You just won the lottery! You now have $25,000! You make a smart decision and invest all $25,000 to earn interest on it over the next 10 years.


You need to find 3 local banks and find their savings interest rates.


Then you need to decide which bank will earn you the most money after investing $25,000 for 10 years. Use the SIMPLE INTEREST FORMULA.


1) Which bank yielded the highest amount of interest earned? Which bank yielded the lowest amount of interest earned?

2) What is the difference in the principal invested for banks that yielded the highest and lowest interests from Question 1? What is the difference in the interest earned for the banks from Question 1?

3) Which bank would you invest your $25,000? WHY?

The proof of AD/DC = AB/CB is given below.

Given that;

Line BD bisects ∠ABC.

Now: Auxiliary Line EA is drawn such that Line AE is parallel to Line BD . Auxiliary Line BE is an extension of Line BC.

Since, Lines EA and BD are parallel,

∠1 = ∠ 4  (Corresponding angles)

So, We get;

∠2 = ∠ 3 (Alternate angles)

∠1 = ∠ 3 (because it is given that BD bisects ∠ABC )

So, by the above three equations, we get

∠ 2= ∠ 4

So, BE=AB (Opposite sides equal to opposite angles are equal)

    .........Equation 1)

Now, consider triangle ACE,

Since AE is parallel to BD.

By Basic Proportionality theorem, which states

" If a line is drawn parallel to one side of a triangle intersecting other two sides, then it divides the two sides in the same ratio."

So, we get

AD/DC = BE/CB

By using equation 1, we get

AD/DC = AB/CB

Hence, It can be proved.

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Explanation:

We replace x with 3 and use PEMDAS to evaluate

8*x+23

8*3+23

24+23

47

Answer:

\(47\)

Step-by-step explanation:

\(8x + 23\)

\(8(3) + 23\)

\(24 + 23\)

\(47\)

Answer:

1/5 or 0.2

Step-by-step explanation:

1/4 x 4/5 =

=1x4/4x5
=4/20 -OR- 1/5 -OR- 0.2

Answer:

Yes.

Step-by-step explanation:

Answer:

yes, they are congruent

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

I said so and I did maths

The midpoint (-1, 1) lies exactly halfway between A(-4, 5) and B(2, -3) along both the x-axis and y-axis.

To find the midpoint of A and B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) can be found by taking the average of the x-coordinates and the average of the y-coordinates.

Let's apply this formula to find the midpoint of A(-4, 5) and B(2, -3).

Midpoint x-coordinate = (x1 + x2) / 2

Midpoint y-coordinate = (y1 + y2) / 2

Substituting the given coordinates, we have:

Midpoint x-coordinate = (-4 + 2) / 2 = -2 / 2 = -1

Midpoint y-coordinate = (5 + (-3)) / 2 = 2 / 2 = 1

Therefore, the midpoint of A and B is (-1, 1).

Geometrically, the midpoint is the point that divides the line segment AB into two equal halves. In this case, the midpoint (-1, 1) lies exactly halfway between A(-4, 5) and B(2, -3) along both the x-axis and y-axis.

It's important to note that the midpoint formula is a straightforward way to find the coordinates of the midpoint between two points in a Cartesian coordinate system. By averaging the x-coordinates and y-coordinates, we can determine the exact location of the midpoint.

'

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The statement is false, the behavior is recorded in discrete intervals of time

In interval recording procedures, the behavior is recorded in discrete intervals of time within the observation period rather than consecutive periods.

Interval recording involves dividing the observation period into equal time intervals and recording whether the behavior occurs or not during each interval.

This method provides an estimate of the occurrence of behavior during specific time segments rather than continuous monitoring of behavior throughout the entire observation period.

So the statement is false.

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Answer:

1/110 =.6/x use cross multiplication and multiply

Step-by-step explanation

Your answer is x=66 miles

Hope this helps!!!

Brainliest???

Answer:

Two expressions for the perimeter would be

22x+23 and 2x+3x+17x+7+16

Step-by-step explanation:

you want to add the variables of the same kind in this case

2x        

3x         7

17x       16

_________

22x  +     23

In summary, the relationships between the corresponding sides and angles of similar triangles are: Corresponding sides are proportional and congruent.

When two triangles are similar, the corresponding sides of the triangles are proportional. This means that the ratio of the lengths of corresponding sides in the two triangles is equal. Similarly, the corresponding angles of similar triangles are congruent. This means that the angles in the two triangles that correspond to each other are equal in measure.

When two triangles are similar, it means that they have the same shape but possibly different sizes. The concept of similarity implies that the corresponding sides of the triangles have the same proportional relationship.

