Quadratic Expressions:Question 1
Which is a factor of x²+ 7x + 10?
Select one:
a x-5
bx-1
cx+5
dx+1

Answers

Answer 1

Answer:

Option C. (x + 5)

Step-by-step explanation:

This quadratic equation can either be solved using the quadratic formula or be factorised using The Double Bubble Method.


Double Bubble Method:

After listing the different pairs of factors 10, the pair (that would add together to give 7) are 2 and 5. These two factors will be used to rewrite +7x:

[tex]x^{2} + 2x + 5x + 10[/tex]

Factorization by grouping (i.e factorising each separate group sharing a common factor) will then be applied:

[tex]= x(x + 2) + 5(x + 2)[/tex]

The common factor, which is the (x + 2) expression, will be extracted:
[tex]= (x + 2)(x + 5)[/tex]

∴ [tex]x^{2} + 7x + 10[/tex] can be factorised to [tex](x + 2)(x + 5)[/tex]

It is observed that a factor of the given quadratic equation is x + 5

∴Option C


Related Questions

What does the notation f(2) mean?
multiply fby 2
the output (y-value) when x = 2
O the value of x when the output is 2

Evaluate f(2)=

Answers

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

y = f(x) represents a function with output value as y and x as an input in the function.

Therefore, f(2) represents value of function (y) at x = 2

so the correct choice here would be : " the output (y - value) when x = 2 "

What is the standard deviation of the discrete random variable if the variance is 1.56?

Answers

Answer: Approximately 1.25

Reason:

The standard deviation is the square root of the variance.

[tex]\text{Standard deviation} = \sqrt{\text{variance}}\\\\\text{Standard deviation} = \sqrt{1.56}\\\\\text{Standard deviation} \approx 1.24899959967968\\\\\text{Standard deviation} \approx 1.25\\\\[/tex]

Round the answer however you need to, or however your teacher instructs. I rounded to two decimal places since 1.56 is to two decimal places.

The standard deviation of the discrete random variable if the variance is 1.56 is 1.25

Given that, a discrete random variable has a variance of 1.56, we need to find its standard deviation

We know that,

The standard deviation is the square root of the variance.

Standard deviation = √ variance

Standard deviation = √1.56

Standard deviation = 1.24899959967968

Standard deviation = 1.25

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Select the correct answer from each drop-down menu. Stacy rolls a pair of six-sided fair dice. The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is , and the two events are exclusive.

Answers

The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is 24/36 = 2/3

The two events are mutually exclusive

"Information available from the question"

Stacy rolls a pair of six-sided fair dice.

Now, According to the question:

Let the probability of getting a multiple of 3 is "A"

Let the probability of getting an even number is "B"

Total number of outcomes=36

Total number of favorable outcomes  of either a multiple of 3 or an even number are:-

(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)

Probability = Number of fav. outcomes/ Total no. of outcomes

The probability that the sum of the numbers rolled is either a multiple of 3 or an even number will be given by counting the numbers that are either even or multiples of 3 and then dividing by the number of possible outcomes, 36.

In our case this will be;

24/36 = 2/3

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At a recent Algebra lover's convention, 4 times as many people attended on Sunday as on Thursday. If a total of 2,910 people attended the convention on the two days combined, how many people attended on Thursday? How many people attended on Sunday?
people attended on Thursday.
people attended on Sunday.

Answers

2,910 people attended the convention on the two days combined. Since 4 times as many people attended on Sunday as on Thursday, we can set up the equation:

4x = 2,910 - x

Solving for x gives us x = 1,455. This means that 1,455 people attended on Thursday and 4 × 1,455 = 5,820 people attended on Sunday.

hope this helps:)

For students majoring in Hospitality Management, it was determined that 5% have visited 1–10 states, 16% have visited 11–20 states, 45% have visited 21–30 states, 19% have visited 31–40 states, and 15% have visited 41–50 states. Suppose a Hospitality Management student is randomly selected. What is the probability that the student has visited 21 or more states?

A . 0.15
B. 0.21
C. 0.45
D. 0.79

Answers

Answer:

D. 0.79

Step-by-step explanation:

To find the probability that a Hospitality Management student has visited 21 or more states, we need to sum up the probabilities of the categories that represent students who have visited 21 states or more.

