Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Factor this expression completely and then place the factors in the proper location on the grid.
36y²-1

Using the Poisson distribution, the probability of an earthquake in the 0.8-0.9 magnitude range sometime in the next 30 years is

1 - 1.9287 x 10⁻²².

It is given that mean recurrence of an earthquake is the 8.0-9.0 magnitude is approximately 1500 years.

We have to find the probability of an earthquake in this magnitude range sometime in the next 30 years.

Since, an occurrence of an earthquake is a rare event, we can use Poisson distribution here.

Poisson distribution gives the probability of occurrence of any event in a given time interval.

Let the average number of event per year in 30 years of period is λ.

[tex]\lambda = \frac{1500}{30}[/tex]

λ = 50

Let, the occurrence of an earthquake is a random variable x.

Then the probability that at least an earthquake occur in next 30 years is calculated as:

P(x ≥ 1) = 1 - P(x<1)

P(x ≥ 1) = 1- P(x=0)   -----(1)

PDF of Poisson distribution with parameter λ is given as:

[tex]P(X = x) = \dfrac{e^{-\lambda}{\lambda}^x}{x!}[/tex]

So, in this case

[tex]P(x=0)= \dfrac{e^{-50}{(50)}^0}{0!}[/tex]

[tex]P(x=0)= \dfrac{1.9287 \times 10^{-22}}{1}[/tex]

[tex]P(x=0)={1.9287 \times 10^{-22}[/tex]

Substitute this value in equation (1)

P(x ≥ 1) = 1 - 1.9287 x 10⁻²²

Hence, the probability of an earthquake in next 30 years is

1 - 1.9287 x 10⁻²².

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Answer:

See attached image

Step-by-step explanation:

The largest factor of the sum of y and z is 24.

The replacement approach has the advantage of providing the precise values for the variables (x and y), which correspond to the site of intersection.

When using the "by substitution" method, you must first solve one of the equations provided (you must choose which one) for one of the variables (you must choose which one), after which you must plug this value back into the other equation provided (you must "substitute" for the chosen variable and solve for the other value). The first equation is then used to back-solve for the first variable. The many procedures required in using the replacement approach to solve problems have been described in full above. Use those to discover the solution to a given system of linear equations.

We are given with three equations having three unknowns:

x = z/4

x + y + z = 26

y = 2z

Using the method of substitution, we can now solve for each of the three unknowns.

Since the first equation, x = z/4, is an equation for x in terms of z, and the third equation, y = 2z, is an equation for y in terms of z, we can replace x and y in the second equation by their equivalent expressions as follows:

x + y + z = (z/4) + (2z) + z = 26

We are left with an equation with just one unknown z. We can now solve for z:

(z/4) + (2z) + z = 26

z/4 + 8z/4 + 4z/4 = 13z/4 = 26

z/4 = 2

z = 8

Now that we know z, we can easily solve for y, then compute y + z (note: we can also solve for x, but since we are not interested in the value of x there is no need to do so):

y = 2z = 2(8) = 16

y + z = 16 + 8 = 24

Since the largest factor of any number is the number itself, the largest factor of the sum of y and z is 24.

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Answer:

16p + 4

Step-by-step explanation:

the first thing you should do when you simplify an equation is to distribute the parenthesis

4p * 4 + 1 * 4

16p + 4

you cannot simplify any further so that is your answer

Given that the second student chosen is a girl, the probability that both students are female is 0.175.

The occurrence of likely events is referred to as probability. It is the branch of mathematics concerned with numerical estimates of the likelihood of an event occurring or a statement being true.

Probability is nothing but likelihood of something is to occur. When we are unsure about the outcome of an event, we can discuss the probabilities of certain outcomes—how likely they are.

The probability of selecting a girl from the class is

[tex]= \frac{Number\ of\ girls}{ Total\ number\ of\ students}= \frac{14}{26}\\\\= \frac{7}{13}[/tex]

It is known that the one of the chosen student from 2 students is girl, the probability of having both girls will be:

[tex]= \frac{7}{16} * \frac{6}{15}\\\\= 0.175[/tex]

Hence, the probability is 0.175.

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Your question is incomplete, here is the complete question.

Your statistics class has 26 students in it - 14 girls and 12 boys.Your teacher uses a calculator to select two students at random to solve a problem on the board. Given that the second student chosen is a girl, what is the probability that the first student was also a girl?

Answer:

The minimum y-value of f(x) is -3.

Step-by-step explanation:

To find the minimum y-value of f(x), we can plug in a value of x that will make the y-value as small as possible. In this case, we can plug in x = 0 to get f(0) = 3² - 3 = 0. Since 0 is the smallest possible value for f(x), the minimum y-value of f(x) is 0.

