A square has an area of 64ft2. What is the length of each side?

After 35 minutes there will be 40 bacteria remaining.

The process of a constant percentage rate decrease in an amount over time is referred to as "exponential decay." The formula to calculate exponential decay is given as, \(N_t=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}\). Here, Nt is the quantity after time t, N0 is the initial quantity, t1/2 is the half-life, and t is time.

For the first situation, Nt=360, N0=900, t=10 minutes. Therefore, substituting the given values get the value of t1/2. So,

\(\begin{aligned}360&=900\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}} \\\frac{360}{900}&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\0.4&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\ \ln(0.4)&=\frac{10}{t_{1/2}}\ln(0.5)\\t_{1/2}&=10\times\frac{\ln(0.5)}{\ln(0.4)}\\&=7.6\end{aligned}\)

Now, for the second situation,  Nt=40.  We have to find the time at which there will be 40 bacteria remaining. Then,

\(\begin{aligned}40&=900\left(\frac{1}{2}\right)^{t/7.6}\\0.04&=\left(\frac{1}{2}\right)^{t/7.6}\\\ln(0.04)&=\frac{t}{7.6}\ln(0.5)\\t&=7.6\times\frac{\ln(0.04)}{\ln(0.5)}\\&=7.6\times4.64\\&=35.26\\&\approx35\end{aligned}\)

The answer is 35 minutes.

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Answer:

dunny but 4950

Step-by-step explanation:

4960-

Answer:

Three linear equations that has a unique solution (1,2,-1) are:-

x+ y+ z =2

2x + y + 3z = 1

x+ 2y+ z  = 4

Step-by-step explanation:

Linear equations in three variables:-

If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0)

then ax + by + cz = r is called a linear equation in three variables. (The

“three variables” are the x, the y, and the z.)

The numbers a, b, and c are called the coefficients of the equation. The

number r is called the constant of the equation.

so from from above explanation we can write 3 linear equations with three variables as.

x+ y+ z =2

2x + y + 3z = 1

x+ 2y+ z  = 4

Now to check if the given point (1,2,-1) is solution or not  these equations must satisfy this point,

x+ y+ z =2

1+ 2- 1 = 2

   2= 2

2x + y + 3z = 1

2×1 +2 - 3×1 = 1

     1=1

x+ 2y+ z  = 4,

1+ 2×2 -1 = 4

    4=4  

therefore all three equations satisfies the given point

hence these are the three linear equation having point (1,2, -1) as the unique solution

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If a number cube is rolled 25 times and 6 appears only four times, then the experimental probability of getting 6 is 4/25.

The experimental probability of an event happening is the number of times the event occurred divided by the total number of trials. In this case, a number cube is rolled 25 times and lands on 6 four times. Here are the steps to determine the experimental probability of landing on 6:

So, the experimental probability of landing on 6 is 4/25, which means that if we roll the number cube many more times, we would expect to get a 6 approximately 4 out of every 25 rolls.

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Answer:

x=−12

Step-by-step explanation:

−6x+5(−2x−11)=137

Step 1: Simplify both sides of the equation.

−6x+5(−2x−11)=137

−6x+(5)(−2x)+(5)(−11)=137(Distribute)

−6x+−10x+−55=137

(−6x+−10x)+(−55)=137(Combine Like Terms)

−16x+−55=137

−16x−55=137

Step 2: Add 55 to both sides.

−16x−55+55=137+55

−16x=192

Step 3: Divide both sides by -16.

−16x/−16=192/−16

Answer:

-6x-10x-55=137

-16x-55=137

-16x=137+55

-16x=192

X=192/16

X=12

a. The population are all subscribers to Bloomberg BusinessWeek in North America.

b. The annual income is a quantitative variable.

c. The ownership of an American Express card is a categorical variable.

d. The study involves cross-sectional data.

e. Bloomberg BusinessWeek might infer that a part of its subscribers who has annual income of $75,000 or more are having an American Express credit card.

The population is the whole set of units from where information is to be obtained and about what inferences are to be made. The population of interest in this study are all subscribers to Bloomberg BusinessWeek in North America.

