The scatter plot shows the relationship between the number of car accidents on a month and the number of drivers attending a program on distracted driving. The equation represents the linear model for this data.

y= -0.0067x+17

What does the number 17 in the equation mean in this context?


There were no accidents per month when there were 17 drivers in the program.


For every 100 drivers in the program, there are 17 accidents per month.


There were 17 drivers in the program when it started.


The number of accidents decreases by 17 for every 100 drivers in the program.


There were 17 accidents per month when there were no drivers in the program.

Find cost per ounce:

1.92 / 16 = 0.12 per ounce

0.12 x 40 = 4.80

The answer is $4.80

Answer:

$4.8

Step-by-step explanation:

In order to find the answer, you would need to divide $1.92 by 16 ounces to get how much cereal it costs for one ounce which is $0.12. After that, you would need to multiply $0.12 times 40 which would equal $4.8

Hope this helps and have a great day:)

The probability of both events E and F occurring, denoted as P(E and F), is equal to 0.12 or 12%. This result is obtained by multiplying the probability of event E given event F (P(E/F)) by the probability of event F (P(F)).

Given that P(F) = 0.2 represents the probability of event F occurring and P(E/F) = 0.6 represents the probability of event E occurring given that event F has occurred, we can calculate P(E and F) using the formula for conditional probability.

Conditional probability states that P(E and F) is equal to the product of P(E/F) and P(F).

By substituting the given values into the formula, we have P(E and F) = 0.6 * 0.2 = 0.12.

Therefore, the probability of both events E and F occurring is 0.12, which is equivalent to 12%. This means that there is a 12% chance of event E happening when event F has occurred, based on the given probabilities.

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The coefficient of the term 2 in the expansion of (1−2a + a²)³ is −3

The binomial expansion of (1−2a + a²)³ is as follows:

(1−2a + a²)³ = 1³ − 3(2a)(1²) + 3(1)(4a²) − 3(1)(a²)² + (a²)³= 1 − 6a + 12a² − 8a³ + a⁴

Therefore, the coefficient of the term 2 is −3, since this term is 12a² (i.e., the coefficient of a² in the expansion of (1−2a + a²)³ is 12, and hence the coefficient of 2 is 12/2 = 6.

Multiplying this by the coefficient of a in the expansion of (1−2a + a²)³, which is −1/2, gives the answer of −3.)

We need to find the coefficient of the term 2 in the expansion of (1−2a + a²)³.

Using the binomial theorem and the fact that 2 = a + (−a), we see that the coefficient of this term is 6 times the product of the coefficient of a and the coefficient of (−a), which are −1/2 and −2, respectively.

Thus, the coefficient of the term 2 is −3.

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Thus the number is 335.

Consider the number is = x

Here we have to find mathematical expression for this question

Since we know by using operations like addition, subtraction, multiplication, and division, a mathematical expression is defined as a group of numerical variables and functions.

Therefore,

According to the question,

He divides it by 5 then = x/5

Then add 2 = x/5 + 2

Therefore it becomes,

x/5 + 2 = 69

      x/5 = 67

Thus, x = 335

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Answer:

A. 86.7

first, the base. length x width.

it's square, so

5.1 x 5.1= 26.01

then the sides. formula for a triangle is base times height divided by 2.

5.1 x 5.95= 30.345 divided by 2 is 15.1725

there are 4 sides, so multiply times 4

4 x 15.1725= 60.69

now, add the base to the sides

26.01 + 60.69= 86.7

Answer: there are 20 pieces of bread.

Step-by-step explanation:

Well, 12*1.5= 18, and 18*1.1111 = 20.

The given sequence is not a geometric sequence, the quotients between consecutive numbers are different.

Remember that the recursive formula for a geometric sequence is:

f(n) = r*f(n - 1)

Where r is the common ratio.