The probabilities of the categories are as follows:

Visited 21–30 states: 45% = 0.45

Visited 31–40 states: 19% = 0.19

Visited 41–50 states: 15% = 0.15

So, the total probability of a student having visited 21 or more states is:

0.45 + 0.19 + 0.15 = 0.79.

Therefore, the probability that a Hospitality Management student has visited 21 or more states is 0.79 or 79%.

Please help!! Number 7

Answers

Answer:

[tex]x = 9[/tex]

Step-by-step explanation:

Solving For #7

We will use the Angle Bisector Theorem

The angle bisector theorem states that in a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

In the figure provided in #7 we see that QS bisects ∠Q forming two smaller triangles ΔPQS and ΔQRS

According to the angle bisector theorem:

[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\[/tex]

Given
[tex]QR = 12.6\\PQ = 7\\RS = x\\PS = 5\\\\[/tex]

[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\\\\\\rightarrow \dfrac{12.6}{7} = \dfrac{x}{5}[/tex]

If we multiply by [tex]5[/tex] both sides of the equation we can get rid of the denominator 5 on the right side:
[tex]\rightarrow \dfrac{12.6}{7} \times 5 = x\\\\9 = x\\\\\boxed{x = 9}[/tex]

1. Let x represent the weight of a single apple picked from a tree. It has been determined that x has a normal distribution with mean 45 oz and standard deviation 3 oz. Let represent the mean weight of 10 apples picked at random. Describe the distribution by answering the following questions.

a) [2 pt] Is normally (or approximately normally) distributed? How do you know?




b) [2 pt] What is the mean, ?

Answers

a) The distribution of the mean weight of 10 apples picked at random is normally distributed.

b) The mean, μ, is 45 oz.

What is normal distribution and mean?

normal distribution: The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean.

Mean: In mathematics, a mean is the average of a data set, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers.

a) The distribution of the mean weight of 10 apples picked at random is approximately normally distributed. This is because, according to the Central Limit Theorem, when the sample size is sufficiently large, the distribution of the sample mean becomes normal regardless of the underlying population distribution.

Here, we have a sample size of 10, which is considered large enough to apply the Central Limit Theorem. Also, we know that the underlying population distribution of the weight of a single apple is normal.

b) The mean weight of 10 apples picked at random is simply the mean of the individual weights of those 10 apples. Since the individual weights of the apples are normally distributed with a mean of 45 oz and a standard deviation of 3 oz, the mean weight of 10 apples will also be normally distributed with a mean equal to the mean of the individual weights, which is 45 oz.

Therefore, the mean, μ, is 45 oz.

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Пожалуйста, напишите вымышленную историю о том, как растут деревья, заранее спасибо.

Answers

Answer:

Step-by-step explanation:

К счастью, другое маленькое дерево поблизости заметило растущее дерево и дало несколько интересных советов о том, как удерживать его распускающиеся листья новыми и интересными способами. Было забавно испытать на других маленьких деревьях множество различных способов расположения листьев. Другие маленькие деревья вскоре заметили это и начали поворачивать свои немногочисленные листья под углом. Другие маленькие деревья могли лишь слегка приподнять свои листья.

Растущее дерево решило, что будет немного приподнимать листья на радость другим деревьям. Но, в конце концов, все маленькие деревья начали отращивать больше листьев на ветвях, которые тянулись еще дальше. С каждым сезоном многие листья невозможно было приподнять. Некоторые из растущих деревьев продолжали шептаться, в то время как некоторые научились громко смеяться, некоторым, казалось, нравилось плакать и падать духом, а некоторые росли вдали от группы из-за того, как многие времена года влияли на них и на другие деревья и животных вокруг них.

За прошедшие годы родительские деревья время от времени мельком смотрели вниз, чтобы увидеть, как растут их семена, и они поднимали свои ветви к небу, чтобы пропустить солнечный свет через полог. Все растущие деревья заметят это и поднимут головы, чтобы насладиться солнечным светом. Те, кто не обращал внимания на поведение своего родительского дерева, обычно подражали другим растущим деревьям и умудрялись собирать немного солнечного света. Иногда растущее дерево переставало расти, потому что не могло достичь солнечного света. Его листья не будут такими обильными, а его ветви будут тянуться дальше, чтобы быть ближе к солнечному свету других растущих деревьев. По прошествии многих сезонов растущие деревья становились все выше и теперь можно было видеть, что их место среди кроны деревьев было довольно тесным.


