Brain Builders

Use the graph for Exercises 24 and 25.
24. Before leaving the grocery store, Kenny wrote the
y-coordinate first and the x-coordinate second when telling
his sister where to meet him. To his surprise, she was at
the right location. If his sister did not make an error, where
did the siblings meet? Explain how you know.

The volume of the parallelopiped is 14 cubic units

The volume of a parallelopiped with vector sides a, b and c is given by

V = (a × b).c

We know that the parallelopiped has sides

Thus, we proceed as follows

(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k

Since

So, we have

(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0

= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0

= 5i  -7j - 2k

= (5, -7, -2)

Since (a × b) = (5, -7, -2)

Thus, the volume of the parallelopiped is

V = (a × b).c

= (5, -7, -2).(4, 0, 3)

= 5 × 4 + (-7 × 0) + (-2 × 3)

= 20 - 0 - 6

= 14

So, the volume is 14 cubic units

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Answer:

incorrect

Step-by-step explanation:

y= 1/3x+2 because the slope(m) going up by 1 takes up 3 spaces going out and u it in rise/run form rise being up and run being out and the y intercept(b) is where the y axis and the slope meet (basically it starts at the 2)

The slope of the horizontal line will be zero.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line is the ratio of the rise to the run.

The horizontal line always has zero slopes because the y coordinate will always be the same for two points.

The slope is calculated by the formula below,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

y₂ = y₁

Slope = ( y₁  - y₁ ) / ( x₂ - x₁ )

Slope = 0

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The probability that a rental car delivered to the firm will need a tune-up is 0.05% and the conditional probability is 0.04%

The probability that a rental car delivered to the firm will need a tune-up

From the question, we have the following parameters that can be used in our computation:

Agency 1 = 0.42%,   Tune up from agency 1 = 0.08%

Agency 2 = 0.08%,   Tune up from agency 2 = 0.02%

Agency 3 = 0.5%,    Tune up from agency 3 = 0.02%

Using total probability, we have the following equation

P(tune-up) = P(tune-up | agency 1) * P(agency 1) + P(tune-up | agency 2) * P(agency 2) + P(tune-up | agency 3) * P(agency 3)

Substitute the known values in the above equation, so, we have the following representation

P(tune-up) = 0.08% * 0.42% + 0.02% * 0.08% + 0.02% * 0.5%

Evaluate the sum of products

P(tune-up) = 0.000452

Express as percentage and approximate

P(tune-up) = 0.05%

(b) The probability that it came from agency 2

This is a conditional probability, and it calculated as

P(Agency 2| Tune up) = P(Tune up and Agency 2)/P(Tune up)

Substitute the known values in the above equation, so, we have the following representation

P(Agency 2| Tune up) = (0.02% * 0.08%)/0.0452%

Evaluate

P(Agency 2| Tune up) = 0.0003539823

Express as percentage

P(Agency 2| Tune up) = 0.03539823%

Approximate

P(Agency 2| Tune up) = 0.04%

So, the probability is 0.04%

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Complete question

The members of a consulting firm rent cars from three rental agencies. It is estimated that 0.42 percent of cars come from agency 1, 0.08 percent of cars come from agency 2, and 0.5 percent of cars come from agency 3. It is also estimated that 0.08 percent of cars from agency 1 need a tune-up, 0.02 percent of cars from agency 2 need a tune-up, and 0.02 percent of cars from agency 3 need a tune-up. Answer the following questions, rounding your answers to two decimal places where appropriate.

(a) What is the probability that a rental car delivered to the firm will need a tune-up?

(b) If a rental car delivered to the firm needs a tune-up, what is the probability that it came from agency 2?

Probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%

If the length of the life of an instrument produced by the machine has a normal distribution with a mean of 12 months and a standard deviation of 2 months, then the random variable X representing the length of the life of the instrument is also normally distributed.

