Which of these expressions is equal to 1?

3/4 + 2/3 + 1/2
2/8 + 1/4 + 1/2
1/4 + 1/2
5/3 + 1/6 + 1/3

Answer:

(x+1)^2*(x+2)*(x+3)

Step-by-step explanation:

(x+1)(x+2)(x+3)x.(x+1)

(x+1)^2*(x+2)*(x+3)

(x+3)

 (((x•(x+1))•(x+2))•—————)•(x+1)

                      x  

(x + 1) • (x + 2) • (x + 3) • (x + 1)

Multiply  (x+1)  by  (x+1)

Answer:

14

Step-by-step explanation:

Answer:

answer: 14

Step-by-step explanation:

got it right

The roots of the equation will be imaginary. Then the number of real solutions will be zero.

The discriminant represents the types of the root. And the discriminant (D) of the equation ax² + bx + c = 0 is given as

D = b² - 4ac

The type of roots will be given below.

The equation is given below.

x² + 4x + 5 = 0

The discriminant of the given equation will be

D = 4² - 4 x 1 x 5

D = 16 - 20

D = - 4

D < 0

The roots of the equation will be imaginary. Then the number of real solutions will be zero.

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Answer:

4

Step-by-step explanation:

The pool water will be 0.006% chlorine after approximately 236.5 minutes, and the percentage of chlorine in the pool after 1 hour (60 minutes) is approximately 0.674%.

Let C(t) be the amount of chlorine in the pool at time t in minutes, measured in gallons of chlorine. Since the volume of the pool is 10,000 gal and the initial concentration of chlorine is 0.01%, we have:

C(0) = 10,000 gal x 0.01% = 1 gal

As city water containing 0.003% chlorine is pumped into the pool at a rate of 6 gal/min and the pool water flows out at the same rate, the differential equation for C(t) is:

dC/dt = (0.003 - C(t)/10,000) x 6 - C(t)/10,000 x 6

Simplifying the right-hand side and solving the differential equation using separation of variables, we get:

C(t) = 30,000(1 - e^(-t/166.7)) - 180,000e^(-t/166.7)

After 1 hour (60 minutes), we have:

C(60) = 30,000(1 - e^(-60/166.7)) - 180,000e^(-60/166.7) ≈ 0.0674 gal

The percentage of chlorine in the pool after 1 hour is:

0.0674 gal / 10,000 gal x 100% ≈ 0.674%

To find when the pool water is 0.006% chlorine, we set C(t) = 10,000 gal x 0.006% = 0.6 gal and solve for t:

30,000(1 - e^(-t/166.7)) - 180,000e^(-t/166.7) = 0.6

Using numerical methods, we find that t ≈ 236.5 minutes.

After roughly 236.5 minutes, the chlorine content of the pool will be 0.006%, and after an hour (60 minutes), it will be approximately 0.674%.

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The distributive property can be applied to which expression \(\rm 12x^{3}-9x^{2} +4x-3\)  the given factors are \(\rm = (3x^{2}+1)(4x-3)\)

To factorise a cubic equation we will be finding one factor we will solve by factor theorem to check that the guess is the root. Then we will divide the cubic equation by factor to obtain a quadratic equation. on getting  the quadratic equation we will be applying the various standard methods to factorise further the quadratic equation.

On factorizing we get,

                      \(=\rm 12x^{3}-9x^{2} +4x-3\\\\=\rm 3x^{2} (4x - 3) + 1(4x- 3)\\\\= (3x^{2}+1)(4x-3)\)

Therefore, The distributive property can be applied to which expression \(\rm 12x^{3}-9x^{2} +4x-3\)  the given factors are \(\rm = (3x^{2}+1)(4x-3)\)

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Answer:

19

Step-by-step explanation:

Product of 5 and a number is 5a

5a - 26 = 69

Add 26 to both sides

5a = 69+26

5a = 95

Divide both sides by 5

A = 19

Check

(5× 19) - 26 = 65

Answer:

N=15

Step-by-step explanation:

Becuase math is math

The value of x will be equal to -1 when the value of h(x) is -2.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that  h(x) = -3x – 5, and the value h(x) = -2. The value of x will be calculated as below:-

h(x) = -3x – 5,

-2=-3x -5

3=-3x

x=-1

Therefore, the value of x will be equal to -1 when the value of h(x) is -2.

