Please help..........

Defined and undefined terms in mathematics work together to create precise definitions and relationships.

Defined terms in mathematics have clear, specific meanings established within a system, while undefined terms are fundamental concepts that are not formally defined. Defined terms can be combined with undefined terms to create more complex definitions and relationships.

Answer:

3/32

Step-by-step explanation:

Labels from 1 to 8:

The probability that he gets a number less than 4 (1, 2, 3) is 3/8

The probability to get a multiple of 4 (4, 8) is 2/8 = 1/4

So

The probability that he gets a number less than 4 or a multiple of 4:

= 3/8 x 1/4

= 3/32

Answer

3/32

Answer:

The answer is 5/8.

I saw an answer that gave 3/32, and since I knew that was wrong I wanted to give my answer to not lead others astray.

Step-by-step explanation:

There are 8 numbers john can pick.

Numbers less than 4 are (1, 2, 3)

Numbers that are a multiple of 4 are (4, 8)

The word "or" in the question implies addition, and adding 3/8 and 2/8 yields a result of 5/8. This is also the answer in the test that I took.

Answer:

5/6

Step-by-step explanation:

Just plug in five where n is.

In this case, it would be:

5/(5+1) or 5/6

Answer:

C

Step-by-step explanation:

Expand the factors to obtain the product.

Each term in the second factor is multiplied by each term in the first factor

(3x + 2)(2x - 3)

= 3x(2x - 3) + 2(2x - 3) ← distribute both parenthesis

= 6x² - 9x + 4x - 6 ← collect like terms

= 6x² - 5x - 6 → C

Answer: C: 156 mi

Step-by-step explanation:

Driving north then east or west is 90 degrees rotation internally. Distance of Chad from his home to his final location is Option B: 130 mi

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

A right angled triangle is a triangle having one of its angle with measure of 90 degrees.

The slant side of that triangle is called Hypotenuse and it is the longest side in that triangle.

Referring to the diagram attached below, as Chad moved from north driving to east driving, thus, he made a 90 degrees angle internally as perpendiculars are with 90 degrees. Then joining his first and final position, we get a right angled triangle. Thus,

Distance of Chad from final point to his home = length of AC = |AC|

A is the starting point of Chad. His speed was 60 mph for the first travel in the north direction. He traveled 2 hours. Since each hour he travels 60 miles(from his speed), and he spent 2 hours so 60 + 60 = 120 miles covered.

Thus, |AB| = distance traveled in north direction is 120 miles.

Similarly, as he traveled in east for 1 hour with speed 50 mph, thus, he traveled 50 miles. Thus,

Length of BC = |BC| = 50 miles.

His distance from his home A to his final position C is calculated as follows.

Using Pythagoras theorem, we get:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{120^2 + 50^2} = \sqrt{16900} = 130 \: \rm miles\\\\[/tex]

(we took positive root since |AC| is length's measure., which is a non-negative quantity)

Thus,

Distance of Chad from his home to his final location is Option B: 130 mi

Learn more about Pythagoras theorem here:

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The heads probability is ½ and the two’s probability is 1/6. So ½ x 1/6 gives you 1/12. The answer is A. 1/12. Hope this helps.

Answer:

A. 1/12

Step-by-step explanation:

There are 2 outcomes for a coin, heads and tails.

To get heads, it's 1/2.

There are 6 outcomes for a six-sided number cube, 1,2,3,4,5,6.

To get a 2, and since there is only one 2, it's 1/6.

Multiply them together, 1/2 times 1/6, you get 1/12.

The explicit formula that will be used to find the cost of cleaning up d day oil spill is:

                  [tex]CoS(d)=532.5d+2[/tex]

The amount of oil, S, in tons, that has been spilled in d days is given by the function:

             S(d)=355d.

The cost to clean a t ton oil spill can be modeled by the function:

                       C(t)=1.5t+2

This means that the cost to clean in d days is given  by the composition function:    

 [tex]CoS(d)=C(S(d))\\\\\\i.e.\\\\\\CoS(d)=C(355d)\\\\\\i.e.\\\\\\CoS(d)=1.5(355d)+2\\\\\\i.e.\\\\\\CoS(d)=532.5d+2[/tex]        

A 5-day spill would cost approximately 2664.5 million dollars to clean up.

Cost of Cleaning Up an Oil Spill

To find an explicit expression that models the costs of cleaning up a d day oil spill, we need to connect the functions C(t) and S(d).

