If you invest $500 at 3% compounded monthly for 2 years, how much interest you do earn? Show work.

Continuous compound is e^rate x time

The formula would be D. 1200e^0.04t

Answer:  OPTION D A = 1200.e(0.04)(t)

Step-by-step explanation:

If the interest is compounded continuously for t years at a rate of r per year, then the compounded amount is given by:

A = P. e rt

P =$1200, r = 4% , t = t years

A = 1200.e(0.04)(t)

Answer: The area of triangle is 25 sq. meters.

Step-by-step explanation:

Given : Area of a triangle = [tex]\dfrac{1}{2}bh[/tex] m, where b= base of triangle

h= height of triangle.

If a triangle has  5 meters long base and a height twice the length of the base,

that means b = 5 meters and h= 2(5) = 19=0 meters

Then the area of triangle becomes [tex]A=\dfrac{1}{2}(5)(10)=25 m^2[/tex]  [Put alll values in the given formula]

Hence, the area of triangle is 25 sq. meters.

Answer:

[tex]\frac{16}{21}=\frac{8}{10.5}[/tex]

or

[tex]\frac{16}{8}=\frac{21}{10.5}[/tex]

Step-by-step explanation:

we know that

If two figures are similar then the ratio of its corresponding sides is proportional

In this problem

triangle YPQ and triangle YXZ are similar by AA Similarity Theorem

so

[tex]\frac{YP}{YX}=\frac{YQ}{YZ}[/tex]

substitute the given values

[tex]\frac{16}{21}=\frac{8}{10.5}[/tex]

Rewrite

[tex]\frac{16}{8}=\frac{21}{10.5}[/tex]

The boxes should be filled with [tex]\frac{16}{21} = \frac{8}{10.5}\\\\\frac{16}{8} = \frac{21}{10.5}[/tex]

As we know that

In the case when two figures are similar so the ratio of its corresponding sides is proportional

In this given situation  

triangle YPQ and triangle YXZ are similar by AA Similarity Theorem

So,

[tex]\frac{YP}{YX} = \frac{YQ}{YZ}[/tex]

[tex]\frac{16}{21} = \frac{8}{10.5}\\\\\frac{16}{8} = \frac{21}{10.5}[/tex]

It can be any of the both.

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11n - 6 is the algebraic expression for six less than the product of 11 and a number

Solution:

Given that,

Six less than the product of 11 and a number

Let "n" be the unknown number

Let us understand and break the given sentence

Six less than the product of 11 and a number

Which means,

six less than product of 11 and "n"

Which can be written as,

[tex]11n-6[/tex]

Thus the given sentence is translated into algebraic expression

The algebraic expression which represents 'six less than the product of 11 and a number' is 11n - 6, where n is the unknown number.

The question is asking for an algebraic expression representing 'six less than the product of 11 and a number'. To translate this to mathematical terms, first, the 'product of 11 and a number' indicates multiplication between 11 and the unknown number, which we represent with the variable n. The 'six less than' part indicates that we subtract 6 from this product.

So, the algebraic expression that represents 'six less than the product of 11 and a number' is 11n - 6.

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Answer: the cost of one cherry pie is $18 and the cost of one pumpkin pie is $20

Step-by-step explanation:

Let x represent the cost of one cherry pie.

Let y represent the cost of one pumpkin pie.

Lea sold 2 cherry pies and 4 pumpkin pies for a total of $116. This means that

2x + 4y = 116 - - - - - - - - - - - - - -1

Kali sold 7 cherry pies and 8 pumpkins pies for a total of $286. This means that

7x + 8y = 286 - - - - - - - - - - - - 2

Multiplying equation 1 by 7 and equation 2 by 2, it becomes

14x + 28y = 812

14x + 16y = 572

Subtracting, it becomes

12y = 240

y = 240/12 = 20

Substituting y = 20 into equation 1, it becomes

2x + 4 × 20 = 116

2x + 80 = 116

2x = 116 - 80 = 36

x = 36/2 = 18

Answer:

  -2

Step-by-step explanation:

We assume you want to find the number. Let it be represented by x.

  (6+2x)·5 = -3x +4 . . . . . the meaning of the problem statement

  30 +10x = -3x +4 . . . . . eliminate parentheses

  26 +13x = 0 . . . . . . . . . add 3x-4 to both sides

  2 + x = 0 . . . . . . . . . . . . divide by 13

  x = -2 . . . . . . . . . . . . . . subtract 2

The number is -2.

