You borrow $4000 from the bank at 3% annual interest compounded monthly. The monthly payment is $200. What is the balance after the third payment?

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:

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:

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

Let m be the no of trucks and n be the no of passenger vehicles...

Then m + n = 600

and 100m + 45n = 29200

Multiplying 1st equation by 45, we have 45m+45n=27000

then subtracting from 2nd eqn we have, 55m = 2200 that is m=40.Then n=560

So we have 40 trucks and 560 passenger vehicle

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:

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:

Answer:74

Step-by-step explanation:

Answer: 74

Step-by-step explanation:

185 divided by 2.50 is 74.

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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Answer:

Step-by-step explanation: its b

First, you'd have to decompose the shape. The way I decomposed it was by splitting the shape into a small rectangle and a large one. The formula for the rectangles is 6 times 3 and 6 by 9. You multiply 6 by 3 and get 18; then you multiply  6 by 9 and get 54. Lastly, you simply add 18 and 54. This gives you an answer; 72.

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.

6km in 30 min so he traveled at a speed of 12km per hour;

In 2 hours he will travel 24km;

12km in 60 min

9km in ? min

?=9x60/12=45 minutes will take to travel 9 km at the speed of 12km/h

Answer:

12km/h.

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.

Answer:

Step-by-step explanation:

We write only the coefficients of the given equation inside the upside down symbol of division.

We first do synthetic substitution and then verify the result by putting g(4) and g(-5) in the original equation. Both should have the same result.

The questions are solved on the image attached.

Answer:

709, 1,708

Step-by-step explanation:

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}.

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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The main difference is that a Bimodal Histogram has two peaks representing the most frequent data values, whereas a Symmetric Histogram has one peak and its data is evenly distributed around a central value. In a symmetric histogram, mean, median, and mode coincide, unlike in a bimodal distribution, where the modes are different from the mean and median.

The difference between a Bimodal Histogram and a Symmetric Histogram relates to the distribution of data within the histogram.

A Bimodal Histogram has two distinct peaks or modes, indicating two prevalent data values within the dataset.

In contrast, a Symmetric Histogram is characterized by a single peak, with the data points arranged evenly around a central value such that it creates a mirror image on either side of the peak.

Symmetric histograms often indicate that the mean, median, and mode of the dataset coincide at the center of the distribution.

However, in a symmetric distribution with bimodality, the modes will differ from the mean and median.

When data is skewed to the left or right, it is not symmetric, and the mean, median, and mode do not align, with the mean being pulled towards the tail of the distribution in skewed datasets.

To visualize these concepts, one may create a histogram by plotting the frequency of data points against specified ranges.

Bimodal histograms will show two high-frequency areas, while symmetric histograms will show a single, central peak, indicating where the bulk of the data lies.

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:

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:

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:

B:  c²/9

Step-by-step explanation:

                                    c²

(c/3)² is the same as ------'

                                     9

Answer:

Step-by-step explanation:

[tex]\text{Use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\left(\dfrac{c}{3}\right)^2=\dfrac{c^2}{3^2}=\dfrac{c^2}{9}[/tex]

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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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.

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.

[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:

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

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

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.

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.

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