Similarly, we can find the minimum y-value of g(x) by plugging in a value of x that will make the y-value as small as possible. In this case, we can again plug in x = 0 to get g(0) = 7 * 0² - 3 = -3. Since -3 is the smallest possible value for g(x), the minimum y-value of g(x) is -3.

Therefore, the correct answer is option A: "The minimum y-value of f(x) is -3."

Answer:

Step-by-step explanation:

A. The minimum y-value of f(x) is -3.

D. The minimum y-value of g(x) is -3.

Factoring a trinomial means expanding an equation into the product of two or more binomials/monomials. It is written as (x + m) (x + n). A trinomial can be factorized in many ways.

A trinomial is ax²+bx+c=0

where,

a= the x^2 term coefficient

b= the x term coefficient

c= the constant value

Quadratic Trinomial in One Variable

In one variable, the general form of the quadratic trinomial formula is ax²+ bx + c, where a, b, and c are constant terms and neither a, b, nor c is zero.  If b² - 4ac > 0, then we can always factorize a quadratic trinomial for the values of a, b, and c. It is equivalent to ax2 + bx + c = a (x + h)(x + k), where h and k are real numbers. Let's look at an example of factoring a quadratic trinomial.

Example: Factorize: 3x² - 4x - 4

Solution:

Step 1:- First multiply the coefficient of x² and the constant term.

3 × -4 = -12

Step 2:- Break the middle term -4x such that on multiplying the resulting coefficient numbers, we get the result -12 (obtained from the first step).

-4x = -6x + 2x

-6 × 2 = -12

Step 3:- Rewrite the main equation by applying the change in the middle term.

3x² - 4x - 4 = 3x²- 6x + 2x - 4

Step 4:- Combine the first two terms and the last two terms, simplify the equation and take out any common numbers or expressions.

3x2² - 6x + 2x - 4 = 3x (x - 2) + 2(x - 2)

Step 5:- Again take (x - 2) common from both the terms.

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

Therefore, (x - 2) and (3x + 2) are the factors of 3x² - 4x - 4.

Quadratic Trinomial in Two Variable

There is no specific way to solve a quadratic trinomial in two variables. Let's take an example.

Example: Factorize: x² + 3xy + 2y²

Solution:

Step 1: These types of trinomials also follow the same rule as above, i.e., we need to break the middle term.

x² + 3xy + 2y² = x² + 2xy + xy + 2y²

Step 2: Simplify the equation and take out common numbers of expressions.

x² + 2xy + xy + 2y² = x (x + 2y) + y (x + 2y)

Step 3: Again take (x + 2y) common from both the terms.

x (x + 2y) + y (x + 2y) = (x + y) (x + 2y)

Therefore, (x + y) and (x + 2y) are the factors of x² + 3xy + 2y²

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The type of linear relationship is positive.

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect. The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables. Its values can range from -1 to 1. A coefficient of 1 shows a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 means there is no linear relationship.

The type of linear relationship is positive.

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Dividing the ones and then put the decimal point and divide the tenths and so on.

what is a meant by decimal point?

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Answer:

[tex] \frac{17}{3} [/tex]

[tex] \frac{17}{9} \div \frac{1}{3} = \frac{17 \times 3}{9} = \frac{17}{3} [/tex]

Errors student make is the % values in the equation were wrongly written and Instead of writing x - 1 for the amount of the 7% solution, write 1 - x.

There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set are called equation.

Given

A student has a 2% salt water solution and a 7% salt water solution. To best imitate salt water at a local beach, he needs 1 liter of a 3.5% salt water solution. He defines x as the amount of 2% solution and writes this equation:

0.2x + 0.7(x – 1) = 0.35(1)

He requires 1 litre of a 3.5% salt water solution to accurately mimic the salt water at a nearby beach.

He constructs the following equation, where x is the volume of the 2% solution:

0.2x + 0.7(x - 1) = 0.35(1)

After resolving the equation, he ascertains that x is around 1.17 litres.

Errors student make:

A) The % values in the equation were wrongly written.

B) Instead of writing x - 1 for the amount of the 7% solution, write 1 - x.

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Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes

First, we are figuring out what is given we are counting numbers or we can add to get to 4:21 PM.

Counting numbers:

[tex]\boxed{3:33=3:34=3:35=3:36=3:37=3:38=3:39=3:40 }[/tex]

Add the numbers:

[tex]\boxed{3:33+7=3:40+10=3:50+10=4:00+21=4:21}[/tex]

If we add the numbers it would be faster.

Therefore, when we add we get are answer.

Therefore, Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes

Answer:

48

Step-by-step explanation:

Answer:

12 visits.

