2. A savings account is started with an initial deposit of $600. The account earns 2.1 % interest compounded annually.

(a) Write an equation to represent the amount of money in the account as a function of time in years.


(b) Find the amount of time it takes for the account balance to reach $800. Show your work.

Answer:

The total number of the games that the eagles played is 12

Step-by-step explanation:

Given:

The eagles soccer team win 40% of the games

Number games won last year = 12

To Find:

Total number of the games that the eagles played = ?

Solution:

Let the total number of games eagles played be X

Then

according to the question,

40% of X = 12

[tex]\frac{40}{100} \times X  = 12[/tex]

[tex]X = 12 \times \frac{100}{40}[/tex]

[tex]X = \frac{1200}{40}[/tex]

X = 30

The Eagles played a total of 30 games last year.

To find the total number of games that the Eagles played last year, we can set up a proportion using the information given. Since the Eagles won 40% of their games, we can say that 40% is equal to 12 games. Let x be the total number of games played. The proportion would be: 40/100 = 12/x. Cross multiplying gives us 40x = 1200. Dividing both sides by 40, we find that x = 30. Therefore, the Eagles played a total of 30 games last year.

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Answer:

Large box weighs 60 pounds and small box weighs 25 pounds

Step-by-step explanation:

Let x be the weight of large box and y be the weight of small box

The combined weight of a large box and a small box is 85 pounds.

[tex]x+y= 85[/tex]

[tex]y= 85-x[/tex]

The truck is transporting 50 large boxes and 65 small boxes. If the truck is carrying a total of 4625 pounds in boxes

[tex]50x+65y= 4625[/tex]

Solve for x  and y using both equations

[tex]y= 85-x[/tex]

[tex]50x+65(85-x)= 4625[/tex]

[tex]50x+5525-65x= 4625[/tex]

[tex]-15x+5525= 4625[/tex]

[tex]-15x= 4625-5525[/tex]

[tex]-15x=-900[/tex]

Divide both sides by -15

x=60

[tex]y= 85-x=85-60=25[/tex]

Large box weighs 60 pounds and small box weighs 25 pounds

Answer:

Random

Step-by-step explanation:

The sampling technique used in this scenario is A) cluster sampling.

Cluster sampling is a method where the population is divided into clusters or groups, and a random sample of these clusters is selected for analysis.

In this case, the population consists of 20 statistics classes at the local community college.

Instead of selecting individual students, the clusters (classes) are randomly selected.

Once the clusters are chosen, all the students from each selected class are interviewed.

This approach is different from other sampling techniques because it focuses on sampling groups rather than individuals within the population.

Hence, the most appropriate sampling technique in this scenario is cluster sampling (option A), where the classes were randomly selected as clusters, and all the students within each selected class were interviewed.

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Answer:

125%

Step-by-step explanation:

In this kind of question, we could choose any arbitrary value for the length of the side of the square.

Let’s say the square is 10m in length, a 50% increase in the length means we add 5 to the original length making the new length to be 15m.

The area of a square is L^2

The former area is 10 * 10 = 100 while the new area is 15 * 15 = 225

The percentage increase is calculated as follows:

We simply subtract the old from the new to yield 225 - 100 = 125

The percentage increase would now be :

125/100 * 100 = 125%

Answer: On the 29th day

Step-by-step explanation:

According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.

On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.

The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are [tex]2^{30} [/tex] lilypads on the 30th, and [tex]2^{29}[/tex] lilypads on the 29th. This can be deduced multiplying succesively by 2.  

Solving the given system of equations involves rearranging one equation to solve for a variable, substituting this into the other equation to find the value of one variable, and then substituting this value back into the rearranged equation to find the value of the other variable.

To solve a system of equations by substitution, we first solve one of the equations for one variable and then substitute this expression into the other equation. Looking at the two given equations, the second equation, 3.25x - y = -14, is easier to solve for y (because the coefficient before y is -1). So, we'll start with that:

This step-by-step process will give the solution to the system by substitution.

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Answer:

  D.  D: 0 ≤ b ≤ 10; R: 0 ≤ W(b) ≤ 120

Step-by-step explanation:

The problem statement tells you Owen can build up to 10 birdhouses, and that b represents that number. Then 0 ≤ b ≤ 10 is the domain described by the problem statement.

It also tells you that W(b) = 12b, so filling in values from 0 to 10 gives a range from 0 to 120: 0 ≤ W(b) ≤ 120.

These observations match choice D.

