67% of all americans are home owners. round your answers to four decimal places. if 37 americans are randomly selected, find the probability that

Answer:

Step-by-step explanation:

To find the possible length and breadth of the rectangle, we need to factor the given expression:

x^2 - 6x + 8 = (x - 4)(x - 2)

Therefore, the length and breadth of the rectangle can be any combination of (x-4) and (x-2).

For example, if we choose (x-4) as the length and (x-2) as the breadth, we have:

Length = x - 4

Breadth = x - 2

Conversely, if we choose (x-2) as the length and (x-4) as the breadth, we have:

Length = x - 2

Breadth = x - 4

So, the possible length and breadth of the rectangle are (x-4) and (x-2), and vice versa.

Answer:(x-4) and (x-2)

Step-by-step explanation:

Answer:

D. The electrician charges $23 per hour.

Step-by-step explanation:

C(h)= 23h+30 is in the form y=mx +b

$30 is the initial fee (b)

$23 is the amount charged per hour (h)

If the midpoint of AB is =M(−6, 2) and one endpoint is =A(−8, 7), then the coordinates of the other endpoint B is (-4, -5)

To find the coordinates of endpoint B, we can use the midpoint formula, which states that the midpoint of a line segment is the average of the coordinates of its endpoints.

The midpoint formula is

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

We know the coordinates of point M, which is the midpoint of the line segment AB:

M = (-6, 2)

We also know the coordinates of one endpoint of the line segment, A:

A = (-8, 7)

Let's use the midpoint formula to find the coordinates of endpoint B:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the values we know:

(-6, 2) = ((-8 + x2)/2, (7 + y2)/2)

Simplifying

-6 = (-8 + x2)/2 and 2 = (7 + y2)/2

Multiplying both sides of each equation by 2:

-12 = -8 + x2 and 4 = 7 + y2

Adding 8 to both sides of the first equation:

-4 = x2

Subtracting 7 from both sides of the second equation:

-5 = y2

Therefore, the coordinates of endpoint B are B = (-4, -5)

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The correct option is B) 0.0634.

1) Standard deviationThe table is shown as below:Number of Times Frequency 1 34 2 73 3 249 4 127 5 72 6 30 7 24 Total 915The given population contains 915 people. Let X be the number of times per week a person dines out for a person sampled at random from this population.The population standard deviation is given by the formula below:$$\sigma = \sqrt{\frac{\sum (X-\mu)^2}{N}}$$where N is the population size, X is the value of the individual element of the population, μ is the mean value of the population. $$\sigma = \sqrt{\frac{\sum (X-\mu)^2}{N}}$$$$= \sqrt{\frac{\sum X^2 - 2X\mu + \mu^2}{N}}$$We need to compute the variance first.$$\sigma^2 = \frac{\sum X^2 - 2X\mu + \mu^2}{N}$$$$= \frac{(1^2 \cdot 34 + 2^2 \cdot 73 + 3^2 \cdot 249 + 4^2 \cdot 127 + 5^2 \cdot 72 + 6^2 \cdot 30 + 7^2 \cdot 24) - 2\cdot 3.176 \cdot (34 + 2\cdot 73 + 3\cdot 249 + 4\cdot 127 + 5\cdot 72 + 6\cdot 30 + 7\cdot 24) + 3.176^2 \cdot 915}{915}$$$$= 3.5689$$Therefore, the population standard deviation is given by:$\sigma = \sqrt{3.5689} = 1.8911\approx 1.9$Hence, the correct option is C) 1.92) The probability of a binomial experiment can be calculated by the formula below:$${\rm P}(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$$where n is the number of trials, k is the number of successes, p is the probability of success for each trial, and $1-p$ is the probability of failure for each trial.Here, n = 15 and p = 0.4.We need to find the probability of getting 12 successes out of 15 trials. Hence, k = 12.Using the formula above, we get$${\rm P}(X=12) = \binom{15}{12}0.4^{12}0.6^{3}$$$$= \frac{15 \times 14 \times 13}{3 \times 2 \times 1} \cdot 0.4^{12} \cdot 0.6^{3}$$$$= 0.0633605376$$Hence, the correct option is B) 0.0634.

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The matrix of predicted rankings UVT is [[48,24,12],[0,0,0],[24,12,6]].

