Maryi had $64.25, but gave Jim $48.86. How much does Mary have now?

There are a total of 279 1/9s in 31.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

To find out how many 1/9's are in 31, you can divide 31 by 1/9.

This can be simplified by converting the division of a fraction to multiplication with its reciprocal:

31 ÷ (1/9) = 31 × (9/1)

Simplifying the expression on the right side gives:

31 × 9 = 279

So there are 279, 1/9's in 31.

Learn more about Simplification here:

https://brainly.com/question/28996879

#SPJ2

Answer: Hello!

Step-by-step explanation:

Your answer would be D :)

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

Learn more on the variance of a set of data here: https://brainly.com/question/30701163

#SPJ1

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

Answer:

Step-by-step explanation:

i need help on that too

The mathematical function describing the cost of car the next year is →

C{n + 1} = C{n} (1 - 3/20).

The depreciation rate is a rate at which the price of a quantity decreases every year.

Given is that the cost of a new car is $32,000 it depreciates at a rate of 15% per year.

We can understand it as follows.

After one year the cost would be -

{x} = 32000 - {15% of 32000}

{x} = 32000 - 4800

{x} = $27200

After second year the cost would be -

{x} = 27200 - {15% of 27200}

{x} = 27200 - 4080

{x} = $23120

This means that after every year, the value decrease by 15% of what it was a year before. We can write -

C{n + 1} = C{n} - (15/100) C{n}

C{n + 1} = C{n} (1 - 3/20)

Therefore, the mathematical function describing the cost of car the next year is →

C{n + 1} = C{n} (1 - 3/20).

To solve more questions on functions & expressions, visit the link below

brainly.com/question/17613163

#SPJ9

Answer:

remember that you start in the [ ] and work your way out

Step-by-step explanation:

Answer:

0.09 = 9% probability that the student is proficient in neither reading nor mathematics

Step-by-step explanation:

We solve this question treating the events as Venn probabilities.

I am going to say that:

Event A: A student is proficient in reading.

Event B: A student is proficient in mathematics.

A total of 82% of the students were found to be proficient in reading

This means that \(P(A) = 0.82\)

74% were found to be proficient in mathematics

This means that \(P(B) = 0.74\)

65% were found to be proficient in both reading and mathematics.

This means that \(P(A \cap B) = 0.65\)

What is the probability that the student is proficient in neither reading nor mathematics?

This is:

\(P = 1 - P(A \cup B)\)

In which

\(P(A \cup B) = P(A) + P(B) - P(A \cap B)\)

With the values that we have:

\(P(A \cup B) = 0.82 + 0.74 - 0.65 = 0.91\)

Then

\(P = 1 - P(A \cup B) = 1 - 0.91 = 0.09\)

0.09 = 9% probability that the student is proficient in neither reading nor mathematics

The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

For more questions on distance

https://brainly.com/question/28342342

#SPJ8

6 small sizes, 3 medium sizes, and 7 large size pizzas were delivered.

What is a system of equations?

A system of linear equations is a set of two or more linear equations involving the same variables. The variables represent unknown quantities that we want to find, and the linear equations are mathematical statements that describe the relationships between these variables.

Let a = number of small pizzas delivered

Let b = number of medium pizzas delivered

Let c= number of large pizzas delivered

(1) a + b + c = 16

(2) 4a + 9b + 11c = 128

(3) 3a + 5b + 10c = 6 * 16 + 7

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

(3) 3a + 5b + 10c = 103

Multiply both sides of (1) by 3

and subtract (1) from (3)

(3) 3a + 5b + 10c = 103

(1) - 3a - 3b - 3c = - 48

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

2b + 7c = 55

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

Multiply both sides of (1) by 4

and subtract (1) from (2)

(2) 4a + 9b + 11c = 128

(1) - 4a - 4b - 4c = - 64

5b + 7c = 64

Subtract:

5b + 7c = 64

- 2b - 7c = - 55

3b = 9

b = 3

and,

5 * 3 + 7c = 64

7c = 64 - 15

7c = 49

c = 7

(1) a + b + c = 16

(1) a + 3 + 7 = 16

(1) a = 6

Hence, 6 small sizes, 3 medium sizes, and 7 large size pizzas were delivered.

To learn more about the system of equations, visit:

https://brainly.com/question/13729904

#SPJ1

Hello !

68/17 = 4

=> yes for 68

84/17 = 4.941...

=> no for 84

357/17 = 21

=> yes for 357

1001/17 = 58.882...

=> no for 1001

Answer:

Step-by-step explanation:

Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.

Thus , the parameter of the exponential distribution is calculated as,

μ = 6

\(\frac{1}{\lambda} =6\)

\(\lambda = \frac{1}{6}\)

a) The required probability is

\(P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}\)

= 0.513

Hence, the probability that a randomly selected car battery will last more than four years is 0.513

b) The variance of the battery span is calculated as

\(\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36\)

The 95% percentile \(x_{a=0.05}\) (α = 5%) of the battery span is calculated

\(x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years\)

c)  

Let \(X_r\) denote the remaining life time of a car battery

i)the probability the battery will last an additional five years is calculated below

\(P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346\)

ii) The average time that the battery is expected to last is calculated

\(E(X_r)=\frac{1}{\lambda} \\\\=6\)

The exponential function giving the number of bacteria after x hours is given as follows:

\(y = 250(2)^x\)

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 250, b = 2.

