Find the principal. Annual rate of interest= 11% Period=3 years Total interest= 825 rupees Principal rupees​

Answer:  The depth was 42 feet below see level after  6 minutes

Step-by-step explanation:

If m represents the minutes then input 6 for m into the expression and solve.

-120 + 13(6)

-120 + 78  = -42

The measurement of 10 mm on the plan represents an actual size of 20000 mm or 20 m (2000 x 10 mm).

Answer:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

Step-by-step explanation:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

this set represent a function because there is one input (x) for the output(y)

(no repetition for x)

Answer:

\(-2x^2-x\). Your answer was wrong because "x-squared" terms didn't cancel.

Step-by-step explanation:

To solve this problem, set up an equation.  We know something is supposed to be added to the expression \(2x^2+2x\), and the result should be x. So:

\(2x^2+2x+(\text{ ? })=x\)

We want to solve for the question mark... the unknown thing that we're adding to the original expression, in order to get x.

It is uncommon to put question marks in equations to represent quantities. Usually we use a letter. Since x is already being used in the equation, we should pick something else ... we could use "y".

\(2x^2+2x+(\text{ } y \text{ })=x\)

...or just...

\(2x^2+2x+y=x\)

Algebra allows us to solve the equation and find out what "y" is equivalent to.

To solve, we want to get the "y" by itself. To do so, we try to eliminate the other "terms" from the left side of the equation.

Understanding "terms" & "like terms"

Terms

"Terms" in an equation are either a number multiplied to other things, or just a single number that isn't multiplied to anything else.

For example, the various terms in our equation above are

\(2x^2\), \(2x\), \(y\), \(x\)

You might ask why the last things, which don't have a number, are considered terms.

Remember that multiplying by 1 doesn't change anything, so we could imagine each of the last two terms as being 1 times the letter.

So, we can rewrite our equation:

 \(2x^2+2x+1y=1x\)

Like terms

"Like terms" are terms where the "other stuff the numbers are multiplied to" is the same, so for instance, the \(2x\) and the \(1x\) are like terms. They are like terms because, the "other stuff" that the numbers are multiplied to are "x" for both terms. Note that \(2x\) and \(2x^2\) are not "like terms" because the "stuff" is different:

\(x\) is different than \(x^2\)

"Like terms" are important because only like terms can be "combined" into a single simplified term.

Solving equations

To solve an equation, we isolate what we're solving for, y, by disconnecting the other terms from it, and simplify.

Starting with subtracting 2x from both sides of the equation:

\(2x^2+2x+1y=1x\\(2x^2+2x+1y)-2x=(1x)-2x\)

Subtraction is the same as "adding a negative":

\(2x^2+2x+1y+(-2x)=1x+(-2x)\)

Since all terms are now connected by addition, we can add in any order we want (because of the Commutative Property of Addition), and we can combine like terms.

Thinking just about the number parts, since \(1+(-2)=-1\),  then \(1x+(-2x)=-1x\).

Returning to our main equation, the right side simplifies:

\(2x^2+2x+1y+(-2x)=1x+(-2x)\\2x^2+2x+1y+(-2x)=-1x\)

On the left side: \(2x\) and \(-2x\) are like terms.

Fact: \(2+(-2)=0\)

So, \(2x+(-2x)=0x\)

Since anything times zero is just zero, \(0x=0\). Furthermore, adding zero to anything doesn't change it.  So when the \(2x\) and \(-2x\) terms on the left side of our main equation are combined, they "disappear" (While we talked through are a lot of rules/steps to justify why that works, it is common to omit those justifications, and to just combine those like terms and make them disappear.)

So, \(2x^2+2x+1y+(-2x)=-1x\) simplifies to:

\(2x^2+1y=-1x\)

Similarly for the \(2x^2\) term, we subtract from both sides:

\(2x^2+1y=-1x\\(2x^2+1y)-2x^2=(-1x)-2x^2\\2x^2+1y+(-2x^2)=-1x+(-2x^2)\)

Combining like terms on the left, they disappear.

\(1y=-1x+(-2x^2)\)

There are no like terms on the right.

Since the two terms on the right are added together, we can use the commutative property of addition to rearrange:

\(1y=-2x^2+(-1x)\)

Addition of a negative can turn back into subtraction, and simplify multiplication by 1.