PSA: this question is a macroeconomics question so please don’t answer if you do not have a clear understanding of it.
In answering the question, you should emphasize the line of reasoning that generated your results; it is not enough to list the results of your analysis. Include correctly labeled diagrams, if useful or required, in explaining your answers. A correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes.
Because bagels and cream cheese are often eaten together, they are complements.
(a) We observe that both the equilibrium price of cream cheese and the equilibrium quantity of bagels have risen. What could be responsible for this pattern—a fall in the price of flour or a fall in the price of milk? Illustrate and explain your answer.
(b) Suppose instead that the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen. What could be responsible for this pattern—a rise in the price of flour or a rise in the price of milk? Illustrate and explain your answer.

Answers

The solution to the question on the equilibrium of the cheese and bagels have been given below

How to get the equilibrium

a) If the equilibrium price of cream cheese and the equilibrium quantity of bagels have both risen, this could be caused by a fall in the price of flour, one of the inputs used to produce bagels.

This decrease in the cost of production would cause the supply of bagels to increase, leading to a rightward shift in the supply curve. At the same time, the demand for bagels would increase as consumers substitute away from other breakfast foods and toward bagels, leading to a rightward shift in the demand curve.

These two shifts would result in a higher equilibrium price for cream cheese, since bagels and cream cheese are complements. The increased demand for bagels would lead to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward.

The diagram below illustrates this relationship. The initial equilibrium is at point A, with a price of P1 and a quantity of Q1. After the decrease in the price of flour, the supply curve for bagels shifts rightward to S', and the demand curve for bagels shifts rightward to D'. The new equilibrium is at point B, with a higher price of P2 and a higher quantity of Q2. The increase in the demand for bagels leads to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward to D'''. The new equilibrium for cream cheese is at point C, with a higher price of P3 and a higher quantity of Q3.

b) If the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen, this could be caused by a rise in the price of milk, one of the inputs used to produce cream cheese.

This increase in the cost of production would cause the supply of cream cheese to decrease, leading to a leftward shift in the supply curve. At the same time, the demand for cream cheese would decrease as consumers substitute away from cream cheese and toward other breakfast foods, leading to a leftward shift in the demand curve.

These two shifts would result in a higher price for cream cheese, but a lower quantity of bagels consumed. The decreased demand for cream cheese would lead to a decrease in the demand for bagels, causing the demand curve for bagels to shift leftward.

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Write an expression: j with a coefficent 4 - 9

Answers

The Expression with coefficient 4 and -9 is 4j and -9j.

What is Expression?

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.

Given:

We have to write the coefficient as 4 and -9.

As, coefficient is the number which is just before the variable like in 2x 'x' is the variable and '2' is the coefficient.

So, with coefficient 4 the expression is 4j

and, with coefficient  -9 the expression is -9j.

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find the size of angle x 164

Answers

Note that the size of angle x = 115°. This is a problem relating to the sum of angles in a circle. See the computation below.

What is the sum of angles in a circle?

The sum of angles in a circle is always equal to 360 degrees or 2π radians.

This means that the sum of the measures of the angles formed by any number of rays or line segments that meet at a common point, or vertex, and whose endpoints lie on the circle, will always add up to 360 degrees or 2π radians. This property is often used in geometry and trigonometry to solve problems involving circles and angles.

With regard to the above problem,

We are given three angles in a circle named as follows:

a) 81°

b) 164°

c) x

The above rule state that

81 + 164 + x = 360°

thus, x = 360 - 81 - 164

x = 360 -245

x = 115°

Thus the value of ∠x is  115°

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Full Question:

See attached image.

How much pure alcohol must a pharmacist add to 10^3 of a 10% alchohol solution to strengthen it to a 70% solution? (ASAP)

Answers

Answer:

60% i mean it sounds right

Step-by-step explanation:

Solve the triangle using law of cosines. Round answer to the nearest tenth.

