Financial algebra: Karen wants to make a deposit of $500 each week into an account that earns %5 interest compounded weekly(52 weeks/year). How much money will be in the account at the end of 1 year?
How much money in interest will be the account earned at the end of the year?

Answer:

\(y=-\frac{5}{2}x+24.\)

Step-by-step explanation:

all the details are in the attachment, step-by-step short explanation:

1) re-write the given equation of the line;

2) to find the normal of the given equation;

3) to calculate the normal of the required equation of the line (based on the perpendicular rule);

4) to write the required equation of the line (the value of 'C' is unknown);

5) in order to calculate the value of 'C' to substitute the coordinates (10;-1) into the required equation of the line;

6) to make up the required equation of the line in common form;

7) to write the required equation of the line in slope-interception form.

Answer:

1.5lb/ounces

Step-by-step explanation:

Given:

Mass of dry ice Carmen uses  = 12lb

Mass of root beet  = 8ounces

Unknown:

Ratio/Proportional constant for number of pounds to number of ounces of root beer extract  = ?

Solution:

To solve this problem,

    Ratio = \(\frac{number of pounds of dry ice}{Ounce of root beer}\)

    Ratio  = \(\frac{12lb}{8ounces}\)   = 1.5lb/ounces

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).

When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).

As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

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Answer:

The answer is false.

Step-by-step explanation:

Answer:

x <−22

Step-by-step explanation:

Let's solve your inequality step-by-step.

−2x+5>49

Step 1: Subtract 5 from both sides.

−2x+5−5>49−5

−2x>44

Step 2: Divide both sides by -2.

2x/ -2 > 44/ -2

The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

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Answer:

6163.2 years

Step-by-step explanation:

A_t=A_0e^{-kt}

Where

A_t=Amount of C 14 after “t” year

A_0= Initial Amount

t= No. of years

k=constant

In our problem we are given that A_t is 54% that is if A_0=1 , A_t=0.54

Also , k=0.0001

We have to find t=?

Let us substitute these values in the formula

0.54=1* e^{-0.0001t}

Taking log on both sides to the base 10 we get

log 0.54=log e^{-0.0001t}

-0.267606 = -0.0001t*log e

-0.267606 = -0.0001t*0.4342

t=\frac{-0.267606}{-0.0001*0.4342}

t=6163.20

t=6163.20 years

PLEASE MARK BRAINLY

Draw a graph of 360 degrees and move in a counterclockwise direction

180 degrees is pi in radians.

Let -360 degrees be x radians, then

We have -360 degrees when we move in a counterclockwise direction.

Answer:

32 and 37

Step-by-step explanation:

Because the difference between the values is 5.

Answer:

C.

Step-by-step explanation:

Scatterplots with weak correlation coefficients are values near zero

The false statement about the correlation coefficient is r = 0 shows that two variables are strongly correlated.

A statistical metric known as correlation illustrates how closely two variables are connected and how they tend to move in tandem. When two variables are positively correlated, they move in the same direction, and when they are negatively correlated, they move in the opposite way. To determine the degree and direction of the association between two variables, a correlation coefficient is utilized.

A correlation coefficient of -1 indicates a perfect negative correlation, a correlation coefficient of 1 indicates a perfect positive correlation, and a correlation coefficient of 0 indicates no correlation between the two variables.

Given data ,

The FALSE statement is:

c. The correlation coefficient r = 0 shows that two variables are strongly correlated.

A correlation coefficient of 0 means that there is no linear relationship between the two variables. It does not indicate the strength of the relationship.

A value of r = 0 indicates that there is no association between the two variables, whereas a value of r = 1 or r = -1 indicates a perfect positive or negative association, respectively.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

This is an example of descriptive statistics. Descriptive statistics involves summarizing and describing the main features of a set of data. In this case, the data consists of the responses from 85 randomly selected fifty-year-old Americans about the amount of money they have saved for their retirement.

The statistics provided, such as the average ($25,000), minimum ($0), and maximum ($1,200,000), are all examples of descriptive statistics that summarize the data and provide information about its distribution.

Inferential statistics, on the other hand, involves making inferences about a population based on a sample. Inferential statistics allow us to use the information from a sample to make educated guesses about the characteristics of the population from which the sample was drawn.

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After an integer is decreased by 2 it falls between 4.9 and -4.9. What is the sum of all the integers that satisfy this condition?