The cost function is given by:

C(t) = 1.5t + 2

The amount of oil spilled over d days is given by:

S(d) = 355d

First, substitute S(d) into the cost function where t represents the amount of oil spilled:

C(S(d)) = 1.5(355d) + 2

Simplify the expression:

C(d) = 532.5d + 2

Therefore, the explicit expression that models the costs of cleaning up a d day oil spill is C(d) = 532.5d + 2 (in millions of dollars).

Example

If the oil leakage lasts for 5 days, then the cost can be calculated as:

C(5) = 532.5(5) + 2 = 2662.5 + 2 = 2664.5 million dollars.

This shows the significant financial impact of prolonged oil spillage.

A study by economist Mark Cohen highlights the economic benefits of preventing oil spills, making more stringent environmental protection justified.

rolling a 5= 11/100

getting tails=71/29

i’m pretty sure you times the fractions together to get an overall probability

The probability of rolling a 5 on number cube and tail on coin is:

            [tex]P(A\bigcap B)=\dfrac{781}{10000}[/tex]

                                      or

          [tex]P(A\bigcap B)=0.0781[/tex]      

Let A denote the event of rolling a 5 on the number cube.

and B denote the event of coin landing on tails.

Let P denote the probability of an event.

Also, event A is independent of event B.

( Since, both the events are not affected by happening of each other )

We are asked to find the probability:  P(A∩B)

We know that:

[tex]P(A\bigcap B)=P(A)\cdot P(B)[/tex]

( Since, both the events are independent )

Also,

[tex]P(A)=\dfrac{11}{100}[/tex]

( Since, 5 occurs 11 times out of a total of 100 times on the number cube )

and

[tex]P(B)=\dfrac{71}{100}[/tex]

Hence, we have:

[tex]P(A\bigcap B)=\dfrac{11}{100}\times \dfrac{71}{100}[/tex]

i.e.

[tex]P(A\bigcap B)=\dfrac{781}{10000}[/tex]

i.e.

[tex]P(A\bigcap B)=0.0781[/tex]

We can only sum matrices with equal order, so we can't sum matrices A and B in the first exercise.

As for the second exercise, we have:

All of these answers depend on the fact that the sum/difference of two matrices is simply the sum/difference of the correspondent elements. So, if the element in the i-th row and the j-th column of A is [tex]a_{ij}[/tex] and the element in the i-th row and the j-th column of B is [tex]b_{ij}[/tex], we have

[tex]C=A+B\implies c_{ij} = a_{ij}+b_{ij}[/tex]

So, the sum between matrices inherits the properties of the sum between numbers: the order matters when you subtract (which is why a and f are false), the sum is commutative (which is why b, c, d are true) and associative (which is why e is true).

Subtracting vectors is akin to adding their opposites, and the operations are commutative and associative. Graphically, vector subtraction involves reversing a vector's direction before adding. Straight-line vector addition or subtraction simply depends on magnitudes and directions.

When dealing with adding and subtracting matrices or vector addition and subtraction, it's important to understand that these operations have straightforward rules. In particular, subtracting vectors can be interpreted as adding vectors in the opposite direction - this is analogous to scalar subtraction, such as how 5 - 2 can be thought of as 5 + (-2). Graphically, this means that when subtracting vectors, you essentially reverse the direction of the vector being subtracted and then perform vector addition as you would normally.

Mathematically, the vector addition is associative and commutative, and these properties extend to matrix addition as well. Likewise, multiplying vectors or matrices by scalars follows the distributive property. In a practical sense, when vectors are aligned on a straight line, adding or subtracting them is simplified since you only need to consider their magnitudes and directions along that line.

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Answer: 51 feet

Since we know George's height, the length of George's shadow, and the length of the flagpole's shadow we have all the information we need

Now we can set up a relationship between George and the flagpole:

[tex] \frac{6}{10} = \frac{x}{85} [/tex]

6 represents George's height

10 represents the length of George's shadow

x is the unknown height of the flagpole

85 is the length of the flagpole's shadow

Now you solve for x:

[tex]x = \frac{85 \times 6}{10} \\ x = \frac{510}{10} \\ x = 51[/tex]

So, the height of the flagpole is 51 feet

Answer:

I would say d bit I'm not 100% sure

Choice A. It is the only answer that makes sense.

Answer:

9 bottles of soda can be bought.

Step-by-step explanation:

Let chips represented by x

and soda represented by y

then

x + y = 14     eq(1)

and

5x + 3y = 52    eq(2)

Solving the equations simultaneously we can find the value of x and y

Multiplying eq(1) with 5 and subtracting from eq(2)

5x + 3y = 52

5x + 5y = 70

-     -        -

___________

-2y = -18

y = -18/-2

y = 9

Putting value of y in eq(1)

x + y =14

x + 9 = 14

x = 14 - 9

x = 5

As y represents the soda, so 9 bottles of soda can be bought.