Step-by-step explanation:

Jocelyn receives a flat 25 reward point, and 12.5 points for each visit. She wants to redeem a free movie ticket that costs 170 points.

Set the equation. Let "each visit" be denoted by the variable, x:

12.5 per visit + a flat 25 reward point ≥ Free movie ticket that costs 170 points.

12.5x + 25 ≥ 170

Isolate the variable, x. Note that what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 25 from both sides of the equation:

12.5x + 25 ≥ 170

12.5x + 25 (-25) ≥ 170 (-25)

12.5x ≥ 170 - 25

12.5x ≥ 145

Next, divide 12.5 from both sides of the equation:

(12.5x)/12.5 ≥ (145)/12.5

x ≥ 145/12.5

x ≥ 11.6

x ≥ 11.6 is your answer. Therefore, Jocelyn would have to make 12 trips to earn her first free movie ticket.

~

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">" makes each inequality statement true. since -19 > -20

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than."

Given three inequalities symbols>, <, and = and we need to compare -19 and -20 as per the problem. Hence -19 > -20

Therefore, Each inequality assertion is true when ">" is used. since -19 > -20

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The probability that less than three of the chosen consumers think that currency won't be used in 20 years is 0.293.

According to the statement, 40% of consumers think cash will be unnecessary in 20 years. Let us assume that eight consumers are chosen at random.

We need to determine the likelihood that fewer than three of the chosen consumers think currency will be obsolete in 20 years.

We will use the properties of probability distribution in the given scenario.

We know that for randomly selected variable the properties of combination are used.

P(X=1) + P(X=2) = C¹₈ × 40 × 60⁷ + C²₈ × 40² × 60⁶

P(X=1) + P(X=2) = 0.293

Therefore, there is a 0.293 percent chance that fewer than 3 of the chosen customers think that cash will be obsolete in 20 years.

The ratio of likely outcomes to all scenarios that are feasible, to all possible outcomes is called probability.

Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.

This claim asserts that under certain conditions, the average of many samples (observations) of a random variable without finite mean and variance is itself a random variable, whose distribution converging to either a normal distribution as the number of samples increases.

Disclaimer: The complete question is :

40% of consumers believe that cash will be obsolete in the next 20 years. Assume that only 8 consumers are randomly selected. Find the probability that less than 3 of the selected consumers believe that cash will be obsolete in the next 20 years .

(Round to three decimal places as needed.)

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The first option is true since the item achieved its maximum height of 73.5 feet.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.

This quadratic equation, which has the form y=a(x-h)2 + k, is referred to as being in vertex form. It is so named because the vertex point (peak point) lies on the graph of this equation (h,k)

We may deduce from the facts above that

-4.9 t2 + 19.6 t + 58.8 = 0

The equation will logically fit into the square upon completion.

y = a(x-h)^2 + k

where h will be the time it takes to get to a height of k.

-[tex]4.9t^{2}[/tex] + 19.6t + 58.8 = 0

-[tex]4.9t^{2}[/tex] + 19.6t = - 58.8

-4.9( [tex]t^{2}[/tex] - 4t ) = -58.8

Now take half the linear term, square it, and add it to both sides.

-4.9( [tex]t^{2}[/tex] - 4t ) = -58.8

-4.9( [tex]t^{2}[/tex] - 4t + 4 ) = -58.8 + 19.6

-4.9 [tex](t-2)^{2}[/tex] = - 78.8

s(t) = -4.9 [tex](t-2)^{2}[/tex] + 78.8

now we have t = 3sec

s(t) = 73.5ft

The object reached its maximum height of 73.5 ft, the first choice is correct.

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The value of the test statistic is 3.371

What is Hypothesis?

A hypothesis is a notion that is consistent with available data but has not been proven true or wrong.

A hypothesis (also known as a statistical hypothesis) is a statement on which hypothesis testing will be based in statistics. The null hypothesis and alternative hypothesis are two of the most important statistical hypotheses.

Given that,

s1 = 8      ,   n1 = 330

s2 =7      ,   n2 = 310

Means

x1 = 33

x2 = 31

standard error is

S ∈ = √S₁²/n₁ + S₂²/n²

S = √8²/330 +7²/310

S = 0.593

Test statistic is Ts = x1-x2/S∈

= 33-31/0.593

Ts = 3.371

The test statistic has a value of 3.371.

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The bookstore sold a total of 150 chemistry textbooks and 225 sociology textbooks.

What is a linear equation in two variables?

An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Let C be the number of chemistry textbooks sold and S be the number of sociology textbooks sold. We can write the following system of equations to represent the given information:

C + S = 375

C = 2S

To solve this system of equations, we can substitute the second equation into the first equation to get C + 2S = 375. Then we can solve for S by subtracting C from both sides to get 3S = 375 - C. Dividing both sides by 3 gives us S = (375 - C) / 3.