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By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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Answer:

6/9

Step-by-step explanation:

Answer:

$147.22

Step-by-step explanation:

100 + 8.25 = 108.25

136/100 X 108.25 = 147.22

The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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Answer:

 16. 1.56

17. 0.8625

18.0.04

Step-by-step explanation:

The solution of the inequality is (-∞, -1] ∪ [2, ∞)

The given inequality is: 2x - 2/x + 1 ≤ 1

We need to solve this inequality and write the answer in interval notation.

First, we need to bring all the terms to one side of the inequality.

2x - 2/x + 1 - 1 ≤ 0⇒ 2x - 2/x + 1 - x/x + 1 ≤ 0⇒ (x - 2)/x + 1 ≤ 0

Now, let's find the critical points.

Critical points are the values at which the numerator and the denominator become zero.

x - 2 = 0⇒ x = 2x + 1 = 0⇒ x = -1

Now, we have to take the test points less than -1, between -1 and 2, and greater than 2.

We know that the inequality is less than or equal to zero because it is of the form: f(x) ≤ 0

We will make a table to check the sign of (x - 2) and (x + 1).x - 1x + 1(x - 2)/(x + 1)−3−11+1−1/2−1.51+1−1/2+1.5As we can see from the table above, (x - 2)/(x + 1) ≤ 0 for x ∈ (-∞, -1] ∪ [2, ∞).

Hence, the solution of the inequality is (-∞, -1] ∪ [2, ∞)

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Answer:

the answer is option D......

Answer:

Step-by-step explanation:

2x-8 ≤ 14

1. Add 8 to both sides of the inequality sign to move the 8 from the left side to the right side.

2x ≤ 22

2. Divide both sides by 2 to get the x alone.

x ≤ 11

3. Make a number line from 8 to 13 (numbers can be changed), draw a circle above the number 11 and fill in the circle.

4. Now, make a line going from the circle to the left and draw an arrow at the end.

The rate of change of the area of the triangle at the given instant is 4 cm²/s. Thus, the correct answer is (B) 4. The rate of change of the area of the triangle can be determined using the formula for the area of a triangle, which is A = (1/2) * base * height.

We are given that the base is increasing at a constant rate of 2 cm/s and the height is decreasing at a rate of 1 cm/s.

At the instant when the height is 5 cm and the area is 5 cm², we can substitute these values into the formula to solve for the rate of change of the area. Let's denote the rate of change of the area as dA/dt.

A = (1/2) * base * height

5 = (1/2) * base * 5

Simplifying the equation, we have:

base = 2

Now, we can differentiate both sides of the equation with respect to time (t):

dA/dt = (1/2) * (dbase/dt) * height + (1/2) * base * (dheight/dt)

Substituting the given rates of change:

dA/dt = (1/2) * (2 cm/s) * 5 cm + (1/2) * 2 cm * (-1 cm/s)

Simplifying further:

dA/dt = 5 cm^2/s - 1 cm^2/s

dA/dt = 4 cm^2/s

Therefore, the rate of change of the area of the triangle at the given instant is 4 cm^2/s. Thus, the correct answer is (B) 4.

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Answer:

128

Step-by-step explanation:

Let's start by figuring out the last side of the triangle

we can use the pathagoryous theroem and get

11.9²+x²=16.9²

Solve this and get x=12

Let's now compute the area of the triangle

b*h*.5

12*11.9*.5=71.4

So 71.4 is the area of the triangle

we now need to find the area of the semi circle.

to do this we are going to find the area and then divide it by 2

We know that the length is equal to 12 which means that the radius is 6

so we have

π6²/2

which is 56.55

We add the 71.4+56.55= 127.94 which rounds to 128

Answer:

212.758

Step-by-step explanation:

Find the semi-circle first, the diameter is 16.9 ft.

To find area:

Formula:

pi x radius x radius x 1/2

16.9 ÷ 2 = 8.45 (radius)

22/7 x 8.45 x 8.45 = 224.407 (Circle)

224.407 ÷ 2 = 112.203 (Semi circle)

Find the triangle:

1/2 x base x height or length x base x height

But for now, we will use the first one.

1/2 x 16.9 x 11.9 = 100.555

Now add them up.

100.555 + 112.203 = 212.758

(I don't know what units you to put for your answer since I don't learn American mathematics, so it's up to you)

Answer:

In step 2, he needed to divide both sides of the equation by 5

Step-by-step explanation:

I'm very positive about this

Hope this helps!!!!!!

Answer:

step 2

Step-by-step explanation:

the probability of randomly selecting a vehicle with 2 occupants is approximately 0.245 or 24.5%.The probability distribution that applies in this scenario is the binomial distribution.

Let p be the probability of a vehicle having two occupants. Since the average occupancy is 1.6 people, we can calculate that the probability of a vehicle having one occupant is 1 - p - p = 0.4.