\(y=-2x^2-x\)

Remembering we chose "y" as the unknown thing we wanted to know, that's why the "correct answer" is what it is.

Verifying an answer

Verifying can double check an answer, and helps explain why the answer you chose doesn't work.

To verify an answer, the original statement said add something to the expression and get a result of "x". So, let's see if the "correct answer" does:

\(2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-2x^2-x)\\2x^2+2x+(-2x^2-1x)\\2x^2+2x+(-2x^2)+(-1x)\)

Combining the "x-squared" terms, completely cancels...

\(2x+(-1x)\)

Combining the "x" terms, and simplifying...

\(1x\\x\)

So it works.

Why isn't the answer what you chose:

\(2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-x^2-x)\\2x^2+2x+(-1x^2-1x)\\2x^2+2x+(-1x^2)+(-1x)\)

Combining the x-squared terms, things don't completely cancel...

\(1x^2+2x+(-1x)\)

Combining the x terms...

\(1x^2+1x\\x^2+x\)

So adding the answer that you chose to the expression would not give a result of "x", which is why it is "wrong"

The closest distance between the points E(5, 3) and point D(4, 3) is (A) 6.1 units

The distance between two points in a coordinate plane is the length of the straight line segment that connects the two points.

The distance between point E and point D can be found using the distance formula:

distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Plugging in the coordinates of point E and point D, we get:

distance = √[(-4 - (-5))^2 + (-3 - 3)^2]

Evaluate

distance = 6.1

hence, the answer is A) 6.1 units.

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If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

Given,

The total amount you had = $150

The amount you spend in each day = $2

Consider the number of days = x

Then the algebraic expression for this situation is 150-2x

Hence, If you had $150, but you are spending $2 each day, then the algebraic expression model of this situation is 150-2x

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Answer:

Step-by-step explanation:

5x+30 is a corresponding angle with 4x-9 so set them equal to each other. 4x-9+2x+3 will equal 180

Answer:

no, the values would be above 180º

Step-by-step explanation:

if...

(4x - 9) + (2x + 3) + y = 180

(5x + 30) + y = 180

then...

(4x - 9) + (2x + 3) = 5x + 30

so...

6x - 6 = 5x + 30

x = 36

plug it in.

4(36) - 9 = 135

2(36) + 3 = 75

already you can see the sum of these two angles surpasses 180 which is not possible for a triangle.

Approximately 16% of the design is black.

Since the radius of each circle increases by 2 inches, the diameter of each circle increases by 4 inches. Thus, the diameter of the largest circle is 2 + 4(5) = 22 inches.

The area of each circle is proportional to the square of its radius, so the area of the smallest circle is π(\(2^2\)) = 4π square inches. The area of the second circle is π(\(4^2 - 2^2\)) = 12π square inches, the area of the third circle is π(\(6^2 - 4^2\)) = 20π square inches, and so on.

The total area of the design is the sum of the areas of all the circles, which is:

4π + 12π + 20π + 28π + 36π = 100π

The black area in the design consists of four quarter circles, each with a radius of 4 inches. The area of a one-quarter circle is:

(1/4)π(\(4^2\)) = 4π

So the total black area is 4 times this, or 16π.

The percent of the design that is black is:

(16π / 100π) x 100% ≈ 16%

Therefore, approximately 16% of the design is black.

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The standard deviation of the inside diameter measurements of the old water tank is approximately 0.165m, and the standard deviation of the height measurements is approximately 2.122m.

To calculate the standard deviation, we first find the mean of the inside diameter and height measurements. For the inside diameter, the mean is (4.4 + 4.2 + 4.5 + 4.2) / 4 = 4.325m. we calculate the squared difference between each measurement and the mean, sum them up, and divide by the number of measurements. The result is the variance. Taking the square root of the variance gives us the standard deviation.