Answer: The density of the paper clips is 0.64 g/ml.

Step-by-step explanation:

Given : Volume of water = 10.0 mL

mass of water =  25.0 g

After 51 clips added to water , the total mass = 28 g

Total volume = 14.7

Mass of clips =  total mass - mass of water

= 28 g-25g = 3g

Volume of clips = Total volume- Volume of water

= 14.7- 10.0 = 4.7 ml

Density of paper clips =[tex]\dfrac{\text{Mass of paper clips}}{\text{Volume of paper clips}}[/tex]

[tex]=\dfrac{3}{4.7}=0.638297\approx0.64\ g/ml[/tex]

Hence, the density of the paper clips is 0.64 g/ml.

Answer:

The density of the paper clips is 0.64 g/m

Step-by-step explanation:

hope this helps :)

See picture for solution and answer.

Answer:

The distance from P to origin is approximately 40.82 units.                                  

Step-by-step explanation:

We are given the following in the data:

The point P(21,35)

We have to find the distance of point P from the origin.

Coordinates of origin: (0,0)

Distance formula:

[tex](x_1,y_1),(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

Putting the values, we get,

[tex](21,35), (0,0)\\\\d = \sqrt{(0-21)^2 + (0-35)^2} = \sqrt{1666} = 7\sqrt{34} \approx 40.82\text{ units}[/tex]

The distance from P to origin is approximately 40.82 units.

The probability that both the woman and her husband fail to get the correct brand of paint is 4/9.

To determine the probability that both the woman and her husband fail to get the correct brand of paint, we need to consider the probability of each event happening independently. Since the woman selects two brands at random out of the three available, the probability of her not getting the correct brand is 2/3. Similarly, the husband also selects two brands at random out of the three, so his probability of not getting the correct brand is also 2/3. Since the events are independent, we can multiply the probabilities together to get the probability that both fail to get the correct brand. Therefore, the probability is (2/3) * (2/3) = 4/9.

The husband's selections are independent of his wife's selections because each brand he chooses is not influenced by the brands his wife chooses. Regardless of what she selects, he still has three brands to choose from and selects two at random. This means that his probability of not getting the correct brand is the same regardless of his wife's choices.

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Answer:

a) 0.0125

b) 0.4579

Step-by-step explanation:

For this question use tree diagram method to solve the question or by simply listing down the probabilities as I have done in the attached picture. Firstly, we need to convert all percentages in to decimal and those decimals will represent probability of each event. For example if we consider probability of quality score A it can be found by diving 77 with 100:

77/100 = 0.77

Similarly all probabilities can be found by simply dividing percentages with 100.

Part (b) is a conditional probability question. Given that a circuit failed is the condition. So we need to use conditional probability method to solve it.

Final answer:

The probability of a circuit failing is 4.87%. If a circuit failed, there is a 45.77% chance that it received a quality score of C or D.

Explanation:

Calculating the Probability of Circuit Failure

To find the probability of a circuit failing, we multiply the probability of receiving each quality score by the probability of failure for that score, then add these together:

A score: 0.77 * 0.02 = 0.0154 (1.54%)

B score: 0.11 * 0.10 = 0.0110 (1.10%)

C score: 0.07 * 0.14 = 0.0098 (0.98%)

D score: 0.05 * 0.25 = 0.0125 (1.25%)

The total probability of failure is the sum of these values: 0.0154 + 0.0110 + 0.0098 + 0.0125 = 0.0487 or 4.87%.

Probability of a Failed Circuit Having a C or D Score

If a circuit failed, to find the probability that it had a quality score of C or D, we divide the sum of the probabilities of failure for C and D by the total probability of failure:

(Probability of C failure + Probability of D failure) / Total probability of failure
= (0.0098 + 0.0125) / 0.0487
= 0.0223 / 0.0487
= 0.4577 or 45.77%.

Answer:

Direct variation is constantly proportional (constant multiple)

Answer:

a) y = - 1/2 x

Step-by-step explanation:

The equation that represents a direct variation is y = -3x. So, correct option is B.

A direct variation is a relationship between two variables where one is a constant multiple of the other. In other words, as one variable increases or decreases, the other also increases or decreases in a consistent manner. The equation for direct variation is typically of the form y = kx, where k is the constant of variation.