To find the probability that X assumes a value greater than 12 months, we need to use the cumulative distribution function (CDF) of the normal distribution. The CDF is given by the formula:

F(x) = (1/2) * [1 + erf((x - μ) / (σ * sqrt(2)))]

where μ is the mean, σ is the standard deviation, and erf(z) is the error function.

Plugging in the given values, we get:

F(12) = (1/2) * [1 + erf((12 - 12) / (2 * sqrt(2)))] = (1/2) * [1 + erf(0)] = (1/2) * [1 + 0] = 1/2

Since the CDF gives us the probability that X assumes a value less or equal than x, we need to subtract F(12) from 1:

P(X > 12) = 1 - F(12) = 1 - 1/2 = 0.5

So the probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%.

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Answer:

Step-by-step explanation:

You want the angles associated with different arc lengths and radii.

The length of an arc is given by the formula ...

  s = rθ . . . . . θ is the angle in radians, r is the radius

Solving for θ gives ...

  θ = s/r

For s=17 in, r=4 in, ...

  θ = (17 in)/(4 in) = 4.25 . . . . radians

For s=12 ft, r=5 ft, ...

  θ = (12 ft)/(5 ft) = 2.4 . . . . radians

For s=8.5 mm, r = 13.6 mm, ...

  θ = (8.5 mm)/(13.6 mm) = 0.625 . . . . radians

Answer: why do we even need math

Step-by-step explanation:

The solution to the inequality is (-∞, 4.05) .An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

Both equations and inequalities are mathematical phrases created by connecting two expressions.

The equal sign (=) in an equation denotes that the two expressions are regarded as equal.

In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.

Given the inequality:

-3(4 – x) 6 < 9 – 2x

Solving the inequality:

(-12 + 3x)6 < 9 - 2x

-72 + 18x < 9 - 2x

20x < 81

x < 4.05

Therefore the solution to the inequality is (-∞, 4.05)

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Answer:

15+5=v

Step-by-step explanation:

Solve

1. Add the numbers

15+5 = v

20 = v

2. Move the variable to the left

20 = v

v = 20

3. Solution

   v = 20

All the table show the linear relationship, but none of the table show the proportional relationship.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

A). x → y

0 → 3

3 → 6

6 → 9

To show the linear relationship:

We have to find the constant first difference.

That means,

6-3 = 3

And 9 - 6 = 3

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/3 = 0,

3/6 = 1/2,

6/9 = 2/3.

The values of this table do not show the proportional relationship.

B). x → y

0 → 4

2 → 6

4 → 8

To show the linear relationship:

We have to find the constant first difference.

That means,

6-4 = 2

And 8 - 6 = 2

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/4 = 4,

2/6 = 1/3,

4/8 = 1/2.

The values of this table do not show the proportional relationship.

C). x → y

0 → 0

6 → 3

12 → 6

To show the linear relationship:

We have to find the constant first difference.

That means,

3-0 = 3

And 6 - 3 = 3

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/0 = undefined,

6/3 = 2,

12/6 = 2.

The values of this table do not show the proportional relationship.

D). x → y

0 → 3

5 → 5

10 → 7

To show the linear relationship:

We have to find the constant first difference.

That means,

5 - 3 = 2

And 7 - 5= 2

The values of this table show the linear relationship.

To show the proportional relationship:

Let x/y = k (k is constant)

We have to find the k:

0/3 = 0,

5/5 = 1,

10/7 = 10/7.

The values of this table do not show the proportional relationship.

Therefore, none of the table show the proportional relationship.

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Answer:

D

Step-by-step explanation:

x²+5x=0

by factorizing;

x(x+5)=0

x=0 or x+5=0

Therefore, x= 0 or x=-5 ---> {0, -5}

The two congruent segments in the figure are LJ and LI.

What is congruency?

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

An included angle is found between two sides that are under consideration.

Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.

In the figure, the two segments marked are LI and LJ these two segments are congruent to each other.