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The number of trials is typically represented by the letter "n" in statistics. This refers to the number of independent and identical observations that are taken during an experiment or study. The population proportion, on the other hand, is often represented by the letter "p".

This refers to the proportion or percentage of individuals in a population that exhibit a certain characteristic or behavior. For example, if we were studying the proportion of people who prefer chocolate ice cream, "p" would represent the percentage of people in the population who prefer chocolate ice cream.

It's important to note that the number of trials and the population proportion are both key factors in statistical analysis, as they can help researchers draw conclusions about the population as a whole based on a smaller sample size.

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To determine whether AB || CD, we need to compare the corresponding ratios of sides. Using the ratio \((6 + AB - CD)/4.5.\) we know that if AB is parallel to CD, then this ratio should be constant regardless of the value of EB.

To determine whether AB || CD, we need to compare the corresponding ratios of sides.

Given that \(C = 8.4, B = 6.3, D = 4.5\), and \(CE = 6\), we can use the concept of proportionality to determine if AB is parallel to CD.

First, we compare the ratios of the corresponding sides AB and CD.

The ratio AB/CD can be calculated as
\((CE + EB)/ED.\)
Plugging in the given values, we have \((6 + EB)/4.5.\)

Next, we can solve for EB by subtracting CE from both sides of the equation: \(EB = (AB - CD).\)

Therefore, the ratio AB/CD becomes \((6 + AB - CD)/4.5.\)

If AB is parallel to CD, then this ratio should be constant regardless of the value of EB.

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AB is not parallel to CD based on the calculation of their slopes.

To determine whether AB is parallel to CD, we can use the concept of slopes. If the slopes of AB and CD are equal, then the lines are parallel.

Let's find the slopes of AB and CD. The slope of a line can be calculated using the formula: slope = (change in y)/(change in x).

For AB, the coordinates of A and B are (8.4, 6.3) and (4.5, 6) respectively. The change in y is 6 - 6.3 = -0.3, and the change in x is 4.5 - 8.4 = -3.9. So the slope of AB is (-0.3)/(-3.9) = 0.0769.

For CD, the coordinates of C and D are (8.4, 6.3) and (6.3, 4.5) respectively. The change in y is 4.5 - 6.3 = -1.8, and the change in x is 6.3 - 8.4 = -2.1. So the slope of CD is (-1.8)/(-2.1) = 0.8571.

Since the slopes of AB and CD are not equal (0.0769 ≠ 0.8571), we can conclude that AB is not parallel to CD.

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The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

4,098734

Step-by-step explanation:

Answer:

\(8*\pi\)

Answer:

f(5)=-12

Step-by-step explanation:

f(5)=-3*f(5-1)

f(5)=-3*(4)

f(5)=-12

Hope this helps

Answer:

\(f(1) = 1 \\ f(2) = - 3f(1) = - 3 \\ f(3) = - 3f(2) = + 9 \\ f(4) = - 3f(3) = - 27 \\ f(5) = - 3f(4) = + 81\)

The probability that a single bulb will burn out within the next 10 minutes is approximately 0.6321. The expected amount of time until the first bulb goes out is 10 minutes. The probability density function (pdf) of the random variable T, representing the time when you leave the room after the last light bulb goes out, is given by \(g(t) = 20 * (1/10) * e^{(-(1/10)t)} * (1 - e^{(-(1/10)t))^(19)}\).

To find the probability that a single bulb will burn out within the next 10 minutes, we can use the exponential distribution. The exponential distribution with a mean of 10 minutes has a rate parameter λ = 1/10.

The probability density function (pdf) for an exponential distribution is given by \(f(x) = λ * e^{(-λx)}\)

In this case, we want to find the probability that a bulb burns out within the next 10 minutes, which corresponds to the cumulative distribution function (CDF) at x = 10. The CDF is given by \(F(x) = 1 - e^{(-λx)\)

So, substituting the values, we have:

\(F(10) = 1 - e^{(-(1/10)*10)\)

\(= 1 - e^{(-1)\)

= 1 - 0.3678794412

≈ 0.6321

Therefore, the probability that a single bulb will burn out within the next 10 minutes is approximately 0.6321.