Let's analyze each given equation:

y = 2/x - This equation does not represent a direct variation because y is not a constant multiple of x.

y = -3x - This equation does represent a direct variation because y is a constant multiple of x. Here, k (the constant of variation) is -3.

y = x² - 2x + 5 - This equation is a quadratic equation, not a direct variation, as it involves x raised to a power greater than 1.

y = √x - This equation does not represent a direct variation as y is not a constant multiple of x.

So, the equation that represents a direct variation is option 2) y = -3x. It has a direct relationship between y and x with a constant of variation of -3.

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Answer:

How Pythagoras theorem relates to Trigonometry ratios

For a right angled triangle ∆ABC,

Let a = hypothenus

b = opposite

c = adjacent

Sin²θ + Cos²θ = 1

Provided that a² + b² = c²

To prove this divide through by c²

Tongive

a²/c² + b²/c² = c²/c²

Sinθ = a/c , Cosθ = b/c

So, the above equation becomes

(Sinθ)² + (Cosθ)² = 1

Sin²θ + Cos²θ = 1

Coterminal Angles

Coterminal Angles are angles who share the same initial side and terminal sides.

Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

Final answer:

The Pythagorean Theorem and trigonometric ratios are related through the relationships between the sides of a right triangle. The theorem helps to calculate the sides involved in defining the sine, cosine, and tangent functions. Coterminal angles share the same trigonometric values despite having different measurements.

Explanation:

The Pythagorean Theorem is intimately related to trigonometric ratios, as it provides the fundamental relationship between the sides of a right-angled triangle. In trigonometry, the ratios of these sides define sine, cosine, and tangent functions. The Pythagorean theorem states that a² + b² = c², where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse of a right triangle. For example, given an angle θ within the right triangle, the cosine of θ is the adjacent side over the hypotenuse (cos(θ) = a/c), which implicitly uses the Pythagorean relationship when solving for the hypotenuse 'c'.

It's also important to remember coterminal angles in trigonometry, which are angles that share the same terminal side. Coterminal angles can be found by adding or subtracting whole multiples of 360° (or 2π radians). Although coterminal angles are different in measure, they have the same sine, cosine, and tangent values because these trigonometric functions are based on the position of the terminal side, not the actual angle measurement. Hence, coterminal angles have identical trigonometric function values.

9 bottles of soda and 10 juice bottles are purchased

Solution:

Given that,

Sugar contained by each soda bottle = 45 grams

Sugar contained by each juice bottle = 35 grams

Let,

x be the number of soda bottles

y be the number of juice bottles

Given that,

Ethan purchased a total of 19 bottles of juice

Therefore, we get,

x + y = 19 ---------- eqn 1

Ethan purchased a total of 19 bottles of juice and soda which collectively contain 755 grams of sugar

Therefore, we frame a equation as:

[tex]45 \times x + 35 \times y = 755[/tex]

45x + 35y = 755 --------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

x = 19 - y --------- eqn 3

Substitute eqn 3 in eqn 2

45(19 - y) + 35y = 755

855 - 45y + 35y = 755

10y = 100

y = 10

Substitute y = 10 in eqn 3

x = 19 - 10

x = 9

Thus 9 bottles of soda and 10 juice bottles are purchased

Answer:

A: -4,3 The x coordinate of the vertex is given by x = -b/2a and the y coordinate of the vertex is given by y= f( -b/2a), we need to transform the equation to the form ax^2 + bx + c We have: 5(x+4)^2+3 = 5x^2+ 20x + 23 Then we substitute x= -20/2*5 y= f(-20/2*5) = -4 = f(-4) =3 So V(-4,3)

Step-by-step explanation:

Answer:

I still dont get what the answer is

Step-by-step explanation:

Answer:

The answer to your question is letter C

Step-by-step explanation:

From the graph, we get the center and the radius

- The center is the point shown in the graph and its coordinates are (2, -1).

- The length of the radius is 4 units, from the center we count horizontally the number of squares (4)

Substitution

                    (x - 2)² + (y + 1)² = 4²

or                 (x - 2)² + (y + 1)² = 16

Answer:

A or B

Step-by-step explanation:

Because of the negtive 1

Answer:

20days

Step-by-step explanation:

The daily progress is 4ft - 3ft = 1ft

20ft/1ft = 20days

The snail will take 20 days to get out of the well.

To find out how long it will take the snail to get out of the well, we need to determine how many days it takes for the snail to climb a distance of 20 feet. Each day, the snail climbs 4 feet but slips back 3 feet at night. So, the net distance the snail covers each day is 4 - 3 = 1 foot.

