Please help me with this!

The balance in the account after 4 years, compounded continuously at 11%, is approximately $3884.25.

The formula for continuous compounding is given by [tex]\(A = Pe^{rt}\)[/tex], where:

- [tex]\(A\)[/tex] is the final amount,

- [tex]\(P\)[/tex] is the principal amount (initial investment),

- [tex]\(e\)[/tex] is the mathematical constant approximately equal to 2.71828,

- [tex]\(r\)[/tex] is the interest rate, and

- [tex]\(t\)[/tex] is the time in years.

In this scenario, [tex]\(P = $2500\)[/tex], [tex]\(r = 0.11\)[/tex] (11% expressed as a decimal), and [tex]\(t = 4\)[/tex] years. Plugging these values into the formula:

[tex]\[ A = 2500 \times e^{(0.11 \times 4)} \][/tex]

Calculate the exponent:

[tex]\[ A = 2500 \times e^{0.44} \][/tex]

Using the approximate value of [tex]\(e \approx 2.71828\):[/tex]

[tex]\[ A \approx 2500 \times 2.71828^{0.44} \][/tex]

[tex]\[ A \approx 2500 \times 1.5537 \][/tex]

[tex]\[ A \approx 3884.25 \][/tex]

Therefore, the balance in the account after 4 years, with an initial investment of $2500 at a continuously compounded interest rate of 11%, is approximately $3884.25.

The question probable maybe:

If $2500 is invested at a rate of 11% compounded continuously, find the balance in the account after 4 years. Use the formula A=Pe^(rt)

The answer is:

There are 17.6 ounces in 0.5 kilograms.

To calculate how many ounces are in 0.5 kilograms, we need to use the following factor:

[tex]1Kg=35.274ounces[/tex]

So, converting we have:

[tex]0.5Kilogram*\frac{35.274ounces}{1Kilogram}=17.637ounces=17.6ounces[/tex]

Have a nice day!

ANSWER

[tex]6{a}^{3} {b}^{4} {c}^{2} [/tex]

EXPLANATION

The given polynomials are:

[tex]3 {a}^{3} c = 3 \times {a}^{3} \times c[/tex]

[tex]6 {b}^{4} = 2 \times 3 \times {b}^{4} [/tex]

[tex]{b}^{2} {c}^{2} ={b}^{2} \times{c}^{2} [/tex]

The least common multiple (LCM) is the product of the highest powers of the common factors;

[tex]2 \times 3 \times {a}^{3} \times {b}^{4} \times {c}^{2} [/tex]

This simplifies to,

[tex]6{a}^{3} {b}^{4} {c}^{2} [/tex]

The LCM is

[tex]6{a}^{3} {b}^{4} {c}^{2} [/tex]

Answer:

6a³b⁴c²

Step-by-step explanation:

Given the polynomials, to find the Lowest Common Multiple of the polynomials, we need to find factors that can go in at least one of the given polynomials and multiply the resulting variables and constant gotten.

Check the attachment for the diagram

The LCM is 6a³b⁴c²

Step-by-step explanation:

[tex]4 {x}^{4} - 28 {x}^{3} + 59 {x}^{2} - 2x + c \: | 2x - 5[/tex]

-

[tex]4 {x}^{4} - 10 {x}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | 2 {x}^{3} [/tex]

then continue

[tex]0 - 18 {x}^{3} + 59 {x}^{2} - 2x + c \: \: \: \: \: \: \: | 2x - 5[/tex]

-

[tex] \: \: \: \: - 18 {x}^{3} + 45 {x}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | - 9 {x}^{2} [/tex]

continue

[tex] \: \: \: \: \: \: 0 + 14{x}^{2} - 2x + c \: \: \: \: \: \: \: \: \: \: \: \: \: | 2x - 5[/tex]

-

[tex] 14{x}^{2} - 35x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | 7x[/tex]

continue

[tex] 0 + 33x + c \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | 2x - 5[/tex]

-

[tex]33x - \frac{165}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | \frac{33}{2} [/tex]

[tex]0 +( c + \frac{165}{2} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: |[/tex]

Since 2x+5 is a factor then

[tex]c + \frac{165}{2} = 0 \\ = > c = - \frac{165}{2} [/tex]

Answer:

3, 50%

Step-by-step explanation:

The interquartile range is the top of the box minus the bottom of the box.  