Quantitative variables are those which can be measured numerically. In this study, the annual income is a quantitative variable because it can be expressed in numbers.

Categorical variables are those which cannot be quantified. Categorical variable can only take on a fixed value. In this case, the question “Do you have an American Express credit card?” can only take on two values, Yes or No. Thus, the ownership of an American Express credit card is a categorical variable.

Cross-sectional data refers to data from many but similar individual groups at a given point in time. For e.g., prices of different varieties of rice on a particular day. In this study, the data gives two different values which describe the same population at the same time. So, it involves cross-sectional data.

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Although part of your question is missing, you might be referring to this full question: A Bloomberg BusinessWeek North American subscriber study collected data from a sample of 2861 subscribers. Fifty-nine percent of the respondents indicated an annual income of $75,000 or more, and 50% reported having an American Express credit card.

a. What is the population of interest in this study?

b. Is annual income a categorical or quantitative variable?

c. Is ownership of an American Express card a categorical or quantitative variable?

d. Does this study involve cross-sectional or time series data?

e. Describe any statistical inferences Bloomberg BusinessWeek might make on the basis of the survey.

In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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Therefore, the initial number of party favor bags Razi had to fill is 20.

To determine the initial number of party favor bags Razi had to fill, we need to analyze the relationship between the time and the number of bags remaining.

Looking at the table, we can observe that the number of bags remaining decreases by 4 for every additional minute of work. This suggests a constant rate of filling the bags.

From the given data, we can see that at the starting time (4 minutes), Razi had 36 bags remaining. This implies that for each minute of work, 4 bags are filled.

To calculate the initial number of bags, we can subtract the number of bags filled in 4 minutes (4 x 4 = 16) from the number of bags remaining initially (36).

36 - 16 = 20

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A geometric shape that could be used to model a building with a quadrilateral base and triangular sides is a pyramid.

A geometric shape is a two-dimensional or three-dimensional object that can be described using mathematical formulas and properties. Examples of two-dimensional geometric shapes include squares, circles, triangles, and rectangles. Examples of three-dimensional geometric shapes include cubes, spheres, cylinders, and cones.

Geometric shapes are used in many different fields, including mathematics, science, architecture, engineering, and art. They are important for understanding spatial relationships and for solving problems related to measurement, area, volume, and other geometric properties.

Specifically, the shape would be a triangular pyramid, with the base being a quadrilateral and the sides being triangles.

A cone also has a circular base and curved sides, while a cylinder has circular bases and straight sides. A sphere is a three-dimensional shape with a curved surface, and would not be an appropriate shape to model a building with a quadrilateral base and triangular sides.

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Answer:

The answer is B. Pyramid I just took the test and got it correct.

To obtain the least common multiple of (l.c.m) we must do it in simultaneous decomposition.

This method consists of extracting the common and uncommon prime factors, then

\(\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{32 \ \ \ 42 \ \ \ 48}\\ 16 \ \ \ 21 \ \ \ 24\\ \ 8 \ \ \ 21 \ \ \ 12\\ \ 4 \ \ \ 21 \ \ \ \ 6\\ \ 2 \ \ \ 21 \ \ \ \ 3\\ \ 1 \ \ \ 21 \ \ \ \ 3\\ \ 1 \ \ \ \ 7 \ \ \ \ 1\\ \ 1 \ \ \ \ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 2\\ 2\\ 3\\ 7\\ \: \end{matrix} \end{gathered}$}\)

              \(\large\displaystyle\text{$\begin{gathered}\sf \bf{L.c.m.(32,42,48)=2\times2\times2\times2\times2\times3\times7} \end{gathered}$}\)

                       \(\large\displaystyle\text{$\begin{gathered}\sf \bf{L.c.m.(32,42,48)=2^{5} \times3\times7} \end{gathered}$}\)

                            \(\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{L.c.m.(32,42,48)=672} \end{gathered}$}}}\)

Therefore, the least common multiple of 32, 42, and 48 is 672.

\(\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}\)

Using the exponential growth formula, the population in 2005 was 161 million.