Here we have the terms:

5, 11, 29, 83

To get the value of r, take the quotient between consecutive terms:

r = 11/5 = 2.2

r = 29/11 = 2.63

r = 83/29 = 2.86

We should get the same value of r for every ofthese quotients, then we can conclude that the given sequence of numbers is not a geometric sequence, is other type of sequence.

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The value of x is 4 for the isosceles triangle has a base that measures x+2 with legs that measure 4x-3 and 2x+5.

Therefore, an isosceles triangle has two equal sides as well as two equal angles. An equilateral triangle is one in which all of its sides are equal, and a scalene triangle is one in which none of its sides are equal. The characteristics of an isosceles triangle are as follows: There is agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

Here,

Since the adjacent sides of isosceles triangles are equal,

4x-3=2x+5

4x-2x=5+3

2x=8

x=4

The isosceles triangle has a base that measures x+2 and legs that measure 4x-3 and 2x+5, so x is equal to 4.

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The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/4.A spinner is a gambling tool used for games and competitions. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result.

When it stops, a pointer will land on one of many different numbered segments of the spinner, each of which corresponds to a particular reward or consequence. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result. Probability is the study of the likelihood of events taking place.

Probability is expressed as a fraction, decimal, or percentage and is always between 0 and 1. The probability of an event can be calculated using the following formula: Probability = number of favorable outcomes / total number of possible outcomes. Given the spinner has a polka-dot section, 2 white sections, and 1 shaded section, it has a total of 4 sections.

Therefore, the probability of the spinner stopping at a polka-dot section is 1/4.Also, after the first spin, the spinner still has 2 white sections. Therefore, the probability of stopping at a solid white section is 2/4 or 1/2 (since there are only 2 possible outcomes after the first spin).

To determine the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section, we must multiply the probability of each event.1/4 × 1/2 = 1/8

Hence, the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

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Answer:

The answer is C

I did the quiz on edge

Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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Answer:

9 or 16... but I'm leaning more to 9

Step-by-step explanation:

Since the graph seems to be going up and down, it seems like its at its highest point and should go down now so it could be 9. But if not and its still going to go higher 16 is possible.

Standard form of given expanded form of a number is 16518.

The expanded form of the number is the splitting of numbers based on the place value, such as ones, tens, hundreds, thousands, ten thousand, and so on. The number that is represented by the sum of each digit multiplied by its place value is called the expanded form of the number.

Given

Expanded form = (5×1,000)+(7×10)+(8×1)+(4×110)+(1×11,000)

We have to convert the expanded form into standard form

= 5000 + 70 + 8 + 440 + 11000

= 16518

Thus, standard form of given number is 16518.

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Answer:

16,518

(or  1.6518 x 10⁴)

Step-by-step explanation:

Expanded form:  The digits of a number are split into individual digits based on their place value.  Each digit of a number can be written in  multiple of 1, 10, 100, 1000, etc.

Standard form:  The combination of digits written together as a single number.

The given number is not quite, but almost, written in expanded form:

(5 × 1,000) + (7 × 10) + (8 × 1) + (4 × 110) + (1 × 11,000)

For it to truly be written in expanded form, the (4 × 110) would be written as (4 × 10) + (4 × 100) and the (1 × 11,000) would be written as either (11 × 1,000) or (1 × 10,000) + (1 × 1,000).

If the number should be written in standard form as defined above, carry out the operations in the parentheses, then add them together:

\(\large\begin{array}{l c r}8 \times 1 & = & 8\\7 \times 10 & = & 70\\4 \times 110 & = & 440\\5 \times 1000 & = & 5000\\1 \times 11000 & = & 11000\\\cline{3-3}& & 16518\end{array}\)

-----------------------------------------------------------------------------------------------------

However, in math there is another type of Standard Form (also called "Scientific notation") that is written in the form of \(a \times 10^n\), where  \(1\leq a < 10\)  and  \(n\) is any positive or negative whole number.

To convert a number into standard form, move the decimal point to the left or right until there is one digit to the left of the decimal point.