For the inside diameter:

Variance = [(4.4 - 4.325)² + (4.2 - 4.325)² + (4.5 - 4.325)² + (4.2 - 4.325)²] / 4 ≈ 0.027m²

Standard Deviation = √0.027m² ≈ 0.165m

For the height:

Mean = (8.8 + 3.9 + 8.6) / 3 ≈ 7.767m

Variance = [(8.8 - 7.767)² + (3.9 - 7.767)² + (8.6 - 7.767)²] / 3 ≈ 4.507m²

Standard Deviation = √4.507m² ≈ 2.122m

These standard deviations indicate the spread or variability of the measurements from the mean. A smaller standard deviation implies that the measurements are closer to the mean, while a larger standard deviation suggests greater variability among the measurements.

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Answer:

a. 24!/19! = 24 × 23 × 22 × 21 × 20

= 5,100,480

b. P[10, 6] = 10!/4! = 10 × 9 × 8 × 7 × 6 × 5

= 151,200

c. C[8, 6] = 8!/(6!2!) = (8 × 7)/(2 × 1) = 56/2

= 28

The value of the factorials and combinations are
a. 24!/19! = 2,401,432,640
b. P[10,6] = 151,200
c. C[8,6] = 28


a. To solve 24!/19!, divide the factors of 24! from 20 to 24 by the factors of 19! (1 to 19). So, 24!/19! = 20 × 21 × 22 × 23 × 24 = 2,401,432,640.
b. P[10,6] represents the number of permutations of 10 items taken 6 at a time. Calculate using the formula P(n, r) = n!/(n-r)!. In this case, P(10,6) = 10!/(10-6)! = 10! / 4! = 151,200.
c. C[8,6] represents the number of combinations of 8 items taken 6 at a time. Calculate using the formula C(n, r) = n!/(r!(n-r)!). In this case, C(8,6) = 8!/(6!(8-6)!) = 8!/(6! × 2!) = 28.

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Answer:

mode = 2

Step-by-step explanation:

mode is the most frequently seen number.

median is the average so 5+4+2+2+2+2+1+1+3+2+2+3+3+2+1/15= 2 1/3

Answer:

Median is 2, Mode is 2

Step-by-step explanation:

1,1,1,2,2,2,2,2,2,2,3,3,3,4,5 to get the median you put the number from smallest to large then you x one out on each side until there is only one number left which would be 2

The mode is 2 because it is the most common number (aka it appears the most in the list)

Answer:

96

Step-by-step explanation:

Because 72/9 = 8 so every hour she earns 8$

8*12=96

The amount of money in dollars earned by Nicole in 12 hours will be $96.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Nicole earned $72 in 9 hours. Then the amount of money in dollars earned by Nicole each hour is calculated as,

Rate = $72 / 9

Rate = $8 for each hour

At this rate, the amount of money in dollars earned by Nicole in 12 hours will be calculated as,

⇒ $8 x 12

⇒ $96

The cash in dollars acquired by Nicole in 12 hours will be $96.

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The proportion of candy bars with fewer than 200 calories cannot be determined without additional information.

To calculate the proportion of candy bars with fewer than 200 calories, we need to know the total number of candy bars and the number of candy bars that have fewer than 200 calories.

Without this information, we cannot determine the proportion. The number of candy bars with fewer than 200 calories could vary greatly depending on the specific dataset or context.

The proportion of candy bars with fewer than 200 calories cannot be determined without additional information regarding the total number of candy bars and the number of candy bars that fall into that category.

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Answer:

Hope it helps!

Step-by-step explanation:

Last year there were 74 students in the seventh grade class. This year there are 86 students in the seventh grade class.

Increase = 86 - 74 = 12

Percent Increase = (12/74) x 100 = 16.2%

The unit circle), and the curve does not oscillate rapidly or change direction abruptly, so we would expect the arc length to be less than 2.

To find the arc length traced out by the parametric curve x = cos(cos(4t)), y = sin(cos(4t)) as t goes through the range 0 to 1, we can use the following formula for arc length:

L = ∫√(dx/dt)^2 + (dy/dt)^2 dt, where the integral is taken over the range of t.

Taking the derivatives of x and y with respect to t, we have:

dx/dt = -sin(4t)sin(cos(4t))

dy/dt = cos(4t)sin(cos(4t))

Substituting these into the formula for arc length, we get:

L = ∫√((-sin(4t)sin(cos(4t)))^2 + (cos(4t)sin(cos(4t)))^2) dt

L = ∫√(sin^2(4t)sin^2(cos(4t)) + cos^2(4t)sin^2(cos(4t))) dt

L = ∫√(sin^2(cos(4t))) dt

L = ∫|sin(cos(4t))| dt

Since we know that the sine function oscillates between -1 and 1, we can see that the absolute value of sin(cos(4t)) is always between 0 and 1. Therefore, the integral of |sin(cos(4t))| over the range 0 to 1 gives us the total distance traced out by the curve, which is the arc length.