The equation f(x) = a(1 + r)^x can also be used to compute exponential growth, where: The function is represented by the word f(x). The initial value of your data is represented by the a variable. The growth rate is represented by the r variable. To calculate growth rates, divide the difference between the starting and ending values for the period under study by the starting value.

Growth factor = (159/154) for the eleven-year period between 1990 and 2001.

The population growth might thus be described by the exponential equation

p(t) = 154(159/154)^(t/11), where t is the number of years since 1990.

The model forecasts a population of... p(15) = 154(159/154)^(15/11)

= 160.86 = 161 million

In 2005, there were about 161 million people living there.

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Correct Question:

A country's population in 1990 was 154 million. In 2001 it was 159 million. Estimate the population in 2005 using the exponential growth formula. Round your answer to the nearest million.

Answer:

6 and 10

Step-by-step explanation:

Let a = the first number(3/5 of the second number namely b)

Let b = the number that is 5/3 of a

a=3/5 b

Assuming they are both positive integers, obviously you will have to add 4 to a.

4+a = b

4 + 3/5 b = b

2/5 b = 4

b = 10

a=6

ONLY ASSUMING IF THEY ARE BOTH POSITIVE INTEGERS

Answer:

81:324

Step-by-step explanation:

3+12=15

405 div 15 =27

3 times 27 = 81

12 times 27 = 324

81:324

The variables examined in the study show the number of hospital visits for cooking-related knife injuries and their frequency during major holidays. The data compiled from emergency departments shows that there is a significant increase in the number of hospital visits for such injuries around major holidays.

This suggests that there may be a correlation between the holidays and the use of knives in cooking, possibly due to increased meal preparation and cooking during these times. Other variables that could be examined in further studies include the types of knives and cooking equipment used, the types of foods being prepared, and the demographics of those who sustain these injuries.

Variables refer to any characteristic, quantity, or attribute that can be measured and that can fluctuate or vary. Variables are of two types:

An independent variable is one that is thought to influence the dependent variable, which is the characteristic or response that is being measured.

The variables examined in the study indicate that the number of hospital visits for cooking-related knife injuries increases around major holidays. This implies that there is a direct relationship between cooking and knife injuries on major holidays. As a result, measures must be put in place to reduce the risk of knife injuries during the holidays. This includes the creation of awareness campaigns and the promotion of safety in the kitchen.

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Answer:

x= -0.36

firstly you need to open the brackets

-3(3x +6) + 2=9

-9x -18 + 2=9

secondly join the like terms together

-9x = 9 + 18 - 2

-9x = 25

thirdly you divide both sides by 25

-9x ÷ 25 = -0.36

x= -0.36

The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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the denominator goes to infinity as x approaches infinity, the limit approaches 0. Therefore, the limit of x/(x^2+5) as x approaches infinity is 0.

If you try to use L'Hopital's rule to find the limit of lim x → ∞ x/(x^2+5), you would end up with an indeterminate form of ∞/∞, which means that L'Hopital's rule is inconclusive. In this case, you can use other methods to evaluate the limit.

One such method is to divide both the numerator and the denominator by the highest power of x, which in this case is x^2. This gives:

lim x → ∞ x/(x^2+5) = lim x → ∞ 1/(x+5/x^2)

what is limit?

In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches a certain value. In other words, the limit of a function f(x) as x approaches a value c (written as lim x → c f(x)) describes the behavior of f(x) near c.

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If their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.

The term taxable income refers to any gross income earned that is used to calculate the amount of tax you owe. Put simply, it is your adjusted gross income less any deductions. This includes any wages, tips, salaries, and bonuses from employers.

The minimum income amount depends on your filing status and age. In 2022, for example, the minimum for single filing status if under age 65 is $12,950. If your income is below that threshold, you generally do not need to file a federal tax return. Review the full list below for other filing statuses and ages.