The domain and range for the function W(b) = 12b are D: 0 ≤ b ≤ 10 and R: 0 ≤ W(b) ≤ 120 respectively. The option D is correct.

The function W(b) = 12b represents the total amount of wood needed to build b birdhouses, where each birdhouse requires 12 square feet of wood. Since Owen can build up to 10 birdhouses, the domain of the function (which represents the number of birdhouses Owen can build) is 0 ≤ b ≤ 10.

For the range of the function, which represents the total amount of wood in square feet, if Owen builds no birdhouses (b = 0) he needs no wood (0 square feet), and if he builds the maximum of 10 birdhouses (b = 10), he would need 120 square feet of wood which is calculated as W(10) = 12 * 10. Therefore, the range of his function would be 0 ≤ W(b) ≤ 120. The appropriate domain and range for the function are D: 0 ≤ b ≤ 10 and R: 0 ≤ W(b) ≤ 120, which corresponds to option D.

Answer:

  H.  13

Step-by-step explanation:

Make use of the Pythagorean theorem twice. The first time, use it to find TS. The second time, use it to find QR.

  TS² + RT² = RS²

  TS² = RS² -RT² = 64 -48 = 16 . . . . subtract RT², fill in numbers

  TS = 4 . . . . . take the square root

Now, QT = QS -TS = 15 -4 = 11, so ...

  QR² = QT² +RT²

  QR² = 11² +(4√3)² = 121 +48 = 169

  QR = √169 = 13

The length of QR is 13.

Step-by-step explanation:

solve it through simultaneous equations

for fun guys : 10+6.5x=y

for game bank : 22+3.5x=y

10+6.5x=22+3.5x

3x=12

x=4

cost is same when game rentals =4

that cost= $36

For 4 games both the game stores charges the same, which is $36.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Fun Guys game rental store charges an annual fee of $10 plus $6.50 per game rented.

Let the number if games be x.

So, total cost =10+6.50x

The Game Bank charges an annual fee of $22 plus $3.50 per game.

So, total cost =22+3.50x

Game rentals will the cost be the same at both stores

Then, 10+6.50x=22+3.50x

6.50x-3.50x=22-10

3x=12

x=4

Total money fun Guys game rental store charges 10+6.50x=36

Therefore, the same money charged by both stores is $36.

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Answer:

New dimensions of the floor is approximately 301.25 ft by 181.25 ft

Step-by-step explanation:

The question is incomplete. The complete question should be:

Manufacture wants to enlarger it's floor area 1.5 times that of the current facility. The current facility is 260 ft by 140 ft. The manufacture wants to increase each dimension the same amount. Write the dimensions of the new floor.

Given:

Length of floor = 260 ft

Width of floor = 140 ft

The floor area is increased 1.5 times.

To find the new dimensions of the floor.

Solution:

Original area of the floor = [tex]length\times width= 260\times 140=36400\ ft^2[/tex]

New area = [tex]1.5\times Original\ Area = 1.5\times 36,400=54,600\ ft^2[/tex]

Let the length and width be increased by [tex]x[/tex] ft.

Thus, new length = [tex](260+x)\ ft[/tex]

New width = [tex](140+x)\ ft[/tex]

Area of the new floor can be given as:

⇒ [tex]new\ length\times new\ width[/tex]

⇒ [tex](260+x)(140+x)[/tex]

Multiplying using distribution.

⇒ [tex]x^2+260x+140x+36400[/tex]

⇒ [tex]x^2+400x+36400[/tex]

Thus we can equate this with new area to get the equation to find [tex]x[/tex]

[tex]x^2+400x+36400=54600[/tex]

subtracting both sides by 54600.

[tex]x^2+400x+36400-54600=54600-54600[/tex]

[tex]x^2+400x+18200=0[/tex]

Using quadratic formula:

For a quadratic equation [tex]ax^2+bx+c=0[/tex]

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

For the equation [tex]x^2+400x-18200=0[/tex]

[tex]x=\frac{-400\pm\sqrt{(400)^2-4(1)(-18200)}}{2(1)}[/tex]

[tex]x=\frac{-400\pm\sqrt{232800)}}{2}[/tex]

[tex]x=\frac{-400\pm482.49}{2}[/tex]

[tex]x=\frac{-400+482.49}{2} \ and\ x= \frac{-400-482.49}{2}[/tex]

∴ [tex]x\approx 41.25 \ and\ x\approx-441.25[/tex]

Since length is being increased, so we take [tex]x\approx41.25[/tex]

New dimensions are:

New length [tex]\approx 260\ ft + 41.25\ ft =301.25\ ft[/tex]

New width [tex]\approx 140\ ft + 41.25\ ft =181.25\ ft[/tex]

Answer:

2.4 hours

Step-by-step explanation:

Distance = rate * time

One train travels at a rate of 70 mph for t hours.  This means that the distance it travels is 70t.

