solve 15-2x=3x
the solution is x=

Answer:

Step-by-step explanation:

3 = 307k

If Ridgewood Savings Bank charges a $27 per check overdraft protection fee. The amount she will owe the bank after July 12 is: $1,071.42.

Total obligation can be defined as the amount a person owe another person or the debt amount a borrower  is expected to payback to a lender.

Balance $1,400

July 9 check ($1,380.15)

Balance $19.85

July 10 check ($765.67)

($670 + $95.67)

Balance -$745.82 (Overdraft)

Now let find the amount she owe

Balance -$745.82

July 11 check $130

Balance -$875.82

July 12 check $87.60

Ending balance -$963.42

Overdraft fee $108

($27 ×4)

Total obligation -$1,071.42

Therefore her total obligation is $1,071.42.

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Answer:

(-∞, -1]∪{5}

Step-by-step explanation:

We know that:

f(x) ≤ 0 is true if the graph of the function is intersecting the x-axis or below the x-axis.

So we can just look at the graph, we can see that in the interval:

(-∞, -1]   (the value x = -1 is included, that is why we use the symbol ] instead of the parenthesis)

the graph is below or intersecting the x-axis

and this also happens at x = 5 or just denoted as {5}

Then the correct notation is:

(-∞, -1]∪{5}

The simplified expression is 2y² - 9.

To subtract the binomials (-3y^2 - 8) - (-5y^2 + 1), we need to distribute the negative sign to the terms inside the second set of parentheses:

(-3y^2 - 8) - (-5y^2 + 1) = -3y^2 - 8 + 5y^2 - 1

Next, we combine like terms by adding or subtracting the coefficients of the same degree:

-3y^2 + 5y^2 - 8 - 1 = (5y^2 - 3y^2) + (-8 - 1) = 2y^2 - 9

Therefore, the simplified expression is 2y² - 9.

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Answer and Step-by-step explanation:

We want to prove that 0.5555... = 5/9.

First, let's set 0.555... equal to x:

x = 0.555...

Now multiply this by 10:

10x = 5.555...

Now subtract the original from this new one:

   10x = 5.555...

-       x = 0.555...

______________

     9x = 5

Note that we could cancel all the recurring terms because they were the same for both 5.555... and 0.555... since the 5's go up to infinity.

We now have 9x = 5, so divide both sides by 9:

x = 5/9, as desired

the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

How to solve?

To solve this problem, we can use the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the expected rate of occurrence.

Let lambda be the expected rate of customer arrivals per minute. If exactly two customers arrive in the first minute, then the expected number of customers to arrive in three minutes is lambda ×3. We can use this expected value to calculate the probability of at least seven customers arriving in three minutes:

P(X ≥ 7 | X ~ ∝(λ×3))

= 1 - P(X ≤ 6 | X ~ ∝(λ×3))

= 1 - ∑[k=0 to 6] (e²(-λ3) ×(lλ3)²k / k!)

where e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k.

To find lambda, we can use the fact that exactly two customers arrive in the first minute. The Poisson distribution assumes that the number of events in a fixed interval of time or space follows a Poisson distribution with parameter lambda, which represents the expected rate of occurrence. Therefore, lambda is equal to the number of customers arriving per minute, which is 2.

Substituting lambda = 2 into the formula, we get:

P(X ≥ 7 | X ~ ∝(2×3))

= 1 - P(X ≤ 6 | X ~ ∝(6))

= 1 - ∑[k=0 to 6] (e²(-6) ×6²k / k!)

Using a calculator or computer software, we can evaluate this expression to get:

P(X ≥ 7 | X ~ ∝(6)) ≈ 0.081

Therefore, the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.

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Answer:

2:1

Step-by-step explanation:

It’s flipped

The probability that a randomly chosen sophomore is taking Algebra 2, given that they do not take Chemistry, is 19/36.