The input (-1/5 1/5 -7/5) without specified operations and unused variables a, b, and c, make it difficult to evaluate as a standard mathematical question. There may likely be a mistake in the original question.

Given the numbers a = -3, b = 4 and c = -5, the provided expression (-1/5 1/5 -7/5) appears to be a sequence of standalone fractions, not a standard mathematical operation or equation. To evaluate fractions, generally, we perform a calculation like addition, subtraction, multiplication, or division. However, the query lacks any specified mathematical operation to apply to these fractions. It seems there might be a mistake in the original question since the given values a, b, and c are also unused. To make it a valid mathematical question, we need to know what needs to be done with the fractions and variables given.

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Final answer:

The question appears to involve solving a quadratic equation using the quadratic formula, but there seems to be a typo in the provided figures. Nevertheless, the solution process entails substituting the given values into the quadratic formula and solving for x, which may result in two possible solutions depending on the discriminant.

Explanation:

The question involves solving a quadratic equation of the form ax² + bx + c = 0 using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). Based on the provided values of a, b, and c, we would substitute these into the quadratic formula to find the solutions to the equation. It seems there may be a typo in the original question, as the given values do not match any standard form of a quadratic equation nor the matrix form of a linear system. However, I will provide a general step-by-step solution for the quadratic equation based on the format provided in the reference information.

First, calculate the discriminant using the formula √(b² - 4ac). Then, use the values of a, b, and c to evaluate the positive and negative solutions of x using the quadratic formula. For example, if a = 1, b = 0.0211, and c = -0.0211, the solutions would be found as follows:

-0.0211 ± √(0.0211)² - 4(1)(–0.0211)

2(1)

It is important to note that this structure is indicative of the process and the actual computations will differ with the correct values provided for a, b, and c.

It’s important to keep PEMDAS in mind (order of operations) when solving this.

PEMDAS stands for: Parentheses, exponents, multiplication, division, addition, subtraction.

So when doing this problem we can see that there are two multiplication problems (8 • 9) and (2 • 5) so let’s put those to the side and solve those.

8 • 9 = 72

2 • 5 = 10

Now we can put the problem back together as 72-10

So ... 72-10=62

Answer:

"B" represents the area of the base so if the base is a square than a capital "B" means to find the area of the base (square). To find the area of a square it would be length x width.

Step-by-step explanation:

Answer:

Choice D for Angle R

70 degrees for Angle P

Step-by-step explanation:

Google "central angles and inscribed angles geometry" for an explanation.

It's actually a poorly worded question.

First, we need to find the area of both the tile and cardboard, so we can calculate how much tile will fit in the cardboard

Final answer:

Karl used a total of 42 square tiles to cover the piece of cardboard, with each tile weighing 3 ounces. Therefore, the combined weight of all the tiles is 126 ounces.

Explanation:

Karl used 2 inch by 2 inch square tiles to cover a 14 inch by 12 inch piece of cardboard. To find out how many tiles he used, we need to calculate the area of the cardboard and divide it by the area of a single tile. The area of the cardboard is 14 inches * 12 inches = 168 square inches. The area of one tile is 2 inches * 2 inches = 4 square inches. So, the number of tiles used is 168 divided by 4, which equals 42 tiles.

Now that we know Karl used 42 tiles, and each tile weighs 3 ounces, we can find the combined weight. The combined weight is 42 tiles * 3 ounces per tile = 126 ounces.

To find out when Ava and Kelly will be 3/4 mile apart, we can set up a distance equation based on their average speeds. The time it takes for Ava and Kelly to be 3/4 mile apart is 22.5 minutes.

To find out when Ava and Kelly will be 3/4 mile apart, we can set up a distance equation based on their average speeds.

Let's assume that the time it takes for Ava and Kelly to be 3/4 mile apart is t. Ava's distance can be represented by the equation 6t, while Kelly's distance would be 8t. We can set up the equation:

6t - 8t = 3/4

Simplifying, we have -2t = 3/4. To solve for t, we can multiply both sides of the equation by -1/2 to eliminate the negative sign:

t = (3/4) * (-1/2) = -3/8

Since time cannot be negative, we can conclude that Ava and Kelly will be 3/4 mile apart after 3/8 of an hour or 22.5 minutes.

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Answer:

They will 3/4 miles apart after 3/8 hours.