Congruency means the shape and the size of the segments will be equal to each other.

Hence, the two congruent segments in the figure are LJ and LI.

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The function for position x(t) could be x(t) = 3t^2 - 2t + 10.

In mathematics, a function is a relation between two sets that assigns to each element of the first set exactly one element of the second set. In other words, it is a rule that describes how one set of values is related to another set of values. Functions are used to model real-world scenarios and to solve mathematical problems. Examples of functions include linear equations, polynomials, and trigonometric functions.

This is determined by using the equation x'(t) = a(t). Differentiating both sides of the equation, we get x'(t) = 6t - 2. Integrating this equation, we get x(t) = 3t^2 - 2t + C, where C is the constant of integration. Since x(1) = 10, we can substitute this value into the equation and solve for the constant of integration. Therefore, we get x(t) = 3t^2 - 2t + 10.

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Answer:

1 unit to the left, 3 units down

Step-by-step explanation:

Take any point: I will take D. In order to get to D', you need to travel 1 unit along the x-axis towards the left, then 3 until along the y-axis downwards. The same applies for any other point.

Answer: C. 20

Step-by-step explanation:

1 inch is equal to 2.54 cm.

So we have to divide the amount of centimeters given by how many centimeters are in an inch to find how many inches.

50.8 ÷ 2.54 = 20

Hope this helps!!! :)

the inequalities that represent the situation are,

Ox+y≤ 30

0y≤6

0 x ≥ 10

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

Here, given that,

A chef makes small and large snacks to sell at a local art show.

He cannot make more than 30

snacks before the show, with no more than 6 large snacks.

The chef must make at least 10 small snacks to earn a profit.

Let,

x represent the number of small snacks

and y represent the number of large snacks.

Given x ≥ 0 and y 20

So, we get,

the inequalities that represent the situation are,

Ox+y≤ 30

0y≤6

0 x ≥ 10

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If you list the number of tickets sold over time, the kind of sequence will you see is a geometric sequence.

What is a geometric sequence?

A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Here,

We assume that the variable x represents the number of tickets sold previously (initial year) and it sold 7 times as many tickets each year as it did the year before, a mathematical expression that models this situation is given by geometric sequence:

x, 7x, 49x, 343x, .....

Verification:

7/1 = 49/7 = 343/49 = 7

Hence, this is a geometric sequence.

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Answer:

there is not enough info but i think it would be (5,11)

Step-by-step explanation:

divide

Answer:

[tex]y=\dfrac{11}{4}x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Choose two (x, y) points from the given table:

Substitute them into the slope formula:

[tex]\implies \dfrac{22-11}{8-4}=\dfrac{11}{4}[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute point (4, 11) and the found slope into the point-slope formula and rearrange to slope-intercept form:

[tex]\implies y-11=\dfrac{11}{4}(x-4)[/tex]

[tex]\implies y-11=\dfrac{11}{4}x-11[/tex]

[tex]\implies y=\dfrac{11}{4}x[/tex]

Using the expand and trade subtraction the mistake Jordan made was not crossing 400 to 300

1 is carried form 4 to 5 then to 3 to get 13

The expanded form of subtraction makes is easier to conceptualize the subtraction, however it has some techniques that should be in mind in other to handle the techniques correctly

The numbers used in the subtraction is examined

453 and 254

the ones have it that 3 in "453" is less than 4 in "254" and hence will require 1 form 5.

When this happens, in the tens, 5 in "453" will turn to 4 and will be less than the 5 in "254" and will requires 1 from 4 in "453" in hundreds

At this point 4 in "453" is in hundreds and will turn to 300

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The domain of the function F(x) = 3 [tex]\sqrt{x-2}[/tex] is {x : x ≥ 2 and x is a real number}.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given function is,

F(x) = 3 [tex]\sqrt{x-2}[/tex]

Domain of this function is all the values of x for which the function is defined.