To find the probability that a randomly chosen sophomore is taking Algebra 2, given that they are not taking Chemistry, we need to consider the number of students taking Algebra 2 who are not taking Chemistry.

Given that there are 318 sophomores in total, and 102 are taking Chemistry, it means that 318 - 102 = 216 sophomores are not taking Chemistry.

Out of the 140 sophomores taking Algebra 2, 26 are also taking Chemistry. Therefore, the number of sophomores taking Algebra 2 but not taking Chemistry is 140 - 26 = 114.

Since we are considering only the students who are not taking Chemistry, the total number of students in this group is 216.

The probability of a randomly chosen sophomore being in this group (taking Algebra 2 but not taking Chemistry) is given by:

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 114 / 216

Simplifying the fraction, we get:

Probability = 19 / 36

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Counterexample

A counterexample is an example that meets the mathematical statement's condition but does not lead to the statement's conclusion. It is used to check the validity of an argument.

We have been given the conjecture:-

"For every integer n, \(n^3\) is positive."

We have to show that the conjecture is false by finding a counterexample.

Let us take an integer n = - 5

Finding its cube we, get

\(n^3\) = -125

We know that,

-125 is not positive, it is negative.

Hence, the conjecture "For every integer n, \(n^3\) is positive." is proven wrong by finding a counterexample which states otherwise.

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If it takes Ron 4 seconds to stack a shingle and Ben 3 seconds to do the same. the number of seconds it will take the two of them together to stack 91 shingles is: 91 seconds.

​Given data:

Ron seconds = 4

Ben seconds = 3

Shingles = 91

First step is to formulate an equation in which we would then make use of the equation to find the the number of seconds

Equation:

91 × 4 ÷ ( 4 + 3)

Simplify

364 / 7

= 52 seconds

Therefore we can conclude that the number of seconds is 52 seconds.

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Step-by-step explanation:

option A corresponding angles

hope this answer helps you dear!...take care

The concentration of the drug in the bloodstream is the greatest at t = 0.63 hours.

To find when the concentration of a drug in the bloodstream is the greatest, we need to find the maximum value of the function C(t) = 6t / (0.4 + t^2). To do this, we'll find the critical points by taking the first derivative of C(t) and setting it equal to 0.

Find the first derivative of C(t) using the quotient rule.
\(\frac{dC}{dt} =\frac{ [(0.4 + t^2)(6) - 6t(2t)] }{(0.4 + t^2)^2}\)

Now, simplify the first derivative.
\(\frac{dC}{dt }=\frac{ [(2.4 + 6t^2) - 12t^2] }{(0.4 + t^2)^2}\\\frac{dC}{dt } = \frac{(-6t^2 + 2.4) }{ (0.4 + t^2)^2}\)

Setting the first derivative equal to 0 and solving for t.
\(0= \frac{(-6t^2 + 2.4) }{ (0.4 + t^2)^2}\)
0 = -6t² + 2.4

Solve for t².
t² = 2.4 / 6

t = 0.4

Take the square root of both sides to find t.
t = √(0.4)
t ≈ 0.63

Therefore, at t ≈ 0.63 hours, the drug concentration in the bloodstream is at its highest.

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There are 833 positive integers not exceeding 1000 that are not divisible by either 8 or 12.

To find the coefficient of x^8y in the expansion of (2x - 4y)^12, we can use the binomial theorem. The binomial theorem states that the expansion of (a + b)^n can be written as:

(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n) * a^0 * b^n

where C(n, k) represents the binomial coefficient, given by C(n, k) = n! / (k!(n-k)!).

In our case, we have (2x - 4y)^12. The term with x^8y will be obtained when we choose x^8 from (2x)^8 and y from (-4y)^4. Therefore, we need to find the coefficient of x^8 in (2x)^8 and the coefficient of y^4 in (-4y)^4.

The coefficient of x^8 in (2x)^8 is given by C(8, 8) * (2^8) = 1 * 256 = 256.