Answers

Using sine law and cosine law, s is 13.6 units and T is 37.7 degrees while U is 59.3 degrees

What is law of cosine

The Law of Cosines, also known as the Cosine Formula, is a fundamental mathematical relationship between the sides and angles of a triangle. It states that the dot product of two sides of a triangle is equal to the product of the third side and the cosine of the angle between the two sides.

The general form of the Law of Cosines is:

C^2 = A^2 + B^2 - 2ABcos(C)

where C is the angle between sides A and B, and A, B, and C are the lengths of the sides of the triangle. The formula can be rearranged to solve for any one of the sides or angles given the other two.

In this problem, we can easily solve for s.

s² = 8² + 12² - 2(8)(12)cos83

s² = 184.601

s = √184.601

s = 13.6 units

The value of angle T is calculated using sine law;

13.6 / sin 83 = 8 / sin T

sin T = 8(sin 83) / 13.6

sin T = 0.58385

T = sin⁻¹(0.58385)

T = 37.7°

Using sum of angle in a triangle;

T + S + U = 180°

83 + 37.7 + U = 180

U = 180 - 120.7

U = 59.3°

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At the 2022 Winter Olympics, one country won a total of 150 medals. A circle graph of the medals is shown.

a circle graph titled 2022 Winter Olympic Medals, with three sections labeled gold 20 percent, silver 30 percent, and bronze 50 percent

How many gold and bronze medals were won?

50
70
105
120

Answers

Answer:

120

Step-by-step explanation:

The total number of medals won is 150, and the circle graph shows that the proportion of medals won as gold is 20 percent, as silver is 30 percent, and as bronze is 50 percent.

To find the number of gold and bronze medals won, we need to calculate the total number of medals won in each category by multiplying the total number of medals by the proportion of medals won in each category.

Gold medals: 150 * 20% = 30

Bronze medals: 150 * 50% = 75

So, a total of 30 + 75 = 105 medals were won as gold and bronze.

Please help me I’m confused

Answers

Answer:

Below

Step-by-step explanation:

Here is what the graph should look like ...you can see that he will have 0 fence left to paint  ( 0 = y ) when time = 3 hrs

4 players are competing in a tennis tournament. Rosh has 50% chance of winning the the tournament. The other players craig, Phil, terry are equally likely to win. what is the probability that craig wins the tournament?

Answers

The probability of Rosh winning the tournament is 50%, which means the probability of one of the other three players winning is 50% divided by 3, or approximately 16.67% each. Therefore, the probability that Craig wins the tournament is 16.67%.

Can you please tell me the graphing points for this equation?
y = 2^(x+5) +1

Answers

The graphing points of the equation is given in the table.

What is an equation?

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

Given equation is [tex]y=2^{x+5} +1[/tex].

To find the graphing points of the functions:

By assuming the value for x and substitute in the given function to find the values of y.

[tex]if x=-2,y=2^{-2+5} +1=9\\ifx=-1, y=2^{-1+5} +1=17\\if x=0,y=2^{0+5} +1=33\\if x=1,y=2^{1+5} +1=65\\ifx=2,y=2^{2+5} +1=129[/tex]

It is given the table format as,

                 x                [tex]y=2^{x+5} +1[/tex]

                -2                     9

                -1                      17

                 0                     33

                  1                     65

                  2                   129  

Hence, these are all the graphing points of the equation.

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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
11
24
Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.

Answers

The value of x is 12. The solution has been obtained by using trigonometry.

What is trigonometry?

The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle. The angles of 0, 30, 45, 60, and 90 degrees are the most typical trigonometric angles to be utilised in computations.

We are given a right - angled triangle with one angle equal to 24° and the length of the base is 11.

Using trigonometry,

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos θ = 11/x

Here, θ = 24°

So,

⇒cos 24° = 11/x

⇒x = 11/cos 24°

⇒x ≈ 12.04

x ≈ 12

Hence, the  value of x is 12.