Substituting this expression for S back into the second equation, we get C = 2((375 - C) / 3). Multiplying both sides by 3 and simplifying gives us 3C = 750 - 2C, or C = 750 / 5 = 150.

Substituting this value for C back into the first equation, we get 150 + S = 375, so S = 375 - 150 = 225.

Hence, the bookstore sold a total of 150 chemistry textbooks and 225 sociology textbooks.

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Answer:

B

Step-by-step explanation:

(4-3x5)/(∛8 +2)

(4 - 15)/(2+2)

-11/4

Answer:

c

Step-by-step explanation:

all triangles equal 180°

By using ratio, it can be calculated that-

Ratio of earnings to the stock’s price = 20 : 1

What is ratio?

Ratio between two quantities tells us how many one quantity is bigger than the other and the comparison is to be made between quantities with same unit. The first part of the ratio is called antecedant and the second part of the ratio is called consequent.

The price of a certain stock is $55.00 per share

Earnings are $2.75 per share

Ratio of earnings to the stock’s price = 55 : 2.75

                                                              = 5500 : 275

                                                              = 20 : 1

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Age of Mike is 56 and Sam is 17 years according to given equation.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical operation, and extraction of roots.

Main body:

Let the age of mike be x and age of sam be y .

According to question :

Mike's age is 5 more than 3 times Sam's age , which means

x = 3y+5                -------(1)

The sum of their ages is 73.

x +y = 73               -------(2)

using eqn 1 in 2,

3y +5 +y = 73

4y = 68

y = 17

x = 3*17 +5

x = 56

hence , age of mike is 56 and sam is 17 years.

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Answer:

–2.4 + 3.2t

Step-by-step explanation:

= –3.6 – 1.9t + 1.2 + 5.1t

= –3.6 + 1.2 – 1.9t + 5.1t

= –2.4 + 3.2t

i hope this helped

We can conclude that due to the help of nurses, the survival time of patients given drugs was the highest.

The nurse takes the patient's cardiac output and makes a decision on how the patient will react to the medication.

What types of tasks does a nurse perform?

Registered nurses (RNs) administer and supervise patient care, educate the public about various ailments, and provide psychological support and counseling to patients' relatives. Most nurses collaborate to doctors in a variety of contexts.

How many years do such people live?

People who have access for informal health information as having a nurse or doctor in the parents 10% more likely to remain past the age of 80, according study released in a journal article by that of the Directorate of Economic Research.

Therefore, we can conclude that due to the help of nurses, the survival time of patients given drugs was the highest.

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The equation of g(x) after the transformation is given as follows:

g(x) = 192x^5 - 36x² + 12.

The equation for function g(x) is obtained applying the rules for each transformation to the parent function f(x).

The parent function f(x) in this problem is defined as follows:

f(x) = 2x^5 - 3x² + 4.

The first transformation is an horizontal shrink by a factor of 1/2, hence the rule for this transformation is described as follows:

g(x) = f(2x).

Thus:

g(x) = 2(2x)^5 - 3(2x)² + 4

g(x) = 64x^5 - 12x² + 4.

The vertical stretch by a factor of 3 means that all these coefficients are multiplied by 3, that is:

g(x) = 3(64x^5 - 12x² + 4).

Applying the distributive property, we have that:

g(x) = 192x^5 - 36x² + 12.

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1. 16%

8/50 = .16 x 100% = 16%

2. 135 x .16 = $21.6

Answer:

7. x=11/3

8. no solutions

Step-by-step explanation:

7.

[tex]2*\sqrt{3x-2} =6[/tex]

Divide both sides by two

[tex]\sqrt{3x-2}=3[/tex]

Square both sides

[tex]3x-2=9[/tex]

Simplify

[tex]x=\frac{11}{3}[/tex]

8.

[tex]\sqrt{43-x}+10=1[/tex]

Subtract 10 both sides

[tex]\sqrt{43-x}=-9[/tex]

Impossible to have a negative answer when square rooting, no solutions

Answer:

m∠1 = 62º

m∠2 = 45º

m∠3 = 24º

Step-by-step explanation:

Angle 1 is supplementary to 118º, so we can solve for its measure by subtracting 118º from 180º.

m∠1 = 180º - 118º = 62º

The interior angles of a triangle are supplementary, so we can solve for it by summing the small triangle's interior angle measures to 180º.

m∠1 + m∠2 + 73º = 180º

62º + m∠2 + 73º = 180º

m∠2 = 45º

Do the same thing as you did for angle 2 for angle 3.

(45º + m∠3) + 62º + 49º = 180º

m∠3 = 24º