Using the binomial probability formula, the probability of selecting a vehicle with two occupants can be calculated as:

P(X = 2) = (100 choose 2) * p^2 * (1-p)^(100-2)

where (100 choose 2) is the number of ways to select 2 vehicles out of 100, p^2 is the probability of selecting a vehicle with two occupants twice, and (1-p)^(100-2) is the probability of selecting a vehicle with one occupant 98 times.

Assuming p = 0.16 (the average occupancy of 1.6 people divided by 2), we can calculate:

P(X = 2) = (100 choose 2) * 0.16^2 * 0.84^98 ≈ 0.245

Therefore, the probability of randomly selecting a vehicle with 2 occupants is approximately 0.245 or 24.5%.

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1. To solve the recurrence

T(n)=T(n/2)+O(1),

we can use the master theorem

where:  a = 1, b = 2, f(n) = O(1)  

The value of logba is 0.

Since f(n) is O(1), c = 0.

Therefore, the recurrence falls under the case 2 of the master theorem.

Hence, T(n) = O(logn).

To verify this,

we can use the substitution method:

Suppose

T(k) <= c.logk

For some constant c and all k < n.

T(n) = T(n/2) + O(1)<= c.log(n/2) + O(1) = c.logn - c + O(1)<= c.logn for c > 1 and n > 1.

The last inequality follows

if we choose c > 1/2, and the base case T(1) = O(1) satisfies the inequality for some c' > 0.

Therefore, T(n) = O(logn).

2. To solve the recurrence

T(n) = 2T((n/2)+17),

we can use the master theorem

where: a = 2, b = 2, f(n) = 0  

The value of logba is 1.

Since f(n) is 0, c = 1.

Therefore, the recurrence falls under the case 1 of the master theorem.

Hence, T(n) = O(nlogn).

To verify this,

we can use the substitution method:

Suppose

T(k) <= c.k.logk for some constant c and all k < n.

T(n) = 2T((n/2)+17) <= 2c.((n/2)+17).log((n/2)+17)<= cn.logn + 34clogn<= cn.logn

for c >= 17, n >= 68.

The last inequality follows

if we choose c >= 17, and the base case T(1) = 0

satisfies the inequality for some c' > 0.

Therefore, T(n) = O(nlogn).

3. To use a recursion tree to determine an asymptotic upper bound on the recurrence

T(n) = 2T(n-1)+1,

we can draw the tree as follows:

At level i, we have 2i nodes with values T(n-2i).

Therefore, the total value of all nodes at level i is 2i.T(n-2i).

Since the recursion stops when n-2i = 1, we can solve for i to get i = logn.

Therefore, the total value of all nodes at the last level is 2logn.T(1).

We know that T(1) = O(1), so we can bound the value of all nodes at the last level by 2logn.

Using the geometric series formula, we can sum the values of all nodes to get:

T(n) = 1 + 2 + 2^2 + ... + 2logn-1 + 2logn.T(1) = 2.2logn - 1 <= 2T(1).2logn = O(2logn) = O(n).

To verify this, we can use the substitution method:

Suppose

T(k) <= ck for some constant c and all k < n.T(n) = 2T(n-1) + 1 <= 2c(n-1) + 1 = 2cn - 2c + 1 <= cn for c >= 1/2 and n >= 2.The last inequality follows if we choose c >= 1/2, and the base case T(1) = 1 satisfies the inequality for some c' > 0.

Therefore, T(n) = O(n).

4. To use a recursion tree to determine an asymptotic upper bound on the recurrence

T(n) = 4T((n/2)+2)+n, we can draw the tree as follows:

At level i, we have 4i nodes with values T(n-2i)+i. Therefore, the total value of all nodes at level i is 4i.(T(n-2i)+i).Since the recursion stops when n-2i = 1, we can solve for i to get i = log(n/2).

Therefore, the total value of all nodes at the last level is 4log(n/2).(T(1) + log(n/2)).We know that T(1) = O(1), so we can bound the value of all nodes at the last level by 4log(n/2).log(n/2) = 2logn - O(loglogn).

Using the geometric series formula, we can sum the values of all nodes to get:T(n) = n + 4(n/2+2) + 4^2(n/4+2+2) + ... + 4log(n/2)(T(1) + log(n/2))= n + 4(n/2+2) + 4^2(n/4+2+2) + ... + 4log(n/2)logn + O(nloglogn)= O(nlogn).

To verify this,

we can use the substitution method:

Suppose T(k) <= ck.logk for some constant c and all k < n.T(n) = 4T((n/2)+2)+n <= 4c((n/2)+2).log((n/2)+2) + n<= 2cnlogn + 4clogn + n <= cnlogn for c >= 1 and n >= 2.

The last inequality follows if we choose c >= 5, and the base case T(1) = O(1) satisfies the inequality for some c' > 0. Therefore, T(n) = O(nlogn).5.

a) T(n) = O(nlogn) b) T(n) = O(n^0.5) c)

The Master Theorem does not apply.

d) T(n) = O(nlog4n) e) T(n) = O(nlogn) f) T(n) = O(n).