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Please help me with this question: Find the limit

Answers

Answer:

1/5

Step-by-step explanation:

Answer:

The solution is 1/5 or 0,2

Step-by-step explanation:

[tex] \displaystyle \sf\lim_{x \to 3} \frac{ {x}^{2} - 5x + 6 }{2 {x}^{2} - 7x + 3} \: \: \: \: \: \: \: \: \: \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)(x - 3)}{(2x - 1)(x - 3)} \\\\ = \displaystyle \sf\lim_{x \to 3} \frac{(x - 2)\cancel{(x - 3)}}{(2x - 1)\cancel{(x - 3)}} \\\\ = \displaystyle \sf \lim_{x \to 3} \frac{(x - 2)}{(2x - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ \sf = \frac{(3 - 2)}{(2(3) - 1)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\\\ = \boxed{\sf \frac{1}{5} \: or \: 0.2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Complete the table.
q=p+7
Р
q
0
1
8
2
3
4
11

Answers

Given expression q=p+7

Expression can be defined as contains one or more variables and constants with one or more arithmetic operators.

Simply put the p values in the expression. solve it and get the q values.

q=p+7 in the place of p submit p=0

q=0+7

q=7

q=p+7  in the place of p submit p=2

q=2+7

q=9

q=p+7  in the place of p submit p=3

q=3+7

q=10

Therefore, The values of q are 7,9,10

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The missing numbers are:

7,9 and 10 when 0, 2, and 3 respectively.

What is an equation?

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

An equation,

q = p + 7.

Substituting the values of p:

When p = 0,

q = 0 + 7

q = 7.

When p = 2,

then q = 9.

And when p = 3,

q = 10

Therefore, all the required values are given above.

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Money A savings account increases from $200 to $206. What is the percent increase of the savings account?

Answers

Answer:

3% increase

Step-by-step explanation:

1 The difference between the simple interest and compound interest on a sum put out for 2 years at 5% was 6.90 .find the sum​

Answers

so we're assuming the compounding period is annual, so hmmm let's call our sum "P", how much is it at simple and compound interest anyway?

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P[1+(0.05)(2)] \implies \boxed{A = 1.10P} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annual, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = P\left(1+\frac{0.05}{1}\right)^{1\cdot 2} \implies \boxed{A = 1.1025P}[/tex]

now, the larger one will be the compound interest one, so, let's subtract the simple interest one from it to get 6.90

[tex]1.1025P~~ - ~~1.10P~~ = ~~6.90\implies 0.0025P=6.90 \\\\\\ P=\cfrac{6.90}{0.0025}\implies {\Large \begin{array}{llll} P=2760 \end{array}}[/tex]

A soccer field (football pitch) has a length of 105.1 m and a width of 67.1 m. Find the total area of the field in square meters (m2) and convert this measurement to square yards (yd2). Use the fact that 1 yard = 0.9144 m. Round your answer to the nearest whole number.

Answers

Answer:

Step-by-step explanation:

A = l x w

A = 105.1m x 67.1m

A = 7052.21m

Convert to yds.

7052.21 / 0.9144  =  7712.4

To the nearest whole, the area is 7712 yds2.

This is a number sequence
2,3,5,9,17,33,65
what are the next two terms?

Answers

The next two terms of the number sequence 2,3,5,9,17,33,65 are given as follows:

129, 257.

How to obtain the next two terms of the number sequence?

This is a recursive number sequence, as each term is obtained multiplying the previous term by 2 and then subtracting one.

Then the term after 65 is given as follows:

65 x 2 - 1 = 130 - 1 = 129.

The term after 129 is given as follows:

2 x 129 - 1 = 257.

Then the next two terms are 129 and 257.

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Coffee: The National Coffee Association reported that 64% of U.S. adults drink coffee daily. A random sample of 225 U.S. adults is selected. Round your
answers to at least four decimal places as needed.

Answers

The mean and the standard deviation are  144 and 4.3200

How to determine the mean and the standard deviation

from the question, we have the following parameters that can be used in our computation:

Proportion, p = 64%

Sample size, n = 225

The mean is calculated as

Mean = np

Substitute the known values in the above equation, so, we have the following representation

Mean = 64% * 225

Mean = 144

The standard deviation is calculated as

SD = √Mean * (1 - p)

substitute the known values in the above equation, so, we have the following representation

SD = √144 * (1 - 64%)

Evaluate

SD = 4.3200

Hence, the mean is 144

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Complete question

Coffee: The National Coffee Association reported that 64% of U.S. adults drink coffee daily. A random sample of 225 U.S. adults is selected. Round your answers to at least four decimal places as needed.