Step-by-step explanation:

To find out when Ava and Kelly will be 3/4 miles apart, we can set up an equation.

[tex]d = 8t-6t=2t[/tex]

t is the time in hours and d is the distance between the two girls in miles. Kelly runs at 8 miles/hour (represented by 8t) and Ava runs at 6 miles/hour (represented by 6t), and the distance between them can be calculated by subtracting Ava's distance from Kelly's distance.

To find out when they will be 3/4 miles apart, set d to 3/4 and solve for t.

[tex]\frac{3}{4} =2t\\\frac{3}{8}=t[/tex]

So, they will 3/4 miles apart after 3/8 hours.

Answer:

130 yards equals 118. 8 meters and 120 meters equals 131 .2 yards so not only are they different measurement types but they also do not equal the same.

Step-by-step explanation:

Follow below steps:

To find the difference in feet between 130 yards and 120 meters:

Convert 130 yards to feet: 130 yards x 3 feet/yard = 390 feet

Convert 120 meters to feet: 120 meters x 3.281 feet/meter = 393.72 feet

Difference in feet = 393.72 feet - 390 feet = 3.72 feet

[tex]

l_t=200m \\

s=20\frac{m}{s} \\

t=2\times60+30=150s \\

l=? \\

s=\frac{l}{t}\Longrightarrow l=st \\

l=20\frac{m}{s}\times150s=3000m=\boxed{3km}

[/tex]

The length of the tunnel is 2.8 kilometers.

Let's first convert the time taken to pass through the tunnel from minutes and seconds to seconds only.

2 minutes is equal to 2 * 60 = 120 seconds.

Adding the 30 seconds, the total time is 120 + 30 = 150 seconds.

We can calculate the speed of the train in meters per second using the formula:

Speed = Distance / Time

Given that the average speed of the train is 20 m/s, we can set up the equation as:

20 = (200 + L) / 150

Where L is the length of the tunnel in meters.

To find the length of the tunnel, we can solve this equation for L.

Multiplying both sides of the equation by 150, we get:

150 * 20 = 200 + L

3000 = 200 + L

Subtracting 200 from both sides, we have:

L = 3000 - 200

L = 2800 meters

Finally, to convert the length of the tunnel from meters to kilometers, we divide by 1000:

Length of the tunnel = 2800 / 1000 = 2.8 kilometers.

Therefore, the length of the tunnel is 2.8 kilometers.

To know more about length:

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Answer:

The range here is the set {8, -10, -4, 20, 32}.

Step-by-step explanation:

Please use " ^ " to denote exponentiation.  Thanks.   f(x)=x^2 + 5x - 4

f(-4)=(-4)^2 + 5(-4) - 4  =  8

f(-2)=(-2)^2 + 5(-1) - 4   = -10

f(0)=0^2 + 5(0) - 4 = -4

f(3) =3^2 + 5(3) - 4      =   20

f(4)=4^2 + 5(4) - 4       = 32

In this problem we have to calculate the actual function values for the given domain (input values).  The range here is the set {8, -10, -4, 20, 32}.

Answer:

100

Step-by-step explanation:

Mixed candy question... Skittles jar... to be filled with Jelly beans.

Let's first calculate the volume of the jar.  We'll assume it's a regular cylindrical prism jar, unlike the one on the photo which is narrower on top.

V = π * r² * h = π * (3.5)² * 11.5 = 140.875 π = 442.6 cubic cm

Now, we don't have the precise measurement of a jelly bean, but we know it's roughly 2-3 cubic cm.  The precision isn't needed to answer this question, just to have a rough idea... it's no 300 cu cm per jelly bean.

So, let's assume a 3 cu cm per jelly bean (2 cu cm wouldn't the final answer)....

442.6 / 3 = 147.5 jelly beans, approximately.

So, can they fit 100,000?  No

Can we fit 10,000 in there?  No

Can we fit 100?  Yes.

Can we fit 1?  Certainly

The most reasonable lower-limit would then be 100.

Answer: $42

Step-by-step explanation:

Answer:

$0.50

Step-by-step explanation:

We have been given that Jack sold magazine subscriptions for $2 each receiving 25% commission on his sales. We are asked to find Jack's income for each subscription.

Jack's income for each subscription will be equal to 25% of $2.

[tex]\text{Jack's income}=\$2\times \frac{25}{100}[/tex]

[tex]\text{Jack's income}=\$2\times 0.25[/tex]

[tex]\text{Jack's income}=\$0.50[/tex]

Therefore, Jack's income for each subscription will be $0.50.