5-2 = 3

Each part is 25 %

From the bottom of the whisker to the bottom of the box is 25%

From the bottom of the box of the middle of the box( median) is 25%

From the median to the top of the box is 25%

From the top  of the box of the last of the whisker of the box( is 25%

Adding from the bottom of the box to the top of the box  

25% + 25% = 50%

Answer:

4x=6

Step-by-step explanation:

The value of the equation is 4x = 6.

The two equations in the system are added or subtracted to produce a new equation with just one variable when using the addition/subtraction method. The other variable must cancel out for the new equation to have just one variable.

Given

eq 1 :8x+3y=14

eq 2 :4x+3y=8

eq1 - eq 2

(8x+3y=14) - (4x+3y=8)

=> (8x-4x) + ( 3y-3y) = (14-8)

=> 4x + 0 = 6

4x = 6.

To know more about the subtraction of two equations refer to :

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Answer:

Vertex: (- 2, -1)

axis of symmetry: x= - 2

Step-by-step explanation:

f(x)=x^2+4x+3

f(x)=(x^2+4x+4)+3-4.......complete the square

f(x)=(x+2)^2-1...................write in vertex form

Answer:

see explanation

Step-by-step explanation:

Given a quadratic function in standard form ax² + bx + c : a ≠ 0

Then the axis of symmetry and the x- coordinate of the vertex, since the vertex lies on the axis of symmetry is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = x² + 4x + 3 ← is in standard form

with a = 1, b = 4, hence

x = - [tex]\frac{4}{2}[/tex] = - 2

Equation of axis of symmetry is x = - 2

Substitute x = - 2 into f(x) for corresponding y- coordinate of vertex

f(- 2) = (- 2)² + 4(- 2) + 3 = 4 - 8 + 3 = - 1

Hence vertex = (- 2, - 1)

Answer:

Option A. [tex]30\ days[/tex]

Step-by-step explanation:

step 1

Find the area of the brownie pan

The area of the trapezoid is equal to

[tex]A=\frac{1}{2}(30+42)(25)=900\ cm^{2}[/tex]

step 2

To calculate the number of days, divide the total area of the brownie pan by 30 square centimeters of brownie

so

[tex]900/30=30\ days[/tex]

Answer: A: 30 days

Step-by-step explanation:

Answer:

a=14.63

c=13.63

Step-by-step explanation:

a = sinA*b

c = sinC*b

Answer is a and c girl

The inequality that will help you find how many hours Rita must work would be: 0.05x 10 x h is greater than or equal to 25

hope this helped you

For this case we have the following rule of three:

10 $ ----------> 100%

x --------------> 5%

Where "x" is the variable that represents 5% of $ 10.

[tex]x = \frac {5 * 10} {100}\\x = 0.5[/tex]

Then Rita saves 0.5 $ per hour.

She wants to save at least $ 25. Then, we propose the following inequality:

[tex]0.5h\geq 25[/tex]

ANswer:

[tex]0.5h\geq 25[/tex]

Answer:

The solution is [tex](3, -2)[/tex]

Step-by-step explanation:

We have the following system of equations

Equation 1) [tex]d + e = 1[/tex]

Equation 2) [tex]-d + e = -5[/tex]

To solve the system of equations add equation 1 with equation 2 and solve for variable e.

[tex]d + e = 1[/tex]

       +

[tex]-d + e = -5[/tex]

--------------------------

[tex]0d + 2e = -4[/tex]

[tex]e = -2[/tex]

Now substitute the value of e in equation 1 or equation 2 and solve for d.

[tex]d + (-2) = 1\\\\d = 3[/tex]

Therefore the solution of the system is the ordered pair

[tex](3, -2)[/tex]

Final answer:

Diego's method may introduce bias by not representing all student subgroups, suggesting that a random, stratified random, or systematic sampling method would better reflect student satisfaction with cafeteria food.

Explanation:

The question asks if selecting the first 25 students who purchase a lunch at the cafeteria is a good way for Diego to sample students to determine satisfaction with the cafeteria food. This sampling method may lead to bias because it does not represent all subgroups within the school population equally. For instance, it may only capture the opinions of students who already have a preference for cafeteria food, thus overlooking those who avoid it due to dissatisfaction. A better approach would be a random sampling method, where every student has an equal chance of being selected, ensuring a more accurate reflection of the entire student body’s opinion.

