Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $10, and each wrench costs $6. If the solution region represents the number of hammers and wrenches that Brody can buy given his budget, determine which graph represents the solution set to the system of inequalities representing this situation.

[tex] |\Omega|=30\\
|A|=24\\\\
P(A)=\dfrac{24}{30}=\dfrac{4}{5}=0.8 [/tex]

You can calculate the number of ways to arrange the flags using the formula for permutations of multi-sets. We substitute the quantities of each flag color into the formula, which yields our answer of 1260 ways to arrange the flags.

The question is asking about permutations of different objects— in this case, flags of multiple colors. For such problem, you can use the formula for permutations of multiset:

P(n1, n2, ..., nk) = (n1 + n2 + ... + nk)! / (n1! * n2! * ... * nk!)

Where n1, n2, ..., nk represent the counts of each distinct item (in this case, flag colors).

For our flags, you would substitute n1=4 (blue flags), n2=3 (green flags), and n3=2 (red flags). Applying the formula gives us (4+3+2)! / (4!*3!*2!) = 9! / (4!*3!*2!) = 1260.

So, "there are 1260 ways to arrange 4 blue flags, 3 green flags and 2 red flags that the student has".

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Sin(x) = .2588     Given

ARCSin (x) = x = ARCSin(.2588)        Using the calculator   = 14.9988 degrees  ( ~ 15 degrees)   

COMPLIMENTARY angle is the angle which added to 'x' will equal 90      so the COMPLIMENTARY Angle is 75 degrees

Using the calculator again    cos (75) = .2588   The same as the complimentary angle's SIN !!!

Add  7.5+9.63 which would be 17.13

17.13+N

Answer: A.) The mean is greater than the median, and the majority of the data points are to the left of the mean.

It is clear that most of the data (around 75%) is consist of value 1, which is the leftmost part of the data. Since it was more than 50% of the data, the median should be 1.

if 75% data is 1, it need 25% data with value at least 5 to make the means equal to 2. The means would be bigger than 1 but less than 2, so most(75% data is 1) of the data would be on the left of the mean

If we draw a normal distribution bell curve as shown in the attachment, we can see that the bell curve is skewed to the right . This means it has a right tail. This means few points are to the right of the mean. In other words, we can say that majority of the data points are to the left of the mean

Since the majority of the data points are to the left, the median will also be to the left of the mean which indicates median is lesser than mean . In other words, mean is greater than median

So, answer is: A.) The mean is greater than the median, and the majority of the data points are to the left of the mean.

The question involves high school level mathematics, specifically geometry and trigonometry, discussing the angle of depression, cross-sectional area, angles, distances, and congruent triangles.

The question relates to the angle of depression and concepts of geometry involving angles and distances. In the context provided, the angle of depression from point R to S is being discussed, but not enough information is given to define the angle. The references to cross-sectional area, small-angle approximation, and congruent triangles touch on topics in geometry and trigonometry that are critical to understanding the properties of shapes, sizes, and angles in mathematical problems.

In the mathematical equations provided, 'S' is used as a variable representing a stress value, with reference to pressure units of N/m², and 'r' represents a radius which is then used to calculate an area. The references to a graph with a slope and 'y = mx + b' appear to relate to linear equations and representations in coordinate geometry.

The descriptions involving angle vector, position vector, arc length vector, and angle of distance between two points separated by an angle further contribute to the idea that this question falls under the Mathematics category, addressing high school level concepts in geometry and trigonometry.

Answer: DA:FA=KE:EF, DF:DA=KF:KE and FA:DA=EF:KE are correct.

Explanation: Since, [tex]\triangle EFA[/tex] and [tex]\triangle KFD[/tex] are similar triangles.

Because, [tex]\angle FAE= \angle FDK[/tex] and [tex]\angle FEA= \angle FKD[/tex] (because EA and KD are parallels. And, [tex]\angle F[/tex] is common angle for these triangles.

Therefore, according to the property of similar triangles.

FE:EK= FA:AD, FE:FK=FA:FD and DF:DA=KF:KE .

Thus, first, second and third options are correct.

The polynomial u^2v^3w is classified as a monomial because it consists of a single algebraic term. Monomials are polynomials with exactly one term, unlike binomials or trinomials which have two or three terms, respectively.

The classification for the polynomial u^2v^3w is a monomial. A monomial is a single term algebraic expression with one or more variables raised to a non-negative integer power. Since u^2v^3w consists of a single term without a plus (+) or minus (-) sign connecting it to other terms, it is considered a monomial.

The classification of polynomials is based on the number of terms they contain:

Knowing the classification of polynomials helps in understanding how to perform operations such as addition, subtraction, multiplication, and division with them.

Answer:

11

Step-by-step explanation:

Answer:

Ratio of the volumes of the cubes = 216 : 343

Step-by-step explanation:

Since surface area of a cube is represented as 6a² where a is the side of a cube.

Let a is one side of large cube and b is the side of smaller one.

Ratio of their surface area = [tex]\frac{6a^{2} }{6b^{2}}=\frac{72}{98}[/tex]

[tex](\frac{a}{b})^{2}=\frac{36}{49}[/tex]

[tex]\frac{a}{b}=\sqrt{\frac{36}{49}}[/tex]

[tex]\frac{a}{b}=\frac{6}{7}[/tex]

Now ratio of the volumes = [tex]\frac{a^{3} }{b^{3}}=(\frac{1}{b})^{3}[/tex]

Ratio = [tex](\frac{6}{7})^{3}=\frac{216}{343}[/tex]

Therefore, ratio of the volumes of the cubes = 216 : 343

Answer:

Option D. [tex]882\pi\ units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

In this problem we have

[tex]r=7\ units[/tex]

[tex]h=18\ units[/tex]

substitute

[tex]V=\pi (7^{2})(18)=882\pi\ units^{3}[/tex] -----> exact value of the volume

The answer to this question is B Ed

The table that represents a direct variation function is

x y

-3 -7.5

-1 -2.5

2 5.0

5 12.5

10 25.0

For a table to represents a direct variation, the following must be true

k = y/x

Where k represents the constant of variation

In table 3,  we have:

k = 25.0/10 = 12.5/5 = 5.0/2 = -2.5/-1 = -7.5/-3

This gives

k = 2.5

The value of k is the same for all input and output values

Hence, the table that represents a direct variation function is the table 3

Read more about direct variation at:

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