The amount of time until the first bulb goes out follows an exponential distribution with a rate parameter of λ = 1/10 (since it has a mean of 10 minutes).

The probability density function (pdf) for the time until the first bulb goes out is given by\(f(t) = λ * e^{(-λt).\)

To find the expected amount of time until the first bulb goes out, we need to calculate the mean (or expected value) of this distribution.

The expected value of an exponential distribution with rate parameter λ is equal to 1/λ. In this case, the expected value is 1/(1/10) = 10 minutes.

Therefore, the expected amount of time until the first bulb goes out is 10 minutes.

To find the probability density function (pdf) of the random variable T, which represents the time when you leave the room (after the last light bulb goes out), we need to consider the distribution of the maximum of the exponential random variables.

Since there are 20 light bulbs in the room, and each follows an exponential distribution with a rate parameter λ = 1/10, the time until the last bulb goes out can be modeled as the maximum of 20 exponential random variables.

The pdf of the maximum of independent exponential random variables with the same rate parameter λ is given by \(g(t) = n * λ * e^{(-λt)} * (1 - e^{(-λt))^(n-1)}\), where n is the number of random variables.

In this case, n = 20, and λ = 1/10. Thus, the pdf of T is \(g(t) = 20 * (1/10) * e^{(-(1/10)t)} * (1 - e^{(-(1/10)t))^(19)}\)

This expression represents the pdf of the random variable T, which denotes the time when you leave the room after the last light bulb goes out.

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The formula for calculating total revenue (TR) is, TR = Price x Quantity

The total revenue is the product of the price per unit of a product or service and the total quantity of that product or service sold.

The formula for calculating total revenue (TR) is:

TR = Price x Quantity

This formula is used to calculate the total amount of money earned by a company or individual through the sale of goods or services.

It is important to note that total revenue does not take into account any expenses or costs associated with producing or selling the product. To determine the profitability of a business, total revenue must be compared to the total cost of production, including fixed costs and variable costs, as well as any other expenses related to running the business.

Therefore, the total revenue = Price × Quantity

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In statistics the sampling method is collecting data based on sample of people who represent a population, whereas the census method involves studying each and every member of the population.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

The differences between census and sampling method is -

The investigator gathers data using the census method, which asks questions about every component of the population.

The investigator gathers data using the sampling method by selecting a sample of the objects that represent the entire population.

The Census Method of Collecting Data is appropriate when the area under inquiry is rather small. The sampling method is preferred when the investigation region is large.

The Census Method requires more time to gather data. The sampling method requires less time to gather data.

Generally speaking, the Census Method is more accurate than the Sampling Method. This accuracy can be attributed to the Census Method's inclusion of a study of every component of the population. The sampling approach has a lower level of accuracy because it examines a smaller sample of the population. However, since there are fewer elements in the sampling method, errors are simple to find and eliminate. Consequently, if that's the case, the sampling method gives more accuracy than census method.

Therefore, the differences for census and sampling method are pointed out.

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What is the difference between census method and sampling method in statistics?

The amount of interest she will earn in one year will be 5 dollars and 12 cents.

The normal interest levied on the amount borrowed from any bank on a yearly basis is called the simple interest.

Given that:-

The simple interest amount will be:-

SI   =   (  P   x   R   x   T  )  / 100

SI  =    (  160   x   x   3.2   x   1  )  /   100

SI   =    $5.12

Therefore the amount of interest she will earn in one year will be 5 dollars and 12 cents.