The number of times you have moved the decimal point is the power of 10 (\(n\)).

If the decimal point has moved to the left, the power is positive.

If the decimal point has moved to the right, the power is negative.

To convert 16518 into standard form:

Move the decimal point 4 places to the left and multiply by 10 to the power of the number of places the decimal was moved (4):

⇒ 1.6518 x 10⁴

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**I have provided both standard forms, as it is not clear from the question which is required.**

Answer:

rocket ships

Step-by-step explanation:

rocket ships

obamnia

Therefore, the solution of the given problem of equation is the  time it will take to double is  4 hours.

When two mathematical expressions in an equation have identical values, the expressions are said to be equal. There is a mathematical formula that proves the equivalence of two variables. The equal ('=') symbol designates it. For instance, 8+2=12-2 is the formula. According to the equation above, the left and right sides of the equation are equal. Therefore, an equation is a statement that "this equals that."

Here,

Given:At 4000 bacteria, a culture of bacteria begins. There are 5000 people left after an hour.

thus,

the amount of time it will take to double is

x is the rate by which it increases

=> 4000*x = 1000

=> x = 1/4

So the time it will take to double is

=> time:

=> y * 1/4 * 4000 = 4000

=>  y *1000=4000

=> y =4

Therefore, the solution of the given problem of equation is the  time it will take to double is  4 hours.

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Using a proportional relationship, it is found that the unit rate of change is of 9.

The relation d = 9t is graphed at the end of the answer.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, we have d as a function of t, hence the relationship is:

d = kt.

When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:

k = d/t = 1.8/0.2 = 9

The relation d = 9t is graphed at the end of the answer.

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The probability of guessing at least 11 out of 15 questions correctly is 0.059.

The probability of guessing any one question correctly is 1/2, and the probability of guessing any one question incorrectly is also 1/2.

Since each question is an independent trial with only two possible outcomes, this situation can be modeled using a binomial distribution with n = 15 (the number of trials) and p = 1/2 (the probability of success on each trial).

To find the probability of guessing at least 11 out of 15 correctly, we need to calculate the probability of guessing 11, 12, 13, 14, or 15 questions correctly, and then add these probabilities together.

Using the binomial probability formula, we can calculate the probability of guessing exactly k questions correctly as:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

where nCk is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

For k = 11, we get:

P(X = 11) = (15C 11) * (1/2)¹¹ * (1/2)¹⁵⁻¹¹ = 0.042

For k = 12, we get:

P(X = 12) = (15 C 12) * (1/2)¹² * (1/2)¹⁵⁻¹²= 0.014

For k = 13, we get:

P(X = 13) = (15 C 13) * (1/2)¹³ * (1/2)¹⁵⁻¹³ = 0.003

For k = 14, we get:

P(X = 14) = (15C14) * (1/2)¹⁴ * (1/2)¹⁵⁻¹⁴ = 0.000

For k = 15, we get:

P(X = 15) = (15C15) * (1/2)¹⁵ * (1/2)¹⁵⁻¹⁵= 0.000

To find the probability of guessing at least 11 out of 15 correctly, we add these probabilities together:

P(guessing at least 11 out of 15 correctly) = P(X >= 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.059

Therefore, the probability of guessing at least 11 out of 15 questions correctly is 0.059.

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a. The length of the arc drawn across the fair landing area is approximately 6.777 meters.

b. The area of the sector bounded by the arc is approximately 162.042 square meters.

To find the length of the arc, we need to calculate the circumference of the circle formed by the landing area.

The central angle of the sector is given as 34.92°, which represents a fraction of the total circumference of the circle.

The formula to find the length of an arc is given by:

Arc Length = (Central Angle / 360°) × Circumference

In this case, the central angle is 34.92° and the circumference is the distance covered by the farthest throw, which is 21.89 meters.