Evaluating the integral, we get:L = ∫|sin(cos(4t))| dt = ∫sin(cos(4t)) dt

Let u = cos(4t), then du/dt = -4sin(4t), and dt = -du/(4sin(4t))

Substituting for dt and u, we have:

L = ∫sin(u) * (-du/(4sin(4t))) = (-1/4) ∫sin(u) du = (-1/4)cos(u) + C

Substituting back for u and simplifying, we get:

L = (-1/4)cos(cos(4t)) + C

To find the constant C, we use the fact that L = 0 when t = 0:

0 = (-1/4)cos(cos(0)) + C = (-1/4)cos(1) + C

C = (1/4)cos(1)

Therefore, the arc length traced out by the parametric curve x = cos(cos(4t)), y = sin(cos(4t)) as t goes through the range 0 to 1 is:

L = (-1/4)cos(cos(4t)) + (1/4)cos(1)

L = (-1/4)cos(cos(4)) + (1/4)cos(1)

L ≈ 0.615

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Answer: H

Step-by-step explanation:

The cost of $5 has not meaning for what we want.  The are only trying to figure out the number each bought so that was thrown in to throw you off.

you know they  bought 14 total DVDs

n+L=14   the number norma bought + number Lauretta bought is 14

Th next key sentence is Norma purchased two and a half times as Luaretta

In the sentence:

Norma is n  

purchased is your = sign  (usually in word problems "is" "costs" etc is =

Two and 1 half  \(2\frac{1}{2}\) = \(\frac{5}{2}\)

times is * (multiplied)

Lauretta is l

Substitute each symbol for each work

Norma(n) purchase(=) two and a half \(\frac{5}{2}\) times* L

n= \(\frac{5}{2}\)L

n+L=14    these are your 2 equations  H

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

Step-by-step explanation:

(x₁, y₁) = (-10, -10)   & (x₂, y₂) = (-5, -10)

y-intercept = b = -10

There is no change in y- coordinates. So, the line is parallel to x- axis

Slope = 0

Equation: y = b

y = -10

Answer:

ur correct

Step-by-step explanation:

if ∠N and ∠Y are the same then we know the missing angle is 30.°  

30

Step-by-step explanation:

do angle sum property

x + z + y = 180

60 + 90 + y = 180

150 + y = 180

y = 180-150

y = 30

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equivalent.

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The  five solution of the linear equation x+y=3 is = (0,3), (1,2), (2,1), (3,0) and (4, -1).

Equations are logical formulations of the connection between two values. A mathematical equation can be defined in a variety of ways. Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

There could be multiple variables in a linear equation. A linear equation is one in which the variable's maximum power is consistently 1.

A one-degree equation is another name for it. At least one variable should be raised to exponent 2 in quadratic equations.

Ax+By=C is the usual form for two-variable linear equations. For example, 2x+3y=5 is a linear equation in standard form.

Let the value of

x = 0,

then,

0 + y = 3

⇒

y = 3

One of the solutions

for x + y =3, is =(0,3)

Similarly, If x = 1,

then,

1 + y =3 ⇒ y = 3 - 1 = 2

One of the solutions for x + y =3, is

(1,2)

If x = 2,

then,

2 + y = 3

⇒ y = 3 - 2 = 1

One of the solutions for x + y =3, is

(2,1)

If x = 3, then,

3 + y = 3

⇒ y = 3 - 3 = 0

One of the solutions for x + y =3, is

(3,0)

If x = 4,

then,

4 + y = 3

⇒ y = 3 - 4 = -1

One of the solutions for x + y =3, is

(4, -1)

Hence,

five

solutions of the equation x + y = 3, are:

(0,3), (1,2), (2,1), (3,0) and (4, -1).