The other train travels at a rate of 90 mph for t hours.  This means that the distance it travels is 90t.  

The total distance they cover together is equal to 384 miles; therefore,

70t + 90t = 384 and

160t = 384 so

t = 2.4 hours

Answer:

 Roni did not make use of the equation for a proportional relationship.

Step-by-step explanation:

For some constant of proportionality k, y is proportional to x if x and y satisfy the equation ...

  y = kx

Roni knows k=7/25, but she did not use this equation. She added instead of multiplying, so did not end with an equation expressing a proportional relation.

___

  y = (7/25)x

Answer:

Step-by-step explanation:

1. Obviously, the figure is rotated CCW by 90°. If the center of rotation were the center of the figure, the image would be in the same quadrant as the pre-image. It is in the quadrant located 90° CCW from the original, so the center of rotation must not be the center of the image. That leaves one viable answer choice.

__

2. The line joining a point and its reflection is always perpendicular to (and bisected by) the line of reflection.

__

3. The theorem tells you a point on the perpendicular bisector is equidistant from the endpoints of the segment bisected. If the surveyor is to apply that theorem, he needs a point equidistant from the original two stakes.

__

4. The square has four (4) lines of symmetry: through the parallel side midpoints, and through opposite vertices. The corresponding lines would be ...

The appropriate choice is ...

  x + y = 4

Answer:

The least value of (r+s) is (12+14)=26

Step-by-step explanation:

Well, first let us solve equation of 11(s-1)=13(r-1), which results in 11s-11=13r-13. Hence, 11s+2=13r. It is stated that r and s both are integers and greater than 1.

To make sure that r and s are integers, the least value of s must be equal to 14 (s=14) then the least value of r becomes 12 (r=12).

Finally, the least value of (r+s) is (12+14)=26.

Answer:

47.75 %

Step-by-step explanation:

It is a very well known issue that in Standard Normal Distribution  porcentages of all values fall according to:

μ  +   σ       will contain a 68.3 %

μ   +  2σ    will contain  a  95.5 %

μ  +  3σ      will contain  a  99.7 %

However it is extremely  importan to understand that the quantities above mentioned are distributed simmetrically at both sides of the mean, that is,  the intervals are:

[  μ - 0,5σ ;  μ  + 0,5σ ]

[  μ -   1σ ;  μ  +      1σ ]

[  μ -   1.5σ ;  μ  +   1.5σ ]

So we have to take that fact into account when applying the empirical rule. Then

With   mean    μ  =  47       and  σ = 10   is equal to say

values between    47    and     57    (  μ  +   σ  )  we are talking about the second interval, but just half of it.

Then the  approximate porcentage of light-bulb replacement requests is

95.5 /2   =  47.75 %

Answer:

Ratio of Quentin new income to Sam new income is [tex]\frac{11}{12}[/tex]

So option (a) will be correct option

Step-by-step explanation:

Let Rex income is 100

Then Paul income is 40 % less than Rex income 100 - 100×0.4 = 100-40 = 60

And Quentin's income is 20 % less than Paul income

So Quentin's income  is 60 - 60×0.2 = 60-12 = 48

Sam income is 40% less than Paul income

So Sam income = 60 - 60×0.4 = 60 - 24 = 36

Now Rex give 60% income Sam

So Sam new income = 36 + 100×0.6 = 60+36 = 96

And Rex give 40% of his income to Quentin's

So Quentin's  new income = 48 + 100×0.4 = 40+48 = 88

Now ratio of  Quentin's  new income to the Sam new income [tex]=\frac{88}{96}=\frac{11}{12}[/tex]

So option (a) will be correct answer

Answer:

The continuously compounded return of Mordice Corporation shares for the period August 1 to August 15 is closest to:______6.90%

Step-by-step explanation:

The question is incomplete. This is the complete version

The weekly closing prices of mordice corporation shares are as follows;

Date. Closing price

Ist August. 112

8 August 160

15 August. 120

Solution

The continuous compounded return of mordice corporation shares can be calculated by taking the natural log change

In(120/112)*100= 6.89% which is closest to 6.90%

Answer:

Step-by-step explanation:

Answer:

B = 53°

C = 74°

The correct option for Suppose that we know that a=5cm, b=5cm, and angle A=53o in a certain triangle. According to the Law of Sines D. There is exactly one triangle that meets the criteria.