The matrix of predicted rankings UVT can be calculated using the formula UVT = UV.The provided initial values for U() and V(0) are as follows:U() = [[2,1],[1,0],[3,-1]]V(0) = [[24,12,6],[0,0,0],[12,6,3]]Using the above values, the matrix of predicted rankings UVT can be computed as follows:UVT = UVU = [[2,1],[1,0],[3,-1]]V = [[24,12,6],[0,0,0],[12,6,3]]UVT = [[2,1],[1,0],[3,-1]] x [[24,12,6],[0,0,0],[12,6,3]]= [[48,24,12],[0,0,0],[24,12,6]]Therefore, the matrix of predicted rankings UVT is [[48,24,12],[0,0,0],[24,12,6]].

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Answer:

C is your answer

Step-by-step explanation:

in my opinion, i think it would be the mode.

The function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)

A function, which produces one output from a single input, is an illustration of a rule. The picture was obtained from Alex Federspiel. The equation y=x2 serves as an example of this.

a) We can see that the function is increasing from approximately x = -3 to x = -1 and from approximately x = 1 to x = 2.5. So, the increasing intervals are (-3,-1) and (1, 2.5)

(b) We can see that the function is decreasing from approximately x = -2 to x = -0.5 and from approximately x = 3 to x = 4. So, the decreasing intervals are (-2, -0.5) and (3, 4)

(c) We can see that the function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)

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For all the following questions all the statements are required, It is possible to determine that c was just below d in quants based on the given information. Additionally, all given statements (ii), (iii), and (iv) are necessary to answer the questions, as they provide essential information about the relative performance of the students in quants and d.

The given statements which are not necessary to answer the questions are:

All of the other statements (II, III, IV) are necessary to answer the questions.

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Answer:

U=8

Step-by-step explanation:

48<5U+8

-5U<8-48

-5U<-40

-5U/-5<-40/+5

U>8

The greatest common factor of 12 and 30 is 6, which is >5 and GCF of 20 and 30 is 10, which is >5. The given pair of numbers are 12 and 30, 6 and 33, 15 and 20, 3 and 20, 25 and 30 and 20 and 30.

The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

Here,

GCF of 12 and 30 is 6, which is >5

GCF of 6 and 33 is 3, which is =3

GCF of 15 and 20 is 5, which is =5

GCF of 3 and 20 is 1, which is <3

GCF of 25 and 30 is 5, which is =5

GCF of 20 and 30 is 10, which is >5

The greatest common factor (GCF), also known as the greatest common divisor (GCD), is a mathematical concept used to find the largest number that divides two or more numbers without leaving a remainder. In other words, the GCF is the largest factor that two or more numbers have in common.

To find the GCF of two or more numbers, you can start by finding the factors of each number and identifying the largest factor that all the numbers share. For example, if you want to find the GCF of 12 and 18, you can list the factors of each number:

12: 1, 2, 3, 4, 6, 12

18: 1, 2, 3, 6, 9, 18

The largest factor that 12 and 18 share is 6, so the GCF of 12 and 18 is 6.

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Complete Question; -

The probability that exactly one-half have some college education is 0.0439 (rounded to four decimal places)

Step by step explanation: We can use the binomial probability distribution formula for this problem, where:p = probability of success (i.e., having some college education) = 0.53q = probability of failure (i.e., not having some college education) = 0.47n = number of trials (i.e., persons chosen at random) = 10x = number of successes (i.e., persons with some college education) = [tex]5P(x = 5) = C(10,5)p^5q^5[/tex] where [tex]C(n,r)[/tex] is the combination function that gives the number of ways to choose r items from a set of n items.

It is given by:[tex]C(n,r) = n! / (r!(n-r)!)[/tex] Thus, we can substitute the given values and compute:[tex]P(x = 5) = C(10,5)p^5q^5 = 252(0.53)^5(0.47)^5= 0.0439[/tex] (rounded to four decimal places)Therefore, the probability that exactly one-half have some college education is 0.0439.