The coefficient of y^4 in (-4y)^4 is given by C(4, 4) * (-4^4) = 1 * 256 = 256.

To find the coefficient of x^8y^4 in the expansion, we multiply the coefficients obtained above:

Coefficient of x^8y^4 = 256 * 256 = 65536.

Therefore, the coefficient of x^8y^4 in the expansion of (2x - 4y)^12 is 65536.

Regarding the second question, we need to find the number of positive integers not exceeding 1000 that are not divisible by either 8 or 12.

To solve this, we can use the principle of inclusion-exclusion. We count the number of positive integers divisible by 8, the number divisible by 12, and subtract the number divisible by both (which is the number divisible by the least common multiple of 8 and 12, which is 24).

Number of positive integers divisible by 8: 1000 / 8 = 125.

Number of positive integers divisible by 12: 1000 / 12 = 83.

Number of positive integers divisible by 24: 1000 / 24 = 41.

Using the principle of inclusion-exclusion:

Number of positive integers not divisible by either 8 or 12 = Total number of positive integers - (Number divisible by 8 + Number divisible by 12 - Number divisible by 24)

= 1000 - (125 + 83 - 41)

= 1000 - 167

= 833.

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Answer:

175 ft

Step-by-step explanation:

From the question,

(a) ΔABC and ΔEDC are similar because all the angles in ΔABC is equal to the corresponding angles in ΔEDC.

I.e, ΔABC is equiangular to ΔEDC. (AAA).

(b) From the diagram.

for similar angle, ratio of corresponding sides are equal

100/d = 4x/7x

100/d = 4/7

where d = distance across the river

solve for d

d = (100×7)/4

d = 175 ft

Answer:

D. 3 1/12

Explanation:

\(\rightarrow \sf 4\dfrac{1}{3} -1\dfrac{1}{4}\)

convert into improper fraction

\(\rightarrow \sf \dfrac{13}{3} -\dfrac{5}{4}\)

make the denominators same. 12 is the common factor of both 3 and 4

\(\rightarrow \sf \dfrac{13(4)}{12} -\dfrac{5(3)}{12}\)

simplify

\(\rightarrow \sf \dfrac{52}{12} -\dfrac{15}{12}\)

join both fraction

\(\rightarrow \sf \dfrac{52-15}{12}\)

simplify

\(\rightarrow \sf \dfrac{37}{12}\)

convert into mixed fraction

\(\rightarrow \sf 3\dfrac{1}{12}\)

Answer:

it's answer is a

Area of a triangle = 1/2 * base * height

= base = (x1 ^2 + y1^2) and height = (x2 ^2 + y2^2)

Step-by-step explanation:

so, area of triangle = 1/2 * (x1 ^2 + y1^2) + (x2^2 + y2^2)

so the answer is a

In a study examining the effect of ignoring text messages on distraction, the variable "trying to ignore text messages" would be the independent variable, whereas the variable "amount of distraction" would be the dependent variable.

The independent variable is the one that is manipulated or controlled by the researcher. In this case, the researchers are interested in studying the effect of attempting to ignore text messages, so they would manipulate the participants' behavior in relation to text messages (e.g., asking them to ignore the messages or not).

The dependent variable, on the other hand, is the variable that is measured or observed to determine the effect of the independent variable. Here, the researchers would measure the amount of distraction experienced by the participants as a result of trying to ignore the text messages.

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Explanation:

0.4 = 4/10 = 2/5

The original slope as a fraction is 2/5

Flip the fraction to get 5/2, then flip the sign to get -5/2 which is the perpendicular slope

The orginal slope 2/5 and perpendicular slope -5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical nor horizontal.

Rephrased another way: -5/2 is the negative reciprocal of 2/5.