Dividing the total distance of 20 feet by the net distance covered each day (1 foot), we find that it will take the snail 20 days to get out of the well.

Hence, the snail will take 20 days to get out of the well.

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Answer:

C. The new tomatoes are more consistent in their weights than the old tomatoes.

Context:

Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of Roma plants produces fruit that averages 74 grams, but 11% of the tomatoes are too small. It is reasonable to assume that a Normal model applies.

The question is asking to compare the consistency of weights in two types of tomatoes based on their standard deviation. Select the option that best fits the standard deviation calculated for each group.

In statistics, standard deviation is a measure of the amount of variation or dispersion in a set of values. A lower standard deviation means that the values tend to be close to the mean (average) value of the set, while a higher standard deviation implies that the values are spread out over a wider range. The question asks you to compare the consistency in weight between two types of tomatoes, determined by their standard deviations.

If the standard deviation of the old tomatoes' weight is lower than that of the new ones', option B ('The old tomatoes are more consistent in their weights than the new tomatoes') would be accurate. On the other hand, if the opposite is true, option C ('The new tomatoes are more consistent in their weights than the old tomatoes') would be correct. Option A would be right if the standard deviations are similar, indicating similar consistency, and option D would apply if along with the new tomato weights being more consistent, their weight distribution is left skewed.

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Yo sup??

From Newton's 2nd law of motion

F*t=Δp

=mv-mu

mu=0.4*15

=6

t=0.2

mv=0

Therefore

F*0.2=6

F=30 N

Hope this helps.

Answer:

2nd option

Step-by-step explanation:

given

BD = 4x

CE = 2x + 2

test each answer option by substituting the given values of x into each of the above equations and see if it is consistent with the given values for BD and CD in the answer options.

1st option, when x = 5,

BD = 4x = 4(5) = 20  (Consistent)

CE = 2x + 2 = 2(5) + 2 = 10 + 2 = 12 ( not consistent with CE=8)

2nd option, when x = 3/7,

BD = 4x = 4(3/7) = 12/7  (Consistent)

CE = 2x + 2 = 2(3/7) + 2 = 6/7 + 2 = 20/7 ( consistent with CE=20/7) (ANSWER)

3rd option, when x = 3,

BD = 4x = 4(3) = 12 (Consistent)

CE = 2x + 2 = 2(3) + 2 = 6 + 2 = 8 ( not consistent with CE=20)

Answer:

-16y -10

Step-by-step explanation:

So basically, since there are no parentheses, we can use PEMDAS:

y - 9 * y - 8 * y - 10

y - 9y - 8y - 10

-8y -8y - 10

-16y -10

The answer is y^-7 I had this in my lesson

Answer:A large Ghirardelli's bar is 28 cm long and 8 cm wide. A smaller Ghirardelli's bar is 7 cm long. If the bars are similar, what is the perimeter of the - 1468665…

Step-by-step explanation:A large Ghirardelli's bar is 28 cm long and 8 cm wide. A smaller Ghirardelli's bar is 7 cm long. If the bars are similar, what is the perimeter of the smaller Ghirardelli's bar?

Answer:

The number of small mowers are 19 and the large mowers are 11.

Step-by-step explanation:

Given:

A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.

Now, to find the number of each type of mower sold.

Let the number of small mower be [tex]x.[/tex]

And the number of large mower be  [tex]y.[/tex]

So, total number of mowers are:

[tex]x+y=30[/tex]

[tex]x=30-y\ \ \ ....(1)[/tex]

Now, the total sales of mowers are:

[tex]249.99(x)+329.99(y)=8379.70[/tex]

Substituting the value of [tex]x[/tex] from equation (1) we get:

[tex]249.99(30-y)+329.99y=8379.70[/tex]

[tex]7499.7-249.99y+329.99y=8379.70[/tex]

[tex]7499.7+80y=8379.70[/tex]

Subtracting both sides by 7499.7 we get:

[tex]80y=880[/tex]

Dividing both sides by 80 we get:

[tex]y=11.[/tex]

The number of large mower = 11.

Now, to get the number of small mowers we substitute the value of [tex]y[/tex]  in equation ( 1 ):

[tex]x=30-y\\x=30-11\\x=19.[/tex]

The number of small mower = 19.

Therefore, the number of small mowers are 19 and the large mowers are 11.

Answer:

option A- The candidate each participant supports.