To improve the survey, Diego could consider using a stratified random sample, where the school population is divided into strata, such as grade levels or lunch periods, and then a random sample is taken from each stratum. This approach helps ensure that all segments of the student population are represented. Alternatively, a systematic sampling method, where every nth person is selected from a list or a line, could provide a more structured yet still random selection process compared to Diego's original plan.

Diego's approach is convenient but prone to bias. Random sampling across various days would improve representativeness and accuracy.

Diego's approach to surveying the students about cafeteria satisfaction has both strengths and weaknesses. Let's break down the pros and cons step by step:

1. **Convenience**: Approaching students during lunchtime in the cafeteria is convenient because it allows Diego to access a large number of students in one place and at a time when they are likely to be available.

2. **Sampling Bias**: However, selecting only the first 25 students who purchase lunch on a Monday might introduce sampling bias. For example, if there is a rush in the cafeteria during that time, Diego might end up surveying students who are in a hurry and may not accurately represent the entire student population.

3. **Limited Sample Size**: The sample size of 25 students is relatively small. While a larger sample size is not always necessary for accurate results, a larger sample size generally leads to more reliable findings. With only 25 students surveyed, there's a risk of the results being skewed by chance variations.

4. **Day of the Week Bias**: Monday might not be the best day to conduct the survey. Students' satisfaction with cafeteria food might vary depending on the day of the week due to factors like menu rotation or weekend leftovers. Therefore, surveying only on Mondays might not provide a comprehensive picture of overall satisfaction.

5. **Response Bias**: There's also the potential for response bias. Students who are particularly satisfied or dissatisfied with the food might be more likely to respond to Diego's survey, leading to results that don't accurately reflect the general sentiment of all students.

6. **Alternatives**: A better approach might be to conduct the survey at different times and days of the week to capture a more diverse range of student experiences. Additionally, Diego could use random sampling techniques to ensure that every student has an equal chance of being surveyed, reducing the risk of bias.

In summary, while Diego's approach is convenient, it may not yield the most accurate or representative results due to potential sampling bias, limited sample size, and other factors. To improve the validity of the survey findings, Diego should consider adjusting his sampling method and survey timing.

Answer:

approx. 251 in³

Step-by-step explanation:

The appropriate formula to use here is V = πr²h.  Substituting 2 in for r and 5 in for h, we get:

V = π(2 in)^2·(5 in), or

V = π(4 in²)(5 in) = 80π in³, or approx. 251 in³

Answer is provided in the image attached.

Answer: C. 4.5

Step-by-step explanation: All you need to do is divide 18 by 4 to find the cost of bowling one game.

18/4 = 4.5

The constant of proportionality between the money spent and the number of games played is C. 4.5.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=5(2)^{x}[/tex]  

This is a exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]  

where

a is the initial value

b is the base

In this problem

a=5

b=2

using a graphing tool

see the attached figure

Answer:

A

Step-by-step explanation:

Edge

Answer:

C

Step-by-step explanation:

looking at the graph, we see a parabola shifted up 6 units. the function is f(x) = x² + 6

we also see a line with a reflection on the y axis and a vertical shift up 6 units. the function is f(x) = -x + 6

x² + 6 is graphed like a normal parabola (u shaped graph) with an open circle on (3,15). the x coordinate is whats important here, which is 3. we see that there are no values to the right of 3, and only to the left of 3. we can say that the statement x < 3 is true of the parabola, as any value less than 3 is a solution to the parabola.

for -x + 6, we see a line graphed with an closed circle on approximately (3,3). again, the x-coordinate is important here which is 3. the line only goes to the right of 3, meaning the inequality x ≥ 3 is true of the line as any value greater than or equal to 3 is a solution

looking at our answer choices we need to find the following answer:

x² + 6 x < 3 and -x + 6 x ≥ 3

this answer would be C

Answer:

C

Step-by-step explanation:

Copied what the person aboved one said

Answer:x

Step-by-step explanation:

solve for the x value in the first equation one and plug it into the second equation in order to find the value of the y

3x -6y = 27

3x+4y=17

solution

3x-6y =27 solve for x

3x-6y + 6y = 27 +6y

3x=27 +6y

usually you would simplify to solve for x

but in this case I would leave it as 3x because the second equation requires the value of 3x

so substituting the 27 +6y for 3x

you end up with the equation of 27+6y + 4y = 17 (combine the like terms)