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Answer:

needddd

Step-by-step explanation:

128 ÷3=42.66

it doesn't say if they have to pay the money back but if they do it's

128-35= 43

43÷3= 14.33

Answer:

1.3

Friend is wrong

Step-by-step explanation:

Given:

friend's claim: height of his building is more than 1.50 times the height of yours

line of sight to the top edge of the other building makes an angle of 21° above the horizontal

line of sight to the base of the other building makes an angle of 52° below the horizontal

Solution:

Let A be the height of your building is A

Let B+A his building is B higher than yours.

Let the distance between the buildings is x.  

then

tan 52 = A/x

tan 21 = B/x  

A/B = tan 52 / tan 21

      =  1.27994 / 0.38386

A/B = 3.33

(A + B) / A = 1.5 0

A/A + B/A = 1.50

1 + B/A = 1.50

B/A is basically (B/x) / (A/x)

So

1+ 3.33 / 3.33

= 4.33/3.33

= 1.3

Since 1.3 is not equal to 1.5

Hence the friend's claim is wrong.

The height of the taller building can be given in relation to the height of

the other building using trigonometric ratios.

Correct response:

The given parameters are;

Angle of elevation to the top of the other building = 21°

Angle of depression to the base of the other building = 52°

The claim of the friend = The height of his building > 1.5 × The height of the other building

Required:

To state whether the claim is right or wrong.

Solution:

Let h represent the height of the smaller building, let l represent the

distance between the two buildings, and let d represent the height by

which one building is taller than the other, we have;

l·tan(21°) = d

l·tan(52°) = h

Height of the taller building, H = h + d = l·tan(52°) + l·tan(21°)

Height of the other building = h = l·tan(52°)

Therefore;

H ≈ 1.3·h

Which gives that the taller building, H, is approximately 1.3 times the other building.

Therefore;

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High clouds are those that form at altitudes of at least 20,000 ft (6000 m).

At high altitudes, ice crystals form due to which cloud formation occurs.   Cirrus, cirrostratus, and cirrocumulus clouds are a few types of clouds. Cirrostratus clouds frequently form a thin, white layer that resembles a veil and covers the entire sky. Small, spherical, white clouds called cirrocumulus develop in long rows. Because they can provide information about changes in atmospheric pressure, temperature, and moisture levels in the upper atmosphere, these high clouds are crucial for meteorologists to investigate.

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The sum of the first 50 terms of the arithmetic sequence is 13500

The arithmetic sequence is defined by a common difference of 10, starting from the first term of 25.

To find the sum of the first 50 terms of the arithmetic sequence, we can use the formula for the sum of an arithmetic series:

Sum = (n/2) * (first term + last term)

Here ,

n = 50 (the number of terms),

First term = 25,

Last term = first term + (n - 1) × common difference

Let's calculate the last term:

Last term = 25 + (50 - 1) × 10

= 25 + 49 × 10

= 25 + 490

= 515

Now we can substitute the values into the formula for the sum:

Sum = (50/2) * (25 + 515)

= 25 * 540

= 13500

Therefore, the sum of the first 50 terms of the arithmetic sequence is 13,500.

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Rounded to four decimal places, the p-value is 0.0844.

To determine the p-value for this hypothesis test, we need to follow these steps:

Step 1: State the null and alternative hypotheses.

Null hypothesis: The percentage of readers who own a laptop is 26%.

Alternative hypothesis: The percentage of readers who own a laptop is different from 26%.

Step 2: Determine the test statistic.

We can use a z-test for proportions since we have a large enough sample size and we know the population proportion. The formula for the test statistic is:

z = (p - p) / √(p(1-p) / n)

where p is the sample proportion, p is the hypothesized population proportion, and n is the sample size.

Using the given values, we have:

z = (0.17 - 0.26) / √(0.26(1-0.26) / 100)

z = -1.72

Step 3: Determine the p-value.

Since this is a two-tailed test, we need to find the area in both tails of the standard normal distribution that corresponds to a z-score of -1.72. Using a table or a calculator, we find that the area in the left tail is 0.0422 and the area in the right tail is also 0.0422.

Therefore, the p-value is the sum of the areas in both tails:

p-value = 0.0422 + 0.0422

p-value = 0.0844

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Answer:

2925km

1170km

4095km

The  distance each driver travels is;  585 km, 1170km and 4095km

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given that Three taxi drivers travel a total of 8190 km in the ratio 5:2:7.

So the total is;

8190 km = 5 + 2 + 7

8190 km = 14p

1 point = 8190 km / 14

= 585 km

Driver 1

585 km

Driver 2 .​

2 x 585= 1170km

Driver 3

7 x 585 = 4095km

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