Let

x ------> an integer

so

x-2 < 4.9

and

x-2 > -4.9

Solve the system of inequalities

x-2 < 4.9

x < 6.9 -------> interval (-infinite, 6.9)

x-2 > -4.9

x > -2.9 ------> interval (-2.9, infinite)

the solution of the system is the interval (-2.9, 6.9)

possible solutions are

-2,-1,0,1,2,3,4,5,6

their sum is

-2+-1+0+1+2+3+4+5+6=18

We can pose the question in the following way:

Because we have two directly proportional amounts and the ratio is constant. Then, solving the latter proportion, we have:

Then, Corey will spend 21 minutes on rides if he plans to spend 60 minutes in lines (according to the given proportion).

Answer:

B

Step-by-step explanation:

a prime polynomial is one which does not factor into 2 binomials.

its only factors are 1 and itself

attempt to factorise the given polynomials

3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )

= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(3x² - 2) ← in factored form

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

3x³ - 2x² + 3x - 4 ( factor the first/second terms

= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored

thus this polynomial is prime

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

4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )

= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term

= (2x + 1)(2x² + 3) ← in factored form

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

4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )

= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term

= (x + 1)(4x² - 3) ← in factored form

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

the only polynomial which does not factorise is

3x³ - 2x² + 3x - 4

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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Answer:

a) the mean percentage of defective item produced is 2.52 %

b) the standard deviation of percentage of defective item produced is 1.01%

Step-by-step explanation:

Given that;

the percentage of defective items produced was 2%, 1.4%, 4%, 3%, 2.2%.

sample size n = 5

a) Calculate the mean for these data

mean percentage of defective item produced will be;

\(x^{bar}\) = ∑x / n

\(x^{bar}\) = ∑x / n = ( 2% + 1.4% + 4% + 3% + 2.2% ) / 5

\(x^{bar}\)  = 12.6 / 5

\(x^{bar}\)  = 2.52 %

Therefore, the mean percentage of defective item produced is 2.52 %

b) Calculate the standard deviation for these data

Formula for standard deviation is;

S = √( (∑(x-\(x^{bar}\) )²) / (n-1) )

so we make a table;

x                   ( x - \(x^{bar}\) )%                ( x - \(x^{bar}\) )²%

2%                 -0.52                         0.2704

1.4%               -1.12                           1.2544

4%                  1.48                          2.1904  

3%                  0.48                         0.2304

2.2%.             -0.32                         0.1024

summation                                     4.048

so (∑(x-\(x^{bar}\) )² = 4.048%  

so we substitute the value into our equation;

S = √( (∑(x-\(x^{bar}\) )²) / (n-1) )

S = √( (4.048%) / (5-1) )

S = √( 4.048% / 4 )

S = √( 1.0121

S =  1.00598 % ≈ 1.01%

Therefore, the standard deviation of percentage of defective item produced is 1.01%

Measure of CAB is 84.4, by using supplementary angle theory.

In geometry, two angles are referred to as supplementary angles if their sum is 180 degrees. For instance, if A + B = 180°, then A and B are considered supplementary angles. Complementary angles always result in a straight angle when combined (180 degrees).

Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.

We have given, CAB= 4x+14 and DAB = 6x-18

Both are supplementary angle

Therefore, CAB + DAB = 180

4x+14+6x-18=180

10x-4=180

10x=176

x=17.6

hence, CAB = 4(17.6)+14 = 84.4

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The average is 40 and  the margin of error is 10.95.

What is margin of error?

The margin of error is a statistic expressing the amount of random sampling in the result of a survey.

Average (A) = sum of all the value/ given set.

A = (51+ 41 + 28)/3 = 40

margin of error = 100/square root of 120 = 10.95.

Therefore, the average is 40 and  the margin of error is 10.95.

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Answer: This, the required number of yellow rattles they sell is 14.

x + y = 108

x / y = 2 / 7

x = 2y / 7

y + 2y/7 = 108

9y = 756

y = 94

x + 94 = 108

x = 14

Answer:

b

Step-by-step explanation:

Answer:

its B i took the test

Step-by-step explanation:

A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.

What theory directly contradicts concept of absolute zero?

All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).

Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.

Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.

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Answer:

the answer is 908. You need to compare the sides.