Taxable income

a. Taxable income:

Taxable income=Gross income - Total taxes due

Taxable income=$63,000-$6,847.50

Taxable income=$56,152.5

b. The marginal tax rate for taxable income  under the income bracket of of $40,526 to $86,375 is 22%.

c. Effective tax rate:

Effective tax rate = Total taxes due/ Taxable income×100

Effective tax rate =$6,847.50/$56,152.5×100

Effective tax rate =10.869%

Effective tax rate =10.87% (Approximately)

Inconclusion if their total taxes due are $6,847.50, their taxable income is: $56,152.2, marginal rate is 22% and the effective tax rate is 10.87%.

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The power series for the function\(f(x) = 8/(3x^2)\), centered at c = 5, is \(8/75 - 16/375(x-5) + 48/9375(x-5)^2 - 64/78125(x-5)^3 + ...\)

To find the power series for the function \(f(x) = 8/(3x^2)\)centered at c = 5, we can use the formula for the Maclaurin series:

\($f(x) = f(c) + \frac{f'(c)}{1!}(x-c) + \frac{f''(c)}{2!}(x-c)^2 + \frac{f'''(c)}{3!}(x-c)^3 + ...$\)

First, we need to find the derivatives of f(x):

\(f(x) = 8/(3x^2)\)

\(f'(x) = -16/(3x^3)\)

\(f''(x) = 48/(3x^4)\)

\(f'''(x) = -192/(3x^5)\)

Next, we evaluate these derivatives at c = 5:

\(f(5) = 8/(35^2) = 8/75\)

\(f'(5) = -16/(35^3) = -16/375\)

\(f''(5) = 48/(35^4) = 48/9375\)

\(f'''(5) = -192/(35^5) = -64/78125\)

Plugging these values into the formula, we get:

\(f(x) = 8/75 - 16/375(x-5) + 48/9375(x-5)^2 - 64/78125(x-5)^3 + ...\)

This is the power series for f(x) centered at c = 5.

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Answer:

1.03 i think

Step-by-step explanation:

To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.

For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.

To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.

The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).

To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

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Answer:

5400

Step-by-step explanation:

Let x represent the cost of a chair and y represent the cost of a table. We can use this to set up a system of equations:

7x=2y

6x+5y=10575

We can solve this system using substitution.

Start by rewriting the first equation in terms of x.

\(7x=2y\\\text{Divide both sides by 7}\\x=\frac{2}{7}y\)

Substitute this into the second equation:

\(6(\frac{2}{7}y)+5y=10575\\\frac{12}{7}y+5y+10575\\\frac{12}{7}y+\frac{35}{7}y=10575\\\frac{47}{7}y=10575\)

Multiply both sides by 7

\(47y=74025\)

Divide both sides by 47

\(y=1575\)

This means...

\(7x=2(1575)\\7x=3150\)

Divide both sides by 7

\(x=450\)

One chair costs 450. Now, multiply this number by 12 to find the cost of 12 chairs.

\(450*12=5400\)

12 chairs cost 5400.

The solution of the system of equations is given by the ordered pair (2, 2).

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = -x + 4    ......equation 1.

y = 1/2(x) + 1 ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I, and it is given by the ordered pairs (2, 2).

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Answer:

Step-by-step explanation:

2a.x=10+5

b. x=11-7

C. x=5*2

Answer:

a. x-5=10

x=10+5

x=15

b. x+7=11

x=11-7

x=4

c. x/2=5

x=5*2

x=10

d. 4x=24

x=24/4

x=6

Answer:

Step-by-step explanation:

amama

Answer:

16.2$

12/35%=4.2+12

Answer:

H

Step-by-step explanation:

Answeni ideAA{

}

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

it's important to keep in mind that you can do anything to an equation as long as you do it to both sides, and it will still be equal.

2x + 5 = 13

subtract 5 from both sides of the equation

2x + 5 -5 = 13 - 5

2x = 13 -5

2x = 8

divide both sides of the equation by 2

2x/2 = 8/2

x = 4

The value of x for the equation 2x + 5 = 13 is x = 4.

Given that:

There is an equation in x which is given as,

2x + 5 = 13

It is required to find the value of x.

That is, solve the equation.

It is required to get the equation in such a way that x is on one side and a constant on the other side.

2x + 5 = 13

Subtract both sides by 5.

2x = 8

Divide both sides by 2.

x = 4

Hence the value of x is 4.

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