Hence the function is given as follows:

\(y = 250(2)^x\)

The problem asks for the exponential function giving the number of bacteria after x hours is given as follows:

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Answer:

8h ≥ 154

Step-by-step explanation:

Mark me Brainllest

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

Answer: Hmm, I want to say it will be about 40 weeks before she can get the bike, hope this helps!

Step-by-step explanation:

Answer:

40 weeks

Step-by-step explanation:

The size of sample are both large enough 40 and 35. The mean and standard deviation of given data is 0.05 and 0.105 respectively.

The shape of the sampling distribution of \(\hat{p}_j - \hat{p}_s\)is approximately normal, according to the Central Limit Theorem. This is because the sample sizes are both large enough (40 and 35, respectively) and the population proportions are unknown but assumed to be independent.

The mean of the sampling distribution is the difference in the population proportions of females, which is 0.54 - 0.49 = 0.05.

The standard deviation of the sampling distribution can be calculated as:

\($\sqrt{\frac{\hat{p}_j(1 - \hat{p}_j)}{n_j} + \frac{\hat{p}_s(1 - \hat{p}_s)}{n_s}}$\)

where \(\hat{p}_j = 0.54$, $n_j = 40$, $\hat{p}_s = 0.49$, and $n_s = 35$.\)Plugging in these values, we get:

\($\sqrt{\frac{0.54(1 - 0.54)}{40} + \frac{0.49(1 - 0.49)}{35}} \approx 0.105$\)

Interpretation: The standard deviation of the sampling distribution tells us how much we can expect the sample proportion difference to vary across different random samples. In this case, we can expect the difference between the sample proportions of females in the junior and senior classes to vary by about 0.105 on average across different samples.

To know more about standard deviation:

https://brainly.com/question/23907081

#SPJ4

Answer:

Number of hours worked overtime = 5.5 hours

overtime rate = $17.925 per hour

overtime pay = $98.59

Step-by-step explanation:

a. Her overtime hours are the number of hours worked over 40 hours, and we are told that she worked 45 1/2 hours last week.

Therefore, her overtime hours = 45.5 - 40 = 5.5 hours

b. overtime rate:

for her overtime rate, we are given that she has a time-and-a-half pay for her overtime hours. This means that she is paid 1.5 times the normal rate for working overtime.

∴ overtime rate = 1.5 × normal rate

overtime rate = 1.5 × 11.95/hour

overtime rate = $17.925/hour

c. overtime pay:

overtime pay = overtime rate × overtime hours worked

overtime pay = 17.925 × 5.5

overtime pay = $98.59

The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

To learn more about GP visit:

https://brainly.com/question/29323941

#SPJ1

Answer:

your answer will be

y=40 x +20

Step-by-step explanation:

have a nice day/night ^_^

The probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

There are 12 marbles in total in the bag, so the probability of selecting a blue marble on the first draw is 4/12.

After the first marble is drawn, there are 11 marbles left in the bag, so the probability of selecting a green marble on the second draw, given that the first marble was blue and has already been removed, is 3/11.

To determine the probability of both events occurring together, we multiply the probabilities. Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is:

(4/12) * (3/11) = 0.0909

Rounding to the hundredth place, the probability is approximately 0.09.

Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

To learn more about probability from the given link:

https://brainly.com/question/30034780

#SPJ1

Answer:

To find net worth, add all assets seperately. Then add the liabilities. Subtract the assests and liabilities to get your net worth.

It says he has $4,250 in his savings, so that's an assest. Due to the savings.

He already had that much, so you could say he started with it.

Step-by-step explanation:

Good luck! <3

Hoped that helped.

Answer:

answer 12.5

Step-by-step explanation:

25% of 50 is 12.5 because 50 ÷ 4 = 12.5 Hope that helps!

Answer:

I don't know if you want to be a good

The test statistic for the hypothesis test using the parameters is 2.05

A test statistic is used to access how consistent  sample data are with the null hypothesis in a hypothesis test.

How to calculate test hypothesis of  given parameters?

Using the parameters

Hₙ: ц=12.5, x=14.1, s=2.7, and n=12

The test statistic (t) is given by the formula

t=\(\frac{x-U}{s/\sqrt{n} }\)

Substituting the given parameters;

t=\(\frac{14.1-12.5}{2.7/\sqrt{12} }\)

t=\(\frac{1.6}{2.7/3.46}\)

t=\(\frac{1.6}{0.78}\)

t=2.05

This figure is round up to 2 decimal places

The test statistic using the parameters is 2.05

Learn more about test statistics on https://brainly.com/question/14128303

#SPJ1

Answer:

2500

Step-by-step explanation:

$10 times 52 is $520 a day so multiply 520 times 5 and you get $2600 so round that and it is $2500