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Answer:144

Step-by-step explanation: a coin has 2 possibilities so 2 coins have 2x2 = 4 possibilities. A normal six-sided dice has 6x6 = 36 possibilities. 4 x 36 = 144 (this might be wrong)

In other words, it shows when the ball hits the ground.

Answer:

Step-by-step explanation:

Compare like sides of the two triangles to write a proportion. See image.

Answer:

woooooooow ooooooooooooooooo

Answer:

None of these can be triangles.

Step-by-step explanation:

All triangles’ side lengths must follow this pattern - the two shortest sides must be GREATER than the longest when added together. 6 + 4 < 10, so this isn’t a triangle. 3 + 8 = 11, so this isn’t a triangle. 8.4 + 7.7 < 16.6, so this isn’t a triangle. Lastly, 4 + 3 < 16, so this isn’t a triangle. Hope this is accurate & helpful! Best of luck.

Answer:

Yes,

You need 88 points.

Step-by-step explanation:

What you need to do here is to set up an equation using algebra (I do this in my master's degree to determine my grade).

\(\frac{x}{.80}\) = 400

x = 320

Your target required points is 320.

320 - 232 = 88 points.

You need 88 points on the exam to get the 80%.  

If the defendeant is guilty, the probability that the jury makes the correct decision is approximately 0.476.

To calculate the probability that the jury makes the correct decision, we need to consider two cases: the defendant is guilty and the defendant is not guilty.

Let's start with the case where the defendant is guilty. The probability that any individual juror makes the correct decision on the defendant is 0.80. Therefore, the probability that at least 10 out of 12 jurors make the correct decision is given by the binomial distribution:

P(at least 10 out of 12 jurors say "guilty") = sum of P(k jurors say "guilty") for k = 10, 11, 12

Using a binomial calculator or formula, we can find that this probability is approximately 0.952.

Now let's consider the case where the defendant is not guilty. In this case, the probability that any individual juror makes the correct decision is 0.20 (since they should say "not guilty"). Therefore, the probability that at least 10 out of 12 jurors say "guilty" when the defendant is actually not guilty is given by the same binomial distribution:

P(at least 10 out of 12 jurors say "guilty" | defendant is not guilty) = sum of P(k jurors say "guilty") for k = 10, 11, 12

Using the binomial formula, we can find that this probability is approximately 0.0003.

To find the probability that the jury makes the correct decision, we need to weigh the two cases by their respective probabilities:

P(correct decision) = P(defendant is guilty) * P(at least 10 out of 12 jurors say "guilty") + P(defendant is not guilty) * P(at least 10 out of 12 jurors say "guilty" | defendant is not guilty)

Plugging in the values, we get:

P(correct decision) = 0.5 * 0.952 + 0.5 * 0.0003 = 0.476

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The area of the semicircle is approximately 112.5π square meters.

To find the area of a semicircle, we will use the following terms: diameter, radius, and area.
Find the radius of the semicircle
Since the diameter is given as 30 meters, we can find the radius by dividing the diameter by 2:
Radius = Diameter/2 = 30 meters/2 = 15 meters.

Use the formula for the area of a circle and adjust it for a semicircle
The area of a full circle is given by the formula

\(A = \pi  \times  r^2,\)

where A is the area and r is the radius.

Since we are dealing with a semicircle (half of a circle), we will adjust the formula to find half the area of a full circle:
Semicircle Area\(= (1/2) \times \pi \times  r^2\)
Step 3: Calculate the area of the semicircle
Substitute the radius value (15 meters) into the formula:
Semicircle Area \(= (1/2) \times  \pi  \times (15 meters)^2\)
Semicircle Area \(\approx (1/2) \times \pi \times  225\) square meters \(\approx  112.5 \times \pi\) square meters.

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The volume of the cylinder can be obtained from the calculation as  1356 \(cm^3\)

We know that the volume of the cylinder is;

π (pi) is a mathematical constant approximately equal to 3.14159

r is the radius of the cylinder's base (the distance from the center to the edge of the circular base)

h is the height of the cylinder (the distance between the bases)

By substituting the appropriate values for the radius and height into the formula, you can calculate the volume of the cylinder.

V = π\(r^2\)h

V = 3.14 *\((12/2)^2\) * 12

h = 1356 \(cm^3\)

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Answer:

30 dollars a week

Step-by-step explanation:

2100/70 is 30