Answer:

your opponent won by 1

Step-by-step explanation:

you made 58

your opponent made 59

Using the formula for calculating total points, we find out that the opponents won the basketball match by 1 point.

To find out who won the basketball match, we need to calculate the total points each team made. The formula to calculate total points is: (Number of 3-pointers * 3) + (Number of 2-point field goals * 2) + (Number of 1-point foul shots).

For your team: (10 * 3) + (8 * 2) + 12 = 30 + 16 + 12 = 58 points

For the opponents: (8 * 3) + (12 * 2) + 11 = 24 + 24 + 11 = 59 points

So, the opponents won the game. To find out by how many points they won, subtract the total points your team made from the opponents' total points: 59 - 58 = 1. Thus, the opponents won by 1 point.

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We shall use the mnemonics SOH-CAH-TOA to find the missing angles.

SOH- means sine ratio is [tex]\frac{Opposite}{Hypotenuse}[/tex]

CAH- means cosine ratio is [tex]\frac{Adjacent}{Hypotenuse}[/tex]

TOA- means tangent ratio is [tex]\frac{Opposite}{Adjacent}[/tex]

11) From the given right-angle triangle,the side length adjacent to [tex]\theta[/tex] is 11 units.

The opposite side  is 8 units.

We use the tangent ratio to obtain:

[tex]\tan \theta=\frac{8}{11}[/tex]

[tex]\theta=\tan ^{-1}(\frac{8}{11})[/tex]

[tex]\theta=36.0\degree[/tex] to the nearest tenth.

12) From the given right-angle triangle,the side length adjacent to [tex]\theta[/tex] is 7 units.

The opposite side  is 13 units.

We use the tangent ratio to obtain:

[tex]\tan \theta=\frac{13}{7}[/tex]

[tex]\theta=\tan ^{-1}(\frac{13}{7})[/tex]

[tex]\theta=61.7\degree[/tex] to the nearest tenth.

13) From the given right-angle triangle,the side length adjacent to [tex]\theta[/tex] is 8 units.

The opposite side  is 11 units.

We use the tangent ratio to obtain:

[tex]\tan \theta=\frac{11}{8}[/tex]

[tex]\theta=\tan ^{-1}(\frac{11}{8})[/tex]

[tex]\theta=54.0\degree[/tex] to the nearest tenth.

14. This time we were given the hypotenuse to be 9.7 units and the opposite side of the right-angle triangle is 7 units.

We use the sine ratio to obtain:

[tex]\sin \theta=\frac{7}{9.7}[/tex]

[tex]\implies \sin \theta=\frac{70}{97}[/tex]

[tex]\implies \sin \theta=\frac{70}{97}[/tex]

[tex]\implies \theta=\sin^{-1}(\frac{70}{97})[/tex]

[tex]\implies \theta=46.2\degree[/tex]

15. For question 15; we the hypotenuse to be 7 units and the adjacent side is 4 units.

We use the cosine ratio to get;

[tex]\cos \theta=\frac{4}{7}[/tex]

[tex]\implies \theta=\cos^{-1}(\frac{4}{7})[/tex]

[tex]\implies \theta=55.2\degree[/tex] to the nearest tenth.

16) From the given right-angle triangle,the side length adjacent to [tex]\theta[/tex] is 13 units.

The opposite side  is 12 units.

We use the tangent ratio to obtain:

[tex]\tan \theta=\frac{12}{13}[/tex]

[tex]\theta=\tan ^{-1}(\frac{12}{13})[/tex]

[tex]\theta=42.7\degree[/tex] to the nearest tenth.

Answer:

She gives 16 ounces to her neighbor

Step-by-step explanation:

How much did you use to make sauce

6 * 3/4 = 18/4 =9/2 = 4.5  lbs

That leaves 6-4.5 = 1.5 lbs

She give 2/3 of this to her neighbor

1.5 * 2/3

Changing the decimal to a fraction

3/2 * 2/3 = 1

She gives 1  pound to her neighbor, but we want it in ounces

16 ounces equals 1 pound

She gives 16 ounces to her neighbor

Answer:

36

Step-by-step explanation:

Answer:

The correct answer is area of given circle = 36π inches²

Step-by-step explanation:

Formula:-

Area of circle = πr²

Where r is the radius of circle

To find the area of circle

Here radius r = 6 inches

Area = πr²

 = π * 6²

 = 36π inches²

Therefore area of  a circle with a radius of 6 inches = 36π inches²

Answer:

the last one

Linear functions are straight lines. The first two go up and down when graphing and the third one is an exponential.

Answer:

D.

Step-by-step explanation: