 18. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 180 and 594, you can use the prime factorization method. First, you need to prime factorize each number. 180 = 2 x 2 x 3 x 3 x 5 and 594 = 2 x 7 x 17. Then, you need to identify the least common multiple among the prime factors of each number. The LCM of 180 and 594 is 2 x 2 x 3 x 3 x 5 x 7 x 17, which is 7,140.

Therefore, the ratio of the LCM to the GCF is 7,140:18.

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The value of x is 2.5.

The centroid theorem states that, the centroid of a triangle equals two-third of the distance from each midpoint of a triangle to each vertex.

Given;

BD = 6x+4

DF = 4x-1

Now,

BD = 2/3(BF)

BD = 2/3(BD+DF)

Substituting the values of BD and DF

4x + 5 = 2/3(6x+4+4x-1)

4x + 5 = 2/3(10x+3)

4x - 6x -20x/3 = 1

(-6x-20x)/3=1

26x/3=1

x=3/26

Therefore, based on the centroid theorem, the value of x will be 3/26.

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The slope represented in terms of the given context will be 2 minutes per mile. Then the correct option is D.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A car is traveling at a constant speed. The table below represents the time it takes the car to travel several distances.

The slope of the car is given as,

Slope = 30 / 15

Speed = 2 minutes per mile

The slope represented in terms of the given context will be 2 minutes per mile. Then the correct option is D.

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