Arc Length = (34.92° / 360°) × 2πr

We need to find the radius (r) of the circle. Since the farthest throw covers the radius, we have:

r = 21.89 meters

Now we can calculate the arc length:

Arc Length = (34.92° / 360°) × 2π × 21.89 meters

Arc Length ≈ (0.097 × 2π × 21.89) meters

Arc Length ≈ 6.777 meters

To calculate the area of the sector bounded by the arc, we need to use the formula:

Area of Sector = (Central Angle / 360°) × π × r²

Using the given central angle of 34.92° and the radius of 21.89 meters, we can calculate the area:

Area of Sector = (34.92° / 360°) × π × (21.89 meters)²

Area of Sector ≈ (0.097 × π × 21.89²) square meters

Area of Sector ≈ 162.042 square meters

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Answer:

The depth of oil in the tin is 9cm

Step-by-step explanation:

The first thing we need to do here is to calculate the volume of the cylindrical tin.

Mathematically, that would be;

V = pi * r^2 * h

now, r = d/2 = 12/2 = 6cm

h = 14 cm

Thus the volume would be;

V = 22/7 * 14 * 6^2 = 1,584 cm^3

Now, to find the the depth of the tin, we have to realize that the content of the cylinder should fill in the tin to a particular height.

Now let’s say the height of the tin is x, this means its volume which is l * b * h = 16 * 11 * x = 176x

So the depth x would be;

176x = 1584

x = 1584/176 = 9 cm

Answer:

The vertex is located on the x-axis between the second and third quadrants

Step-by-step explanation:

Whereby the function is f(x) = (x + 3)², we have;

f(x) = (x + 3)² = x² + 6·x + 9

The vertex, (h, k), of the quadratic function given in general form, a·x² + b·x + c is found as follows;

h = -b/(2·a) and k = f(h)

Therefore by comparison of the given quadratic function and the general form of a quadratic function, we have;

a = 1, b = 6, c = 9

h = -6/(2 × 1) = -3

k = f(-3) = (-3)² + 6 × (-3) + 9 = 0

The vertex (h, k) = (-3, 0)

Therefore, the location of the vertex is on the x-axis axis between the second and the third quadrant.

Let

y -----> number of quarters

x ----> number of dimes

we have that

the inequality that represents this situation is

Remember that

1 quarter =$0.25

1 dime=$0.10

so

rewrite the variables

see the attached figure to better understand the problem

Part 4b

The solution of the given inequality is the shaded area above the solid line 0.25q+0.10d=8.50

A solution to this inequality could be the point (50,50)

that means

the number of quarters is 50 and the number of dimes is 50

the ordered pair must satisfy the inequality

Verify

Part 4c

we have that

d=25 dimes

substitute in the inequality and solve for q

so

solve for q

the number of quarters must be greater than or equal to 24

Answer:

Ummmm... I'm sorry but there is no graph or equation, so I can't answer this question with them...

The objective function is option D. Minimize C = 0.1x + 0.01y.

The objective function is the equation that represents the quantity that needs to be optimized or minimized. In this case, the company wants to keep the cost as low as possible. The cost is determined by the amount of chicken and grain used in each bag of dog food. Therefore, the objective function is the cost equation.

The cost of chicken is $0.10 per ounce and the cost of grain is $0.01 per ounce. Thus, the cost equation is:

C = 0.10x + 0.01y

where C is the total cost of the dog food in dollars, x is the number of ounces of chicken, and y is the number of ounces of grain.

Therefore, the correct answer is option D. Minimize C = 0.1x + 0.01y.

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The cost of the popcorn is $8.