27+10y = 17  

subtract the 27 form both sides 10y = 17-27 which simplifies to 10y = 10

divide both sides by 10 and you get y = -1

you then take the value of y which is -1  : y = -1        

3x-6y = 27

3x - 6(-1) = 27  :substitute -1 into the top equation

3x +6 = 27 :  multiply the -6(-1)

3x=27-6 :subtract both sides by -6

3x = 21 divide both sides by 3

x = 7

Answer:

Well the answer is 857.4 meters per minute

Step-by-step explanation:

The reason is because 1.429 times 60= 85.74 That means that you walk 85.74 meters per second. Then that times 10 is 857.4 . Can I get brainliest

Answer:

$199.99 multiply by .20 = 39.998

$199.99 minus $39.99 or $40

the sale price of the four wheeler is $159.99

Step-by-step explanation:

Answer:

adult = £5

child = £2

Step-by-step explanation:

a = adult c = child

3a + 4c = 23

1a + 5c = 15

multiply second equation by 3 and rewrite

3a + 4c = 23

3a + 15c = 45

subtract

0 - 11c = - 22

-11c = -22

11c = 22

c = £2

subsitute into one of the equations and solve for a

1a + 5c = 15

a + 5(2) = 15

a + 10 = 15

a = £5

The question can be solved using systems of linear equations. The cost of an adult's ticket is £5, and the cost of a child's ticket is £2.

The problem given can be solved using systems of linear equations. We can denote the cost of an adult's ticket as 'a' and the cost of a child's ticket as 'c'. Then you set up two equations:

To solve the system, we can multiply the second equation by 3:

Now we subtract the first equation from this one:

If you divide by 11, you get c=2. Now, substitute c into the second initial equation: a + 5*2 =15, and you get that a=5. Therefore, the cost of an adult's ticket is £5 and the cost of a child's ticket is £2.

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Answer:

Mean

Step-by-step explanation:

Means tell the average of something

Answer:in order to get a more accurate result, the teacher would not add in the score

Step-by-step explanation:

im pretty sure the correct answer is D

Let's start with y = 4x + b (since 4 is the slope);

We need to find what number should be put instead of b;

Then, let's see what needs to be done;

Plug in the y and x values from the coordinate (22,12) into y=4x+b;

12 = 4(22) + b

Solve;

12 = 88 + b

12 - 88 = b

b = -76

Remember the equation y = 4x + b? Put the -76 instead of b:

y = 4x + -76

or: y = 4x - 76

That is the equation.

To make it standard form, put x and y both in the left side, with x first then y:

-4x + y = -76

^^Answer!

Final answer:

The equation of the line which passes through the point (22, 12) with a slope of 4, when written in standard form, is -4x + y = -76.

Explanation:

To write the equation of a line that includes the point (22, 12) and has a slope of 4 in standard form, we begin with the point-slope form of a line equation, which is y - y1 = m(x - x1). Substituting the given point and slope values, we have y - 12 = 4(x - 22).

Next, we simplify and convert this equation to standard form Ax + By = C. Standard form requires that x and y terms are on the left side and the constant is on the right:

y - 12 = 4x - 88
Add 12 to both sides:
y = 4x - 76
Subtract 4x from both sides:
-4x + y = -76

This is now in standard form and matches one of the given choices.

Answer:

7,200

Step-by-step explanation:

One sheet: 12 rows

1 row: 6 coupons

6 x 12 = 72

To find out how many coupons are in 1 sheet, multiply 6 by 12

So, in one sheet there are 72 coupons

1 sheet = 72 coupons

100 sheets = ? coupons

To find out how many are in 100 sheets, multiply 72 by 100

72 x 100 = 7,200

Therefore, there are 7,200 coupons in 100 sheets

I hope this helps! :)

Answer:

110 in. = 9  1/6 ft, or 9 ft 2 in

Step-by-step explanation:

Please try to do a better job of formatting your next question.  Thanks.

110 in       1 ft

-------- * --------- = 9 1/6 ft  or  9 ft 2 in

   1          12 in

110 in = 9 ft  2 in.