Given:

a = 5, b = 5,  A = 53°

⇒ a/sin A = b/sin B ⇒ Sin B = Sin A

                               ⇒ B = A (or) 180-A

                               ⇒ B = 53° (or) 127°

B = 53°:

           C = 180-A-B = 0 (not possible)

    ⇒ B = 53°, C = 74° ⇒ C = (Sin C)  (b/sin B) ≅ 6.02 cm

Generally, the law of sines is used to solve the triangle, when we know two angles and one side or two angles and one included side. It means that the law of sines can be used when we have ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria.

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Answer:

[tex]z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155[/tex]  

[tex]p_v =2*P(Z<-0.155)=0.877[/tex]  

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .  

Step-by-step explanation:

1) Data given and notation

n=298 represent the random sample taken

X=29 represent the events claimed

[tex]\hat p=\frac{29}{298}=0.0973[/tex] estimated proportion

[tex]p_o=0.1[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion is 0.1 or no.:  

Null hypothesis:[tex]p=0.1[/tex]  

Alternative hypothesis:[tex]p \neq 0.1[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(Z<-0.155)=0.877[/tex]  

And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .  

We can do the test also in R with the following code:

> prop.test(29,298,p=0.1,alternative = c("two.sided"),conf.level = 1-0.05,correct = FALSE)

Answer:

Simon's Age = 47

Marcie's Age = 11

Step-by-step explanation:

The question is to find Simon's age and Marcie's age.

Let Simon's age be x and Marcie's age be y

Simon is 3 years more than 4 times marcie, so we can write:

x = 4y + 3

Also,

Sum of their ages is 58, so we can write:

x + y = 58

or x = 58 - y

Now, we substitute this into 1st equation and solve for y first:

[tex]x = 4y + 3\\58-y = 4y + 3\\58-3=4y+y\\55=5y\\y=\frac{55}{5}\\y=11[/tex]

We know

x = 58 - y

so,

x = 58 - 11

x = 47

So,

Simon's Age = 47

Marcie's Age = 11

Answer:The area of the reduced backyard is 112.5 square feet

Step-by-step explanation:

The initial length of the backyard is 40.5 feet long.

The initial width of the backyard is 25 feet wide.

In order to install a pool, the yard needs to be reduced by a scale of 1/3. This means that the new length of the backyard is would be

40.5 × 1/3 = 40.5/3 feet lonng

The new width of the backyard would be

25 × 1/3 = 25/3 feet wide

The backyard is rectangular in shape. Area of a rectangle is length × width. The area of the reduced backyard becomes

40.5/3 × 25/3 = 1012.5/9 = 112.5 square feet

Answer:

112.5 square feet... edg2020

Answer:

∠5 = 55°

Step-by-step explanation:

Since l and m are parallel lines, then ∠5 and ∠1 are same- side interior angles and are supplementary, thus

∠1 + ∠5 = 180°, that is

125° + ∠5 = 180° ( subtract 125° from both sides )

∠5 = 55°

Answer:

55 degrees.

Step-by-step explanation:

m < 2 = 180 - 125 = 55 degrees (adjacent angles).

m < 5 = m < 2 (alternate angles).

Therefore m < 5 = m < 2  = 55 degrees.

Answer:

C. 28 = (2x - 1)(x)

Step-by-step explanation:

There is a rectangular swimming pool.

Width of swimming pool is x  

Length is  one less than twice the width

Area of the swimming pool is  28 sq ft.

To Find : Equation could be used to model the area of the swimming pool.

Solution:  

Since we are given that Length is one less than twice the width.

And width is x (given)

So, length = 2x-1

Area of the swimming pool is  28 sq ft.

Now ,

Formula of area of rectangle : Length*Width

⇒28= (2x-1)(x)

So,  equation used to model the area of the swimming pool: 28= (2x-1)(x)

Hence Option c is correct.

Answer:

28=(2x-1)(x)

Step-by-step explanation:

The swimming pool is rectangular in shape.

Hence the area of it is given by:

l * w

where l = length of the rectangular swimming pool

          w = width of the rectangular swimming pool

In this question it is given:

width = w = x

length = l = 2x - 1

Area = 28 sq.ft

Hence:

Area = l * w = (2x-1)(x)

28 = (2x-1)(x)

Answer:

Compatible width of rectangular banquet hall could be 90 feet approximately.