(a) Find the mean

(b) Find the standard deviation

Solve the following equation for y. 22x+2y=-14

Answers

Step-by-step explanation:

22x + 2y = -14

2y = -22x - 14

y = -11x - 7

The median home value in Pennsylvania and Nevada (adjusted for inflation) are shown below.

Year Pennsylvania Nevada
1950 42400 53700
2000 97000 142000


If we assume that the house values are changing linearly,

a) In which state have home values increased at a higher rate?
Nevada
Correct

b) If these trends were to continue, what would be the median home value in Pennsylvania in 2010?
$


c) If we assume the linear trend existed before 1950 and continues after 2000, the two states' median house values will be (or were) equal in what year? (The answer might be absurd)
The year

Answers

According to the given statement Nevada's property prices have grown more rapidly , median home value 148,880 and median house values will be 15.6.

What does the median in housing mean?

The selling price of the middle property in a list of properties listed by highest sale price through lowest over a predetermined time period is the median house price. Thus, if 71 homes were sold, the median home price would correspond to the sale price of the 36th home.

Rate of change for Pennsylvania  [tex]= (97000 - 42400) / (2000 - 1950) = 1092[/tex]

Rate of change for Nevada [tex]= (142000 - 53700) / (2000 - 1950) = 1816[/tex]

As a result, Nevada's property prices have grown more rapidly.

b) Median home value of Pennsylvania in 2010[tex]= 42400 + 1092 * (2010 - 1950) = $148,880[/tex]

c) Pennsylvania[tex]= 42400 + 1092x[/tex]

Nevada[tex]= 53700 + 1816x[/tex]

[tex]42400 + 1092x = 53700 + 1816x\\724x = 11300\\x = 15.6[/tex]

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If F(x) = f(g(x)), where f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, find F'(4).
F'(4) =

Answers

Answer:

36.

Step-by-step explanation:

o find F'(4), we need to use the chain rule of differentiation. The chain rule states that if F(x) = f(g(x)), then F'(x) = f'(g(x)) * g'(x).

Given that f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, we can calculate F'(4) as follows:

F'(4) = f'(g(4)) * g'(4) = f'(-2) * g'(4) = 9 * 4 = 36

Therefore, F'(4) = 36.

Write an equation for the polynomial graphed below

Answers

The equation of the polynomial is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2

How to determine the equation of the polynomial

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following readings:

A root of multiplicity 1 at x = -3 A root of multiplicity 1 at x = -2A root of multiplicity 1 at x = 1A root of multiplicity 2 at x = 3y-intercept = 2

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x + 3)(x + 2)(x - 1)(x - 3)^2

The y-intercept is 2

So, we have

a * (0 + 3)(0 + 2)(0 - 1)(0 - 3)^2 = 2

This gives

a = -1/27

Hence, the expression is P(x) = 1/27(x + 3)(x + 2)(x - 1)(x - 3)^2

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Let X,X2, ...,X25 denote 25 random draws (with replacement) from the following list of 5 numbers: 0, 1,0,0,0. What is E(X)?
(a) 0.875
(b) 1/3
(c) 0.5
(d) 2.0

Answers

As per the probability, the value of E(X) is option (a) 0.8

In statistics, the expected value or mean is a measure of central tendency that represents the average outcome of a random variable over an infinite number of trials.

To find the expected value of X, we need to calculate the probability of each possible outcome and multiply it by its corresponding value. In this case, the possible outcomes are 0 and 1, and their probabilities can be calculated as follows:

The probability of drawing a 0 is 4/5 because there are 4 zeros in the list and 5 total numbers.

The probability of drawing a 1 is 1/5 because there is only one 1 in the list and 5 total numbers.

Using these probabilities, we can calculate the expected value of X as follows:

E(X) = (0 x 1/5) + (1 x 4/5)

The first term in this equation represents the probability of drawing a 0, multiplied by its value (which is 0), and the second term represents the probability of drawing a 1, multiplied by its value (which is 1). Simplifying this equation gives:

E(X) = 4/5 =0.8

Therefore, the answer to this problem is (a) 0.8, since the expected value of X is 0.8 of the possible outcomes.

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