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Answer:

b

Step-by-step explanation:

2(h-8)-h=h-16

step 1 distribute 2 to whats in the parenthesis

2h-16-h=h-16

step 2 combine like terms

h-16=h-16

add 16 to each side

h=h

subtract h from each side  

0=0

this would have an infinite amount of solutions

To calculate the amount of money you will have in the account after 3 years with an interest rate of 6% per year, we can use the formula for compound interest:

A = P(1 + r)^n

Where:

A = the final amount

P = the principal amount (initial deposit)

r = the interest rate per period (in decimal form)

n = the number of periods

In this case:

P = $3,875

r = 6% per year, or 0.06 (in decimal form)

n = 3 years

Substituting the values into the formula:

A = 3,875(1 + 0.06)^3

Calculating:

A = 3,875(1.06)^3

A = 3,875(1.191016)

A ≈ 4,614.76

After rounding to two decimal places, you will have approximately $4,614.76 in the account after 3 years.

The expression is simplified to give -4( x + 37/2)

Given the expression:

\((\frac{-3}{4}x - 8) - ( -17 + \frac{2}{8} x)\)

With the knowledge of BODMAS, we solve the bracket

Find the LCM

\((\frac{-3x - 16}{4} ) - ( \frac{-136 + 2x}{8} )\)

expand the bracket

\(\frac{-3x - 16}{4} + \frac{136 + 2x}{8}\)

Find the LCM

\(\frac{2( -3x - 16) + 136 + 2x }{8}\)

\(\frac{-6x + 12 + 136 + 2x}{8}\)

collect like terms

\(\frac{-4x + 148}{8}\)

-4( x + 37/2)

Thus, the expression is simplified to give -4( x + 37/2)

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Answer:

7.19

Step-by-step explanation:

Take the total cost and subtract the eyebrow pencil to find the cost of the concealer.

14.13

- 6.94

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

7.19

The correct inequality written in factored form represents the graphed region is,

⇒ y ≥ (x + 6) (x - 18)

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The graph shows the inequality.

And, The point on the graph is, (- 4, - 44)

Now, By all options;

The correct inequality is satisfy the given point on the graph.

From (i);

The inequality is,

⇒ y ≥ (x + 6) (x - 18)

Put x = - 4, y = - 44

⇒ - 44 ≥ (- 4 + 6) (- 4 - 18)

⇒ - 44 ≥ (2) (- 22)

⇒ - 44 ≥ - 44

Hence, It is the correct inequality written in factored form represents the graphed region.

Thus, The correct inequality written in factored form represents the graphed region is,

⇒ y ≥ (x + 6) (x - 18)

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Answer:

Step-by-step explanation:

nth term = 3n+2

a) first term = 3+2 = 5

Second term = 3(2)+2 = 8

Third term = 3(3) +2 = 11

b) tenth term = 3(10)+2 = 32

Answer:

d)3

Step-by-step explanation:

y=mx+b

x-3y=-1

reform as the equation above

x+1=3y

simplify --> y=1/3x+1/3

perpendicular lines have opposite-reciprocal slopes

so the answer is 3

Epidemiologic studies are of significant value to scientists who use the information from these studies to formulate dose-response estimates to predict the risk of various health outcomes or diseases.

By analyzing data on exposure levels and corresponding health effects in a population, researchers can establish the relationship between the dose (amount of exposure) and the response (risk or occurrence of the outcome). This allows them to estimate the potential risks associated with different levels of exposure to specific factors such as environmental pollutants, medications, lifestyle choices, or occupational hazards. These dose-response estimates help inform public health interventions, risk assessments, and policy-making decisions aimed at minimizing the occurrence and impact of health risks in populations.

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The selling price to earn $10 per Bible if 5,000 Bibles are printed when the fixed costs per print is $15,000 and variable costs are $25 per Bible, is $38.

The target profit is the profit that is expected by a manufacturer from the sale of its product.

The target profit can be established and used to determine the selling price.

When the target profit is added to the fixed cost per unit and the variable cost per unit, the resultant figure is the selling price.

Fixed costs per print = $15,000

Number of Bibles per print = 5,000

Fixed costs per Bible = $3 ($15,000/5,000)

Variable costs per Bible = $25

Expected profit per Bible = $10

The selling price = $38

Thus, the selling price to earn $10 per Bible if 5,000 Bibles are printed when the fixed costs per print is $15,000 and variable costs are $25 per Bible, is $38.

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