Answer:

the answer is  4.979

Step-by-step explanation:

Answer:

The answer is 4.979

Step-by-step explanation:

Answer:

\(x = 3\)

Step-by-step explanation:

Step 1:  Determine the equation

So we know that our equation does not have a y-intercept which means that it doesn't intersect ANYWHERE on the y-axis.  Therefore, this means that our equation will be a straight vertical line that doesn't move side to side and just goes straight up and down.  We also know that our point is (3, 6) which means that our x-value will be 3 and this is where the equation will be located.  

There are several ways to display our answer where x = 3 is the most common way which basically means give me all of the y-values for the same x value of 3.  Another way of saying it is x - 3 = 0 which either way when adding 3 to both sides gives you x = 3 which is what I usually go with.

Answer: \(x = 3\)

Answer:

x = 3 or x - 3 = 0

Step-by-step explanation:

Given

Solving

Answer:

C. m represents the slope and b represents the y-intercept.

Step-by-step explanation:

The equation of straight line is usually expressed as:

       y  = mx + b

Where y is the vertical axis component

           x is the horizontal axis component

           m is the slope

           b is the y-intercept

At the y-intercept, x = 0

Also, the slope is the rise divided by the run.  

Answer:

Step-by-step explanation:

Given:

The discount amount:

The discount percentage:

Answer:

  -2x^3 +13x^2 +3x -54

Step-by-step explanation:

The product is found using the distributive property.

  (x -6)(-2x^2 +x +9) = x(-2x^2 +x +9) -6(-2x^2 +x +9)

  = -2x^3 +x^2 +9x +12x^2 -6x -54

  = -2x^3 +13x^2 +3x -54

Answer:

C

Step-by-step explanation:

Area = π\(r^{2}\)

r means radius

radius = d/2

d = diameter

8 /2 = 4

4 is radius

\(4^{2}\) = 16

^ ( its 4 x 4 ) ^

so then,

Area = 16π

Answer:

Step-by-step explanation:

\(A=\pi r^2,\ r=\frac{d}{2}\\ \\ A=\frac{\pi d^2}{4},\ d=8cm\\ \\ A=\frac{64\pi}{4}\\ \\ A=16\pi cm^2\)

Given:

There are 5 numbers followed by 2 letters.

Solution:

To find the answer, we will have a plate number that consists of 5 numbers followed by 2 letters. In that 5 numbers, each place has 10 choices-from 0 to 9. It will be: 10 * 10 * 10 * 10 * 10 = 100,000 .

Now, for the letters, there are 26 letters in the alphabet. We have two places for the letters and each place have 26 choices-from A to Z that will give us: 26 * 26 = 676

We will now multiply the acquired data for both the numbers and letters to arrive at the correct answer.

100,000 * 676 = 67,600,000

ANSWER: 67,600,000 possible license plates

Answer:

35492421.7263

Step-by-step explanation:

Answer:

hope it helps

If a prestigious program accepts 2 out of every 9 applicants per year than the program will accept 360 applicants out of 1620.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

the ratio is given:

2/9 = 360/x

solving for the value of x;

x/9=360/2

x=(180)9

x=1620

this is the required value of applicants that were not accepted.

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Hello!

\(\large\boxed{x + 2}\)

\(\frac{2x^{2} +x}{2x-2} + \frac{x-4}{2x-2}\)

The denominators are equal, so we can simply combine the numerator:

\(\frac{2x^{2} +x+ x - 4}{2x-2}\)

Combine like terms in the numerator:

\(\frac{2x^{2} +2x - 4}{2x-2}\)

Factor out 2 from the entire fraction:

\(\frac{2(x^{2} +x - 2)}{2(x-1)}\)

Cancel out 2 from both the numerator and denominator:

\(\frac{x^{2} +x - 2}{x-1}\)

Factor the numerator to simplify further:

\(\frac{(x + 2)(x - 1)}{x-1}\)

Cancel out x - 1:

\(x + 2\)

Answer:

the measures of an angle would be 49.2 degrees

Step-by-step explanation:

hope this helps

so so so sorry if this answer is wrong

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