The expression [tex]\sqrt{x-2}[/tex] is defined only when the value of x - 2 is positive.

x - 2 > 0 ⇒ x > 2

So the function will be defined for all x > 2.

Hence the domain of the function is the set of all x such that x > 2.

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Answer:

commutative property of addition

Step-by-step explanation:

commutative property of addition

The commutative property of addition allows you to change the order of the numbers in an addition.

For example, 1 + 2 = 2 + 1

Answer:

Step-by-step explanation:

a.we should Make their denominators the same.

16[tex]x^{8}[/tex]÷4x=4[tex]x^{7}[/tex]

b.molecule multiply 4[tex]x^{7}[/tex], 5·4[tex]x^{7}[/tex]=20[tex]x^{7}[/tex]

c.finally, we get it

the answer is 20[tex]x^{7}[/tex]

The total number of satsumas eated by George are 2[tex]\frac{1}{6}[/tex].

Fractions represent the parts of a whole or collection of objects. A fraction has two parts namely numerator (upper part) and denominator (lower part).

Given is that George peels and eats 2 whole satsumas. He then splits another satsuma into 6 equal segments and eats 1 of these segments.

The total number of satsumas eated by him can be written as -

2 + 1/6

2[tex]\frac{1}{6}[/tex]

Therefore, the total number of satsumas eated by George are 2[tex]\frac{1}{6}[/tex].

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Answer:

8x² + 11x + 6

Step-by-step explanation:

6x + 7 + 8x² + 5x - 1 ← collect like terms

= 8x² + (6x + 5x) + (7 - 1)

= 8x² + 11x + 6

Answer:What is a triangle with 2 congruent sides and an obtuse angle

Step-by-step explanation:

Answer:

N = 2

Step-by-step explanation:

We must solve for N.

Solve inside the parenthesis if needed, otherwise open them

7n + 21 = (14) + (21)

Now solve, then simplify

7n + 21 = 35

7n = 35 - 21

7n = 14

N = 2

Answer:

You would first divide the amount of months by the total amount of money that she has earned in 5 months.

(You put down 25, 00, 000 so Ima just write it as 2,500,000)

25,000,000/5 = 5,000,000

She earns 5,000,000 a month, and would earn 60,000,000 per year.

Anual salary is how much money you would earn per year, so the answer is 60,000,000. (sixty million).

Step-by-step explanation:

Hope it helps! =D

The population change for each period is given as follows:

Hence the average annual change for the period between 1970 and 1995 is given as follows:

7,932,000 people a year.

The population change over a period is given by the subtraction of the population at the end of the period by the population at the beginning of the period.

The population data for each year is given by the table on the image presented at the end of the answer.

Hence the changes are obtained as follows:

The change between 1970 and 1995 is of:

5.691 - 3.708 = 1.983 billion.

This period is composed by 25 years, hence the average annual change is of:

1.983/25 = 0.07932 billion people a year = 7,932,000 people a year.

The chart is given by the image presented at the end of the answer.

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Answer:

Answer:Step-by-step explanation:GivenRequiredDetermine g(w)First, we'll write an expression for g(w)From the question, we understand that she withdrew $40 from her account balance in w weeks.This implies that:Where f(w) is the account balance in w weeks and $40 is the withdrawn amountSubstitute 250 + 10w for f(w)Collect Like TermsRecall that:This means that function f(w) when shifter by 40 units downward, gives g(w)

Step-by-step explanation:

The effect of subtracting 2 from the input on the graph of the function is a translation of 2 units to the right.

For any function f(x), we define a horizontal translation of N units as:

g(x) = f(x + N)

And what this does, is translate the graph N units horizontally.

if N > 0, then the translation is to the left.

if N < 0, then the translation is to the right.

Here we want to subtract 2 from the input, so we will get:

f(x - 2)

By using the definition above, we know that we will have a translation of 2 units to the right.

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