To convert 110 inches to feet and inches, we need to know the conversion factor that:

[tex]1\ foot = 12\ inches[/tex]

So, first, divide the total inches by 12 to get the number of feet:

[tex]\frac{110\ inches}{12\ inches/foot} = 9\ feet[/tex] with a remainder.

The remainder represents the inches that do not make up a full foot. The remainder can be calculated as follows:

[tex]110\ inches - (9\ feet \times 12\ inches/foot) = 110\ inches - 108\ inches = 2\ inches[/tex].

So, 110 inches is equal to 9 feet and 2 inches.

Therefore, 110 inches = 9 feet 2 inches.

The second is ones.

The third is tens.

I don’t know the first one 100% so I don’t want to guess and have you get it wrong!! But pls mark me love(:

1. Hundred thousands

2. Ones

3. Tens

Answer:

The product of two rational numbers is a rational number

Step-by-step explanation:

I'll quickly recap the proof: a rational number is, by definition, the ratio between two integers. So, there exists four integers m,n,p,q such that

[tex]a=\dfrac{m}{n},\quad b=\dfrac{p}{q}[/tex]

If we multiply the fractions, we have

[tex]ab = \dfrac{mp}{nq}[/tex]

Now, mp and nq are multiplication of integers, and thus they are integers themselves. So, ab is also a ratio between integer, and thus rational.

Answer:

the product of two rational numbers is a rational number!

Step-by-step explanation:

Answer:  [tex]Range:[/tex]{[tex]1,3,4,7[/tex]}

Step-by-step explanation:

We know that, by definition, the Domain is the set of all the x-coordinates of the ordered pairs  and the Range is the set of all the y-coordinates of the ordered pairs.

Therefore, given [tex]f=(2,3),(5,7),(5,4),(9,1)[/tex], you can observe that the set of all second elements of ordered pairs (the values of "y") is the following:

{[tex]3,7,4,1[/tex]}

 Therefore, we can conclude that if [tex]f=(2,3),(5,7),(5,4),(9,1)[/tex] , then the range is:

 [tex]Range:[/tex]{[tex]1,3,4,7[/tex]}

Answer:

The range of f is {1 , 3 , 4 , 7}

Step-by-step explanation:

* Lets revise the relation

- f is a relation between x and y

- x is the input of the relation

- y is the output of the relation

- x is called the domain of the relation

- y is called the range of the relation

- The range is the corresponding value to x

* Now lets solve the problem

∵ f = {(2 , 3) , (5 , 7) , (5 , 4) , (9 , 1)

∵ x = {2 , 5 , 9}

∴ The domain of f is {2 , 5 , 9}

∵ y = {1 , 3 , 4 , 7}

∴ The range of f is {1 , 3 , 4 , 7}

Answer:

80% markup

Step-by-step explanation:

You first subtract the original amount from the final to get:

54-20 = 24

Then you divide it by the original:

24/30 = .80

You multiple this by 100% to get 80%

Answer:

The markup is 80%

Answer:

The equation of the parabola is (y + 3)² = -6(x - 7/2)

Step-by-step explanation:

* Lets revise the equation of a parabola

- If the equation is in the form (y − k)² = 4p(x − h), then:

• Use the given equation to identify h and k for the vertex, (h , k)

• Use the value of k to determine the axis of symmetry, y = k

• Use h , k and p to find the coordinates of the focus, (h + p , k)

• Use h and p to find the equation of the directrix, x = h − p

* Now lets solve the problem

∵ The directrix ⇒ x = 5

∴ The form is (y − k)² = 4p(x − h)

∵ The directrix is x = h - p

∴ h - p = 5 ⇒ (1)

∵ The focus is (h + p , k)

∵ The focus is (2 , -3)

∴ k = -3

∴ h + p = 2 ⇒ (2)

- Add (1) and (2) to find h

∴ 2h = 7 ⇒ ÷ 2 for both sides

∴ h = 7/2

- Substitute this value in (1) or (2) to find p

∴ 7/2 + p = 2 ⇒ subtract 7/2 from both sides

∴ p = -3/2

* Now we can write the equation

∴ (y - -3)² = 4(-3/2) (x - 7/2)

∴ (y + 3)² = -6(x - 7/2) ⇒ in standard form

* The equation of the parabola is (y + 3)² = -6(x - 7/2)

Answer:

Step-by-step explanation:

I’m not sure but I think it’s C