Describe and correct the error in writing an equation of the line that passes through (4,-5) and is parallel to the line y=1/3x+5.

Step-by-step explanation:

SWT + TWU =180º therefore SWU must be a line. Aka SWU is linear. So SWT and TWU must be a linear pair.

SWT + SWT = 180º therefore 2SWT=180º deviding both sies by 2 we get SWT = 90º Therefore SWT is replacing TWU. SWT is substituted into TWU. So substitution.

SU | TV basically means the line that passes through both points S and U is perpendicular to the line that passes through both points T and V. Therefore it is the Defenition of perpendicular lines.

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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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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:

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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It is true that the objective function and the restrictions in a linear programming problem must be linear functions of the choice variables.

The method of choosing the best result from a linear function is known as linear programming. Making a few straightforward assumptions is the easiest way to accomplish linear optimization. As the goal function, the linear function is referred to. Real-life relationships can be quite challenging. However, such interactions can be represented using linear programming, which facilitates analysis of such relationships.

When the need of a mathematical model are represented by linear relationships as, the optimal result can also be obtained using a technique known as the linear programming (LP), sometimes known as linear optimization. A particular type of mathematical programming is linear programming.

Formally speaking, linear programming is the method for optimizing a linear objective function under the restrictions of the linear equality and linear inequality. Convex polytopes, a set defined as the total intersection of a finite number of half spaces, each of which is determined by the linear inequality, make up viable region.

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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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Answer: answer set C

The square root of 195 is irrational. Even if there is a divisor of 2 after we square the number, the number still remains irrational.

The rest of the choices have rational numbers. There is an 8.22 repeating, but the repeating decimal indicates that the number is still rational. Negative numbers are rational integers.

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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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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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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Answer:

m∠C is 113°

Step-by-step explanation:

Well since we don't have the measurements of the sides to determine what kind of triangle this is. All we can do is take the fact that a triangle equals 180° and create and equation to solve for x.

[tex]180=30+37+x[/tex]

[tex]180=67+x[/tex]

[tex]67+x=180\\-67=-67\\[/tex]    Subtract 67 on both sides

[tex]180-67=113[/tex]

Answer:

B

Step-by-step explanation:

(4-3x5)/(∛8 +2)

(4 - 15)/(2+2)

-11/4

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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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

The angle that the line 3y = 2x + 6 makes with the [x] axis is (θ) = 33°69'.

Given is the equation -

3y = 2x + 6

The given equation is -

3y = 2x + 6

y = (2/3)x + (6/3)

y = (2/3)x + 2

Slope of the line -

m = 2/3.

We know slope is also given by -

m = tan(θ)

So -

tan(θ) = 2/3

(θ) = tan⁻¹(2/3)

(θ) = 33°69'

Therefore, the angle that the line makes with the [x] axis is (θ) = 33°69'.

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Answer:

4 is the answer is this equation

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:

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

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

Answer:

BC = 32

Step-by-step explanation:

the diagonals of a rectangle are congruent , then

BC = AD = 32

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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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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a) 28 minutes are taken to have the same amount of water.

b) Both pools have an amount of 1134 liters when 28 minutes have passed.

Linear functions have a graph that is a straight line. A linear function takes the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.

Physically speaking, the capacity (Q₁ and Q₂) of each pool, in liters, is equal to the product of flow rate (Q), in liters per minute, and time (t), in minutes.

Hence, we derive the following linear functions for each pool:

For the first pool

Q₁ = 735 + 15.25(t) .............. (1)

For second pool

Q₂ = 0 + 41.50(t) ...................(2)

According to the question, the time needed to find both pools with the same amount of water is found by the following expression as linear functions: Q₁ = Q₂.

so eq (1) = eq  (2)

735 + 15.25 (t) = 41.50 (t)

41.50 (t) - 15.25 (t) = 735

26.25 (t) = 735

          t =[tex]\frac{735}{26.25}[/tex]

          t = 28 min

Therefore, 28 minutes are taken to have the same amount of water.

[part b]

Now to calculate the total amount and know that then we have the time t = 28 min.

So, the corresponding amount will be calculated from eq (2):

Q₂ = 0 + 41.50(t) ...................(2)

Q₂ = 41.50(28)

Q₂ = 1134 litters

Both pools have an amount of 1134 liters when 28 minutes have passed.

Therefore, (a)28 minutes are taken to have the same amount of water.

(b)Both pools have an amount of 1134 liters when 28 minutes have passed.

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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]

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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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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Answer:

c

Step-by-step explanation:

all triangles equal 180°

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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