Step-by-step explanation: the question asks about the 'statistics in the experiment', meaning the major factor or say the most important data to be considered to achieve the desired aim/result of the experiment.

From the question, the aim/result of the Research poll was to get 'the PROPORTION of people supporting each presidential candidate in the fall election'. Note that to find 'PROPORTION',  you must first find the individual values and then compare them. That's what 'PROPORTION' is all about - comparing number of things or people.

So to achieve this, the most important data-'statistics' in this experiment is knowing the candidate each participant supports.

For example, if there are 5 presidential candidates: Mr A, B, C, D & E and after interviewing 2,010 adults, you find out that:

134 people supports Mr A;

268 people supports Mr B;

402 people supports Mr C;

536 people supports Mr D and

670 people supports Mr E.

Now because you know the candidate each participant supports, you can now derive the 'PROPORTION' of people supporting each candidate which is 134:268:402:536:670. NB: you have to always leave your answer in its lowest term, so the proprtion here is 1:2:3:4:5.

Answer:

The proportions of participants who support each presidential candidate.

Step-by-step explanation

Answer:

C

Step-by-step explanation:

The recommended daily intake of a nutrients supplement for a certain age group is 800 mg per day.

Actully supplements needs vary from person to person  plus or minus 50 mg.

This means the minimum value is 800 - 50 = 750 mg per day and the maximum value is 800 + 50 = 850 mg per day.

Let x mg be a possible daily amount of nutrients supplement. Then

[tex]750\le x\le 850[/tex]

Subtract 800:

[tex]750-800\le x-800\le 850-800\\ \\-50\le x-800\le 50[/tex]

This inequality can be rewritten using absolute value notation as

[tex]|x-800|\le 50[/tex]

Answer:

Step-by-step explanation:

Given

Plane travels 240 miles [tex]10^{\circ}[/tex] East of North

Position vector [tex]\vec{r_1}=240(\cos(10)\hat{j}+\sin (10)\hat{i})[/tex]

Then the plane travels 180 miles [tex]67^{\circ}[/tex] East of North

[tex]\vec{r_{21}}=180(\cos(67)\hat{j}+\sin (67)\hat{i})[/tex]

[tex]\vec{r_2}=\vec{r_{21}}+\vec{r_1}[/tex]

[tex]\vec{r_2}=\left ( 240\sin (10)+180\sin (67)\right )\hat{i}+\left ( 240\cos (10)+180\cos (67)\right )\hat{j}[/tex]

[tex]\vec{r_2}=\left ( 207.36\right )\hat{i}+\left ( 306.68\right )\hat{j}[/tex]

Total distance traveled in North direction is given by coefficient of \hat{j}

i.e. North[tex]=306.68\ miles\approx 307\ miles[/tex]

Total distance traveled in East direction is given by coefficient of \hat{i}

East [tex]=207.36\ miles\approx 207\ miles[/tex]

Answer

7.5 pounds

Step-by-step explanation:

Since adding x grams of salt will bring th percentage of the salt to 25

Hence. 10% of the 50 gram gives. 5 gram initial salt before it is added.

5+ x/ 50 * 100= 25/

5+x /50 = 0.25

5+x = 12.5

X= 12.5- 5

X= 7.5pounds

Yo sup??

This question can be solved by applying the properties of similar triangles

the triangle with sides 5x and 20 is similar to the triangle with sides 45 and 35

The similarity property used here is called AAA ie angle angle angle property as all the three angles of the 2 triangles are equal.

therefore we can say

5x/45=20/36

x=5 units

Hope this helps

Answer:5 sqrt(2)

Step-by-step explanation:

All the sides of the square are congruent by the markings. Therefore they all measure 5 and because all 4 sides are congruent it is a square. Because it is a square the corners are right angles and you can use the Pythagorean Theorem. a^2 +b^2 = c^2.

5^2 + 5^2 = x^2

25 + 25 = x^2

50= x^2

X = square root of 50

X= square root of 25 Times Square root of 2

X= 5square root of 2

Answer: 5 sqrt (2)

Step-by-step explanation:

ABCD is a square

BCD is a triangle

BC=DC=5

To find DB

Let BC= a, DC=b, BD=c.

using Pythagoras Theorem in Triangle BCD

c2 = a2+b2

c2 = 52+52

c2= 25+25

c= √(50)

c2= √(25)×√ (2)

c= √(5× 5) √(2)

c=  5√(2)   or    c=5sqrt(2)  

Rmbr,  Let BC= a, DC=b, BD=c.