The equation that represents the total cost of your friend's purchase, including the cost of the popcorn, can be written as:

Total cost = Cost of the drink + Cost of the popcorn

To know more about how to calculate the total cost of your friend's purchase, refer here:

To calculate the total cost, we need to add the cost of the drink to the cost of the popcorn. Given that the drink cost $6, we can represent it as "Cost of the drink = $6." Let's denote the cost of the popcorn as "Cost of the popcorn = P." Since we want to find the total cost, we can substitute the given values into the equation:

Total cost = $6 + P

The total cost of your friend's purchase was given as $14. Substituting this value into the equation, we get:

$14 = $6 + P

To solve for the cost of the popcorn, we need to isolate the variable P on one side of the equation. We can do this by subtracting $6 from both sides:

$14 - $6 = $6 + P - $6

$8 = P

The answer is $8, the cost for popcorn is $8.

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Answer:a

Step-by-step explanation:

a

Answer:

The answer should be:

\(=\frac{8x^3-18x}{3x+2}\)

The closest answer is A, so I'll go with that.

Step-by-step explanation:

So we have the rational expression:

\(\frac{4x^3-9x}{2x-7}\div\frac{3x^2+2x^2}{4x^2-14x}\)

First, remove the division sign. To do so, turn the division into multiplication and flip the second term:

\(\frac{4x^3-9x}{2x-7}\cdot \frac{4x^2-14x}{3x^2+2x}\)

Now, simplify. From the first term, in the numerator, factor out a x. On the second term, factor out a 2x in the numerator and a x in the denominator:

\(\frac{x(4x^2-9)}{2x-7}\cdot\frac{2x(2x-7)}{x(3x+2)}\)

Multiply straight across:

\(\frac{x(4x^2-9)(2x)(2x-7)}{(2x-7)(x)(3x+2)}\)

Cancel out the (2x-7):

\(\frac{x(4x^2-9)(2x)}{x(3x+2)}\)

Cancel out the x:

\(\frac{(2x)(4x^2-9)}{(3x+2)}\)

At this point, we can factor the (4x^2-9) term, but we won't be able to cancel it out. Thus, this is the simplest it can get.

To get the answer, expand the numerator:

\(=\frac{8x^3-18x}{3x+2}\)

Thus, the answer is...

A?

Answer:

The right solution is option a : \(\frac{8x^2 - 18}{3x+2}\)

Step-by-step explanation:

We have to simplify the following rational expression,

\(\frac{4x^3-9x}{2x-7}\) ÷ \(\frac{3x^3+2x^2}{4x^2-14x}\)

Take into account the rule (a / b) / (c / d) = ad / bc. This simplifies the expression a bit further --- (1)

\(\left(4x^3-9x\right)\left(4x^2-14x\right)\) ÷ \(\left(2x-7\right)\left(3x^3+2x^2\right)\)

Let's now factor each individual expression as demonstrated below. Afterwards we can substitute back into the expression above --- (2)

Goal - Factor : (4x³ - 9x)(4x² - 14x),

4x³ - 9x ⇒ x(4x² - 9)

4x² - 14x ⇒ 2x(2x - 7)

\(x\left(4x^2-9\right)\cdot \:2x\left(2x-7\right) = 2x^2\left(4x^2-9\right)\left(2x-7\right)\)

That leaves us with the following expression,

\(2x^2\left(4x^2-9\right)\left(2x-7\right)\) ÷ \(\left(2x-7\right)\left(3x^3+2x^2\right)\)

As you can see the " 2x - 7 " cancel out, and the " x² " cancel as well, leaving us with a further simplified expression,

\(2\left(4x^2-9\right)\) ÷ \(3x+2\)

Which can also be rewritten as \(8x^2 - 18\) ÷ \(3x + 2\) = \(\frac{8x^2 - 18}{3x+2}\), in other words the first option.

The equation that represents n; the number of pages Steph read on Monday is B (52 − 16) × 2 = n

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The following can be deduced:

Lara read 52 pages.

Jack read 16 fewer pages than Lara.

Steph read 2 times as many pages as Jack.

The pages for Steph will be:

= 2(52 - 16)

In conclusion, the correct option is B.

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Answer:

x≤-4 or x≥0.5

Step-by-step explanation: