You decide to put $5,000 in a savings account to save for a $6,000 down payment on a new car. If the account has an interest rate of 7% per year and is compounded monthly, how long does it take until you have $6,000 without depositing any additional funds?

Using the mathematical operations of addition and subtraction, the quantity of almond milk that Lucas should add to his recipe to make three 8-fluid-ounce servings of the smoothie is 1¹/₈ cups.

Mathematical operations include addition, division, subtraction, and multiplication.

In this situation, we can determine the needed quantity of almond milk using multiplication, subtraction, and addition.

The total quantity of smoothie is obtained by multiplying three cups by 8 fluid ounces.  The quantity of almond milk is determined by subtracting the sum of other ingredients from the total quantity.

Lucas' usual recipe for two 8 fluid ounces:

Berries 3/8 cups

Mango 1/2 cups

Yogurt = 3/4 cups

Almond Milk = 3/8 cups

Total cups made = 2 cups (16 fluid ounces = 2 x 8)

New recipe for three 8 fluid ounces:

Berries 5/8 cups

Mango 1/2 cups

Yogurt = 3/4 cups

Almond milk = x

1 cup = 8 fluid ounces

Total cups to be made = 3 cups (24 fluid ounces = 3 x 8)

5/8 + 1/2 + 3/4 + x = 24/8

= 15/8 + x = 24/8

x = 9/8 (24/8 - 15/8)

= 1¹/₈ cups

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Lucas makes a smoothie using the recipe (berries 3/8, mango 1/2, yogurt 3/4 cups) and adds almond milk for two 8 fluid-ounce servings. (There are 8 fluid ounces in 1 cup.​)

The conversion from cents to Dollar we get :

4 cent  = 4/100 = $ 0.04

70 cents = 70/100 = $ 0.7

58 cents = 58/100 = $.58

204 cents = 204/100 = $ 2.04 = $2 and 4 cents

.75 cents = .75 / 100 = $ 0.0075

3009 cents = 3009/100 = $ 30.09 = $30 and 9 cents

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. For instance, 12 inches equals one foot when converting between inches and feet.

Cents are equivalent to one dollar. Dollars are represented by paper banknotes, which come in denominations of $100, $50, $20, $10, $5, and $1. Coins include cents.

The act of converting one value into another, such as from inches to millimeters or from liters to gallons, is known as conversion. The following measurements: length, weight, capacity, temperature, and speed are all measured in units.

The values in cents

4 cent  = 4/100 = $ 0.04

70 cents = 70/100 = $ 0.7

58 cents = 58/100 = $.58

204 cents = 204/100 = $ 2.04 = $2 and 4 cents

.75 cents = .75 / 100 = $ 0.0075

3009 cents = 3009/100 = $ 30.09 = $30 and 9 cents.

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y = log (x)

Logarithmic functions are the inverse of exponential functions. Logarithmic is usually shortened to log.

Logarithmic Operation

Logarithmic functions help solve exponential equations. For example, the exponential function: bˣ = a, could be difficult to solve. To find x, we can use the log operation. By taking the log of both sides we can change this exponential function into a log function. In log form, the function becomes [tex]log_{b} (a)=x[/tex]. This is pronounced, "log-base b of a equals x." If you plug this into a calculator or use a different technique to solve, you can find x and solve the original exponential function.

Common Log and Natural Log

Although logarithmic functions can have any base, some are more frequent than others. One such base is base 10. If the base of the log is 10, then we do not write the 10, it is just implied. This log is called common log. The answer choice y = log (x) is common log. Another common base is Euler's constant, e. Log with the base of e is called natural log. Natural log is written as ln (x).

Answer:

Step-by-step explanation:

3/ B is a salesperson and C is a programmer.

The correct option is: 2/ B is a programmer, and C is a salesperson

Let's analyze the statements and determine what B and C are:

A mumbled a response that the visitor couldn't hear clearly. We don't have any information from A's response.

B said, "A said that he is a salesperson." Since we know that salespeople always lie, we can infer that B is lying about A's response. Therefore, if A is a programmer (telling the truth), then B must be a salesperson.

C said, "Don't believe B; he is lying!" If we already determined that B is a salesperson (lying about A's response), then C is suggesting that B's statement is false, which means A's response is the opposite of what B said. So if B claimed that A is a salesperson (which was a lie), then A must be a programmer (telling the truth).

Based on the above analysis:

A is a programmer.

B is a salesperson.

C is a programmer.

So, the correct option is: 2/ B is a programmer, and C is a salesperson.

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Answer:

full answer in below

Step-by-step explanation:

To prove that the limit of (2x^4-6x^3+x^2+3)÷(x-1) as x approaches 1 is equal to -8, we can use the definition of a limit and the fact that (x-1) is not equal to zero at x=1.

The definition of a limit states that:

If we have a function f(x) and a number L, then the limit of f(x) as x approaches a is L, if and only if, for every ε > 0, there exists a δ > 0 such that for every x:

|f(x) - L| < ε when 0 < |x - a| < δ

So, to prove that the limit of (2x^4-6x^3+x^2+3)÷(x-1) as x approaches 1 is -8, we need to show that:

|(2x^4-6x^3+x^2+3)÷(x-1) + 8| < ε when 0 < |x - 1| < δ

We know that (x-1) is not equal to zero at x=1, so we can safely divide both sides of the equation by (x-1) and simplify it to:

|2x^4-6x^3+x^2+11| < ε when 0 < |x - 1| < δ

Now, we can choose ε = 0.1 and δ = 0.1, so we have:

|2x^4-6x^3+x^2+11| < 0.1 when 0 < |x - 1| < 0.1

If we plug in x=1, we have:

|2(1)^4-6(1^3)+(1)^2+11| < 0.1

which simplifies to:

|11| < 0.1

and we see that this is true, since |11| = 11 is less than 0.1.

We can also plug in some values around x=1, for example x=0.99 and x=1.01:

|2(0.99)^4-6(0.99)^3+(0.99)^2+11| < 0.1

and

|2(1.01)^4-6(1.01)^3+(1.01)^2+11| < 0.1

In both cases, we can see that the inequality is true, and the absolute value of the expression on the left side is less than 0.1.

Therefore, we have shown that for any ε > 0, there exists a δ > 0 such that for every x:

|(2x^4-6x^3+x^2+3)÷(x-1) + 8| < ε when 0 < |x - 1| < δ

And thus, by the definition of a limit, we have proven that the limit of (2x^4-6x^3+x^2+3)÷(x-1) as x approaches 1 is -8.

Answer:

is that calculus?

am confuse in your question

can you try take derivative both numerator and denominator with respect to x

by using L - Hospitable rule

Answer:

infinitely many solutions and x=y

a) The least score that you need to get on the last test and still earn a C is given as follows: 34.

b) With the least score counting twice, the least score that you need to earn a C is given as follows: 52.

The mean of a data-set is obtained as the sum of all the elements in the data-set divided by the number of elements in the data-set.

The scores for this problem are given as follows:

83, 70, 83, 80 and x.

(in which x is the score of the fifth test).

The least score that you could get on the last test and still earn a C is found when the mean is of 70, hence>:

(83 + 70 + 83 + 80 + x)/5 = 70

316 + x = 350

x = 350 - 316

x = 34.

With the final test counting twice, you would have the equivalent to six scores, which would be given as follows:

83, 70, 83, 80, x and x.

Hence the least score would be obtained as follows:

(83 + 70 + 83 + 80 + 2x)/6 = 70

316 + 2x = 420

2x = 104

x = 104/2

x = 52.

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The choice that shows 13 · (7 · 4) correctly rewritten using the associative property and then correctly simplified is presented as follows;

The associative property of multiplication stated that the multiplication of three numbers produces the same result in any way the numbers are grouped.

Mathematically, the associative property of multiplication can be presented as follows;

(a × b) × c = a × (b × c)

The specified operation involving the multiplication of three numbers are presented as follows;

13 · (7 · 4)

The associative property of multiplication indicates that we get;

13 · (7 · 4) = (13 · 7) · 4

13 × 7 = 91

Therefore, (13 · 7) · 4 = (13 × 7) × 4

(13 × 7) × 4 = 91 × 4 = 364

The option that shows the associative property correctly written and then correctly simplified is therefore;

The possible options in the question, obtained from a similar online question are;

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The area of the triangle shown is 51.96 unit²

An equation is a expression that shows the relationship between numbers and variables.

The area of a triangle can be found given two adjacent sides and an angle between the two sides. It is given as:

Area = (1/2) * product of adjacent sides * sin(angle)

Hence:

Area of triangle shown = (1/2) * 10 * 12 * sin(60) = 51.96

The area is 51.96

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Answer:

Step-by-step explanation:

Given :

Null Hypothesis :

Alterative Hypothesis

two tailed test

claim is Ha

Alterative Hypothesis: Ha: u ≠ 1

The alternative hypothesis that would be used to test the mean quantity is different from 1 liter is u ≠ 1.

An assertion used in statistical inference experiments is known as the alternative hypothesis. It is contradictory to the null hypothesis and denoted by Ha or H1.

Given that the claim in the null us that u = 1.

Since, an alternative hypothesis is one in which the researchers anticipate a difference (or an effect) between two or more variables; thus, the observed pattern of the data is not the result of chance.

Therefore,

The alternative would be that u is not equal to 1.

Hence, the alternative hypothesis that would be used to test the mean quantity is different from 1 liter is u ≠ 1.

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Answer:

a) General Equation for this scenario is

[tex]\boxed{P_n = P(.98)^n\\\\}[/tex]

where P is the starting population and Pₙ is the population at the end of n years

For this specific case,
[tex]\boxed{P_n = 20000(0.98)^n}[/tex]

b) Population in 2025 will be the population after 25 years:
[tex]P_{25} = 20000(0.98)^{25} = \boxed{12,069}[/tex]

Step-by-step explanation:

In general, if the population at year 0 is P and it decreases by 2% each year then the population after one year will be given by

P - decrease in one year

Decrease in population for 1 year = 2% of P [tex]= 0.02P[/tex]

So P(after 1 year) :  
[tex]P - 0.02P\\\\ = P(1-0.02) \\\\= 0.98P[/tex]

After 2 years the population will be population after 1 year (0.98P) - decrease in population for 1 year (0.02 x 0.98P)

So population at end of 2 years would be
 [tex]0.98P - 0.98P(0.02)\\\\= 0.98P(1-0.02)\\\\=0.98P(0.98)\\\\= P(0.98)^2[/tex]

In general after n years the population would be
[tex]P(0.98)^n\\\\[/tex]

If the population in year 2000 is 20,000 then population at the end of 25 years is:

[tex]20000(0.98)^{25}[/tex]
[tex]\rm\:{=\:12,069\:\;\:rounded\:down\:to\:the\:nearest\:integer}[/tex]  

As a result, slant asymptotes of y = x -4 are found to be the solution to the provided function problem.

Mathematics includes the study of numbers and their variations, equations and associated structures, and the regions and potential uses of geometry. A "function" is the connection between a collection of inputs that individually produce a related output. An output-input relationship known as a function is one in which each input leads to a single, identifiable outcome.

Here,

Because there are no restrictions on the kind of rational function, it is possible to build one from each of the 3 asymptotes.

In addition to the graphs of the linear equation it represents, this is shown in the accompanying graph. The function's asymptotes are these.

The horizontal points include x = -4 and

There are two horizontal asymptotes: y = 0 and

Y = x – 4 are the slant asymptotes.

Additional comments

In our example function, an exponential function is used. That isn't frequently thought of as a polynomial, despite the fact that it may be stated as an infinite degree polynomial. Most authors define a rational function in terms of the fraction of polynomials.

As a result, slant equipotential lines are y = x and are the answer to the given function problem.

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The surface area of the square pyramid is 224 ft²

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Surface area is the total area occupied by the surface of the object. It is gotten by summing the individual area of each surface.

For the pyramid:

Surface area = 4 * area of triangle + Area of square base

Substituting gives:

Surface area = (8 ft * 8 ft) + 4(1/2 * 8ft * 10 ft) = 224 ft²

The surface area is 224 ft²

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Answer:

Step-by-step explanation:

What is the surface area?

5 cm

6 cm

5 cm

6 cm

4 cm

square centimeters

According to the given expression, the account's initial deposit is 750, the balance after one year is 845, and the balance after two years is 952.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, The amount of money in a savings account is modeled by A(x) = 750(1.01)^12x, where x represents number of years.

Expression for money is given

Thus, balance at x = 0

Balance A(0) = 750

Balance at x = 1

Balance A(1) = 750(1.01)^12*1

A(1) = 845.11

Balance at x = 2

Balance A(2) = 750(1.01)^12*2

A(2) = 952.43

Therefore, In the account initial deposit is 750, balance after 1 year  is 845, and balance after 2 years will be 952 as per the given expression.

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We know that Nevaeh initially deposited $2,100, and now she has $2,131.50 in her account. The interest earned is $2,131.50 - $2,100 = $31.50. To find out how many months has she been investing her money, we can use the following formula:

Time (in months) = (Interest / Principal) x (12 / Interest Rate)

Where Principal is the initial deposit amount, Interest Rate is the annual interest rate, and Interest is the amount of interest earned.

Plugging in the given values, we get:

Time (in months) = ($31.50 / $2,100) x (12 / 0.06)

Time (in months) = 0.0149 x 200

Time (in months) = 2.98

Since time cannot be in fraction of months, it has to be rounded off. So, Nevaeh has been investing her money for approximately 3 months.

The sum of A + B, considering that the ten-digit number is divisible by 36, is given as follows:

A + B = 6.

The sum of A and B is obtained considering the rule for a divisibility by 36.

To be divisible by 36, the numbers must be divisible by both 4 and 9, for which the rules are given as follows:

The ten-digit number is given as follows:

3872649A0B

The sum of the digits is given as follows:

3 + 8 + 7 + 2 + 6 + 4 + 9 + A + 0 + B = 39 + A + B.

Hence the condition for a divisibility by 36 is given as follows:

39 + A + B = 45

A + B = 6.

Which is the result for the sum in the context of this problem.

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The graph that has a slope of negative three halves and a y-intercept of 2 is the graph of a line passing through the points (0,2) and (3,0).

What is the slope?

One of the most important things to understand about lines is the definition of slope. The slope is the 'steepness' of the line, also commonly known as rise over run. We can calculate the slope by dividing the change in the y-value between two points over the change in the x-value.

To find the slope of the line, you can use the point-slope formula which is (y2-y1)/(x2-x1) = m,

where m is the slope and (x1,y1) and (x2,y2) are points on the line.

So using the given points in the question, we get (0-2)/(3-0) = -2/3 = -0.66 = -3/2.

And the y-intercept is the point where the line crosses the y-axis, which is 2 in this case.

Hence, the graph that has a slope of negative three halves and a y-intercept of 2 is the graph of a line passing through the points (0,2) and (3,0).

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The z score for a student who received a score of 310 is 0.75

An equation is an expression composed of variables and numbers linked together by mathematical operations.

The z score shows by how many standard deviation the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

Given that the eighth-grade math test is Normal, (282, 40), hence mran = 282, stand. deviation = 40

For a score of 310:

z = (310 - 282) / 40 = 0.75

The z score is 0.75

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Answer:

first answer is

1.31

Step-by-step explanation:

and second is

7.47

hope it help you

hi friend

(a) The population of interest to the researchers is private water wells in or near the Barnett Shales in Texas.

(b) The sample is 100 private water wells, 91 of which are located within 5 km of an active gas well using fracking, 4 private wells with no gas wells located within a 14 km radius, and 5 wells outside of the Barnett Shale with no gas well located within a 60 km radius.

(c) The characteristics of the population of interest to the researchers are the levels of potential contaminants such as arsenic and selenium in the private water wells.

(d) A measure of reliability of the inferences is important because it allows the researchers to determine the degree of confidence they can have in the findings of the study, and to identify any potential sources of error in the study design or measurement.

The sample is a subset of this group that is representative of the population, whereas the population of interest is the entire unit of people you are considering for the study. When using sampling, you typically collect information from the sample before extrapolating the results to the entire population.

Without a measure of reliability, it would be difficult to assess the generalizability of the study's findings to the broader population of private water wells in the Barnett Shale region.

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Answer:

C{-3,-2.5}

Step-by-step explanation:

Brainliest pls

The maximum allowed ratio for the cord such that the maximum allowable normal stress is 8.77 kilopascals is equal to 2.081.

Let assume that the cork is made of a ductile material, in this case we find that the normal stress (σ), in kilopascals, and shear stress (τ), in kilopascals, are described below:

Normal stress

σ = F / A

Shear stress

τ = (3 · V) / (2 · A')

Where:

Let assume that cork is at static equilibrium and at inminent motion, then the shear and normal forces are, respectively:

F = P

V = P / 2

And the transversal areas are introduced below:

A = π · R²

A' = 2 · R · H

Where:

If we know that σ = 8.77 kPa and τ = 4.98 kPa, then the maximum allowed ratio between the cork height and the cork radius is:

8.77 = P / (π · R²)

8.77 = [1 / (π · R)] · (P / R)

4.98 = 1.5 · (0.5 · P) / (2 · R · H)

4.98 = [0.75 / (2 · H)] · (P / R)

Then, we eliminate P / R of the two equations:

8.77π · R = 13.24 · H

H / R = 8.77π / 13.24

H / R = 2.081

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Answer:

x = -2,  x = 9

Step-by-step explanation:

Given quadratic equation:

[tex]x^2-7x-18=0[/tex]

To factor a quadratic in the form ax²+bx+c, first find two numbers that multiply to ac and sum to b.

[tex]\implies ac=1 \cdot -18=-18[/tex]

[tex]\implies b=-7[/tex]

Therefore, the two numbers are: -9 and 2.

Rewrite b as the sum of these two numbers:

[tex]\implies x^2-9x+2x-18=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x-9)+2(x-9)=0[/tex]

Factor out the common term (x - 9):

[tex]\implies (x+2)(x-9)=0[/tex]

Apply the zero-product property:

[tex]\implies x+2=0 \implies x=-2[/tex]

[tex]\implies x-9=0 \implies x=9[/tex]

Therefore, the solutions to the given quadratic equation are:

Answer:

(14x+13)(x-1)

Step-by-step explanation:

14x²-x-13

14 × 13 = 182

Search for factors of 182 that contain a difference of 1 when subtracted because -x is the same as -1x.

Since 14 × 13 = 182

and

13 - 14 = -1

They are our 2 chosen numbers which will be displayed as :

14x² - 14× + 13x - 13

where -x is replaced by -14x + 13x

Proceed to factorise normally

14x(x-1) + 13(x-1)

Grouping

(14x+13)(x-1)

Answer:

In an absolute value graph, the slope of one side of the graph is the negative of the other side.

For example, if the slope of one side of an absolute value function is 2, then the other side of the equation has a slope of -2.

The equation that represents the relationship is:

x + (x + 1) + (x + 2) = 42

And the 3 consecutive numbers are 13, 14, and 15.

Here we know that the sum of three consecutive integers is 42.

If the first number is x, then the two consecutive numbers are:

x + 1

x + 1 + 1 = x + 2

Then the sum of these 3 consecutive numbers can be written as:

x + (x + 1) + (x + 2)

And that is equal to 42, then the equation is:

x + (x + 1) + (x + 2) = 42

So the first option is the correct one.

And the solution is:

x + (x + 1) + (x + 2) = 42

3x + 3 = 42

3x = 42 - 3

3x = 39

x = 39/3

x = 13

The 3 numbers are:

13, 14, and 15.

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Anazlysing the conditions given in the question we can  conclude that there is a statistically significant increase in the consensus estimate of economists.

Financial analysts often use the whisper number, which is a late-breaking estimate of a key economic indicator, to make predictions about the stock market and inform their investment decisions. They may use it to identify potential opportunities for buying or selling stocks based on whether the whisper number is higher or lower than expected.

While the whisper number can provide insight into the current economic conditions, it is not a foolproof way to predict the stock market. It is just an estimate based on a sample of economists' predictions and can be affected by various unpredictable factors. Therefore, it's important to take other economic indicators and market conditions into account when making investment decisions.

To conduct a hypothesis test, we need to first define the null hypothesis and alternative hypothesis.

Null Hypothesis: The whisper number (sample mean) is equal to the consensus estimate (population mean)

H0: μ = 250,000

Alternative Hypothesis: The whisper number (sample mean) is greater than the consensus estimate (population mean)

H1: μ > 250,000

The next step is to calculate the test statistic and p-value. We can use a one-tailed t-test since the sample size is less than 30 and we don't know the population standard deviation.

Test statistic:

t = (266,000 - 250,000) / (24,000 / sqrt(20))

P-value:

Using the t-distribution table with 19 degrees of freedom, the p-value is less than 0.01, which is the significance level we set.

Since the p-value is less than the significance level (0.01), we can reject the null hypothesis and conclude that there is a statistically significant increase in the consensus estimate of economists.

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Answer:

94

Step-by-step explanation: PQS = (7x - 6)°

SQR = (4x + 15)° since QS bisect PQR these two expressions must be equal

so

7x - 6 = 4x + 15 transfer like terms to the same side of the equation

7x - 4x = 15 + 6

3x = 21 divide both sides by 3

x = 7

also the sum of these two would give us the measure of PQR

7x + 4x + 15 - 6 = PQR

11x + 9 = PQR replace x with 7

11*7 + 9 = 86 this is the measure of angle PQR and also supplementary to PQT so the measure of PQT = 180 - 86