Step-by-step explanation:

Given

Area of a rectangular banquet hall = 7400 square feet

Length of rectangular banquet hall = 82 feet

We need to calculate width of the rectangular banquet hall.

Now Area of rectangle is equal to length times width.

Framing in equation form we get;

[tex]Area\ of \ Rectangle= length \times width[/tex]

Substituting the given values we get;

[tex]82 \times width = 7400\\\\width = \frac{7400}{82} = 90.2439[/tex]

Now by definition of Compatible numbers which state that:

"Compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally.  Compatible numbers are close in value to the actual numbers that make estimating the answer and computing problems easier."

Now By Using width as 90 feet and length as 82 feet we get area as 7380 sq ft. which is closet to actual area which is 7400 sq ft.

Hence we can say compatible width could be 90 feet approximately.

Answer:

No, she is not correct as her speed is 0.25 miles per minute.

Step-by-step explanation:

Given:

Ratio of distance  to time taken is 15 : 60.

Distance is in miles and length of time is in minutes.

We know that, average speed is given as the ratio of the distance traveled and the length of the time taken.

So, the ratio above is nothing but the average speed of Reese for cycling.

Thus, average speed of Reese is given as:

[tex]\textrm{Average speed}=\frac{Distance}{Time}\\\\\textrm{Average speed}=\frac{15}{60}\ miles\ per\ min\\\\\textrm{Average speed}=\frac{1}{4} = 0.25\ miles\ per\ min[/tex]

Therefore, the average speed of Reese is 0.25 miles per minute which is not equal to the one mentioned by Reese as 4 miles per minute.

So, Reese conclusion of her average speed is incorrect. It's not 4 but the reciprocal of 4 which is 0.25 miles per minute.

Answer:

Option C.

Step-by-step explanation:

Given information: In triangle ABC, ST║AC, SB=10 ft, BT=9 ft and CT=2.7 ft.

Triangle proportionality theorem: If a line segment parallel to a side of a triangle then the line segments divides the remaining sides proportionally.

Using triangle proportionality theorem we get

[tex]\dfrac{SA}{SB}=\dfrac{CT}{BT}[/tex]

[tex]\dfrac{SA}{10}=\dfrac{2.7}{9}[/tex]

On cross multiplication we get

[tex]9\times SA=2.7\times 10[/tex]

[tex]9SA=27[/tex]

Divide both sides by 9.

[tex]SA=3[/tex]

The length of SA is 3ft.

Therefore, the correct option is C.

Answer: C on edg.

Step-by-step explanation:

Answer:

  60 m, 61 m

Step-by-step explanation:

If "a" and "b" represent the lengths of the sides adjacent to the right angle, the area is ...

  area = (1/2)ab

Filling in the given information, we can find the other side to be ...

  330 m² = (1/2)(11 m)b

  60 m = b  . . . . . . divide by the coefficient of b

Then the remaining side can be found from the Pythagorean theorem:

  c² = a² + b² = 11²  + 60² = 3721

  c = √3721 = 61 . . . meters

The lengths of the other two sides are 60 m and 61 m.

Answer:

0.784

Step-by-step explanation:

Given that you are  analyzing the allele frequencies for fur color in a population of squirrels where black fur is dominant to red fur.

As part of your research, you collect the following data:

Total individuals: 1,000

Red fur individuals: 216

So black fur individuals = [tex]1000-216\\=784[/tex]

p2 = proportion of black fur individuals to total individuals

= [tex]\frac{784}{1000} \\=0.784[/tex]

Final answer:

The value of p2 in the population of squirrels is calculated using the homozygous recessive genotype for red fur (q2), which is found to be 0.216. We find q by taking the square root of q2 and then calculate p as 1 - q. The value of p2 is then p squared, resulting in approximately 0.286.

Explanation:

To determine the value of p2 in the population of squirrels for the trait of fur color, we first need to understand that red fur individuals represent the homozygous recessive genotype, which is indicated by q2 in Hardy-Weinberg equations. Since the total number of red fur individuals is given as 216 out of 1,000, we can calculate q2 by dividing the number of red fur individuals by the total number of individuals, which is 216/1000 = 0.216. To find the value of q, we need to take the square root of q2, so q = sqrt(0.216). Then, according to the Hardy-Weinberg principle, we know p + q = 1. Thus, we can calculate p by subtracting q from 1. Finally, to find p2, we just square the value of p.

The calculations are as follows:

Thus, the value of p2 in this population is approximately 0.286.