16 in x 20 in= 320 in

42in x 14 in = 588

all together it's 908

Answer:

I think the answer is 1108

Step-by-step explanation:

Area1 = 26in × 20in =520^2

Area2 = 42in × 14in =588in^2

total area = 1108in^2

Answer:

A

Step-by-step explanation:

Unit Test on a Edge today. ; )

Answer:

its A

Step-by-step explanation:

i got a 100  on my quiz

The equation representing the number of gallons of paint remaining y  is y = 73 - 2x.

Let quantity of paint still in gallons, y.

Let x be the total number of classrooms.

There are x classrooms, each using 2 gallons, for a total of x gallons.

They use 2 gallons of paint to paint x classrooms.

Then, the equation becomes.

2x + y = 73

The amount of pain remaining is-

y = 73 - 2x

Thus, the equation representing the number of gallons of paint remaining y  is y = 73 - 2x.

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Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

Answer:

Im pretty sure you are correct

Step-by-step explanation:

Belive in urself m8

Answer:

no I don't think this is correct

Step-by-step explanation:

(no btw)

Using the given data on the table, we must fill the missing cells with the correct answer.

First, let's try to solve for the FICTION Books for ADULTS.

Since we are given the total number of Fiction books, as well as the number of Kids and Teens Fiction books, we can add up the number of Kids and Teens Fiction book to the Total number of fictions book in order to get how many Adult Fiction books there are.

ADULT FICTION = TOTAL FICTION - (KIDS FICTION + TEENS FICTION)

ADULT FICTION = 105 - (75 + 20)

ADULT FICTION = 105 - 95

ADULT FICTION = 10

Therefore, there are 10 Adult Fiction Books.

Next, we will find the number of KIDS NON FICTION books.

Just like what we did on the first one, we are given the total, and the number of KIDS FICTION book. Therefore, we just need to substract the number of KIDS FICTION to the TOTAL amount of kids book.

KIDS NON FICTION = TOTAL KIDS BOOK - KIDS FICTION

KIDS NON FICTION = 80 - 75

KIDS NON FICTION = 5

Therefore, we have 5 Non Fiction Books for Kids.

We will use the same process for finding how many TEEN NON FICTION books are there.

TEENS NON FICTION = TOTAL TEENS BOOK - TEENS FICTION BOOK

TEENS NON FICTION = 50 - 20

TEENS NON FICTION = 30

Therefore, we have 30 Non Fiction Books for Teens.

Next, to find the total number of NON FICTION Books, we just need to add up the number of KIDS NON FICTION books, TEENS NON FICTION books, and ADULT FICTION books.

TOTAL N-FICTION=KIDS N-FICTION+TEENS N-FICTION + ADULT N-FICTION

TOTAL NON FICTION BOOKS = 5 + 30 + 15

TOTAL NON FICTION BOOKS = 50

Therefore, the total number of Non Fiction books are 50.

Next, we will do the same to find the total number of ADULT BOOKS.

TOTAL ADULT BOOKS = ADULT FICTION + ADULT NON FICTION

TOTAL ADULT BOOKS = 10 + 15

TOTAL ADULT BOOKS = 25

Therefore, we have a total of 25 Adult Books.

Finally, we will just add up the number of TOTAL NON FICTION books and TOTAL NON FICTION books to get the TOTAL NUMBERS OF BOOKS.

TOTAL NUMBER OF BOOKS = TOTAL FICTION + TOTAL NON FICTION

TOTAL NUMBER OF BOOKS = 105 + 50

TOTAL NUMBER OF BOOKS = 155

Therefore, we have a total of 155 books altogether.

The probability of randomly choosing a green marble after you have chosen red is 4.4%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given

A jar has 20 marbles: 3 green, 12 blue, 5 red.

Probability;

In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.

The total number of marbles = 20

The number of green marbles= 3

The number of blue marbles = 12

The number of red marbles = 5

The probability of choosing a red marble = Number of red marbles / Total number of marbles

= 5/20

The probability of choosing a green marble is =  Number of green marbles / New total number of marbles

= 3/19

Therefore,

The probability of randomly choosing a green marble after you have chosen red is;

= 5/20 * 3/19

= 3/68

percentage = 3/68 * 100 = 4.4%

Hence, the probability of randomly choosing a green marble after you have chosen red is 4.4%

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