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As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

A variable is a symbol or letter that is used to indicate a variable quantity in mathematics. The context or issue under consideration can alter the value of a variable. In order to express relationships between quantities, variables are frequently utilized in equations, formulae, and functions. For instance, x and y are variables in the equation y = mx + b, which depicts the linear relationship between x and y. Variables in statistics can reflect various traits or features of a population or sample, such as age, body mass index, or income.

given

To get the mean and variance of y, we can apply the characteristics of expected value and variance:

We can start by determining the expected value of y:

E[y] = 2E[x1] = E[2x1x2 + 3x1 + 2]

By the linearity of expectation, E[x2] + 3E[x1] + 2 is 2(10)(10) + 3(10) + 2 = 203.

Next, we may determine y's variance:

Var(y) = Var(3x1 + 2 + 2 + 3x1 ) = 4

Var(x1)

Var(x2) + 9

Var(x1) + Var(constant) = 4(5)(5) + 9(5) + 0 = 85 since x1 and x2 are independent.

As a result, y has a mean of 203 and a variance of 85 as let x1 and x2 be two independent random variables both with mean 10 and variance 5.

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We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).

To find the inverse of a module m using Euclid's algorithm, the steps are as follows:

1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.

2. Let a = GCD * s + m*t, where s is the inverse of a module m.

3. The GCD in terms of a and my is written as 1 = m-s*a.

4. Find s = -a, so the inverse of a module m is -a (or m+s).

For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).

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The volume of lemon juice in the glass is 0.38 cubic inches.

Explanation:

Given,

Let the volume of the lemonade in the glass be V cubic inches

Therefore, the volume of lemon juice in the lemonade is [tex]$\frac{1}{12}$[/tex] V cubic inches

Volume of water in the lemonade is [tex]$\frac{11}{12}$[/tex] V cubic inches

The volume of the cylindrical glass is given by:

[tex]$V_{\text{cylindrical glass}} = \pi r^2h$[/tex]

Here,

Radius r = 1 inch

Height h = 6 inches

[tex]$V_{\text{cylindrical glass}} = \pi r^2h = \pi (1)^2(6) = 6 \pi$[/tex]

Since the glass is half full of lemonade, the volume of lemonade in the glass is:

[tex]$V_{\text{lemonade}} = \frac{1}{2}V_{\text{cylindrical glass}} = \frac{1}{2} 6 \pi = 3\pi$[/tex]

The volume of lemon juice in the lemonade is given by:

[tex]$V_{\text{lemon juice}} = \frac{1}{12}V$[/tex]

Therefore

[tex]$V_{\text{lemon juice}} = \frac{1}{12}3\pi = \frac{1}{4}\pi = 0.7854$[/tex] cubic inches

Hence, the volume of lemon juice in the glass is 0.38 cubic inches (rounded to the nearest hundredth).

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It is 7.5

the steps are in the photo

In the fractions prompts given, the correct output are:

A fraction represents a part of a whole. It consists of a numerator and a denominator, with the numerator indicating the number of parts and the denominator indicating the total number of parts.

The calculations are given as follows;

1 )

= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]

= 1/8

2) (1/5) ÷ 2

= (1/5) x (1/2)

= 1/10

3)

(1/3) ÷ 5

= (1/3) x (1/5)

= 1/15

4) (1/4) ÷ 4

= (1/4) x (1/4)

= 1/16

5) One day, Amy baked a cake and wanted to divide it equally among 3 of her friends. She realized she only had half a cake left, so she decided to divide it into equal parts. Each friend received 1/6 of a cake. To check her calculation, she multiplied 1/6 by 3 and got 1/2. Thus, (1/2) ÷ 3 = 1/6, since dividing by 3 is the same as multiplying by 1/3.

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The first game brought in more money than the last game.

Any number of equal parts is represented by a fraction, which also symbolizes a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are when spoken in everyday English.

According to question:

The baseball team made more money at their first game because 6/7 is less than 1. This means that they made less money at their last game than at their first game. For example, if they made $100 at their first game, then they made 6/7 x $100 = $85.71 at their last game, which is less than $100.

Therefore, the first game brought in more money than the last game.

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Based on the information in the graph, it can be inferred that the false sentence is: The ball landed 11 feet from the person (option C).

To identify the false option we must read all the options and check them with the information in the graph:

According to the above, the correct answer to this question would be option C because the sentence is false with respect to the information in the graph.

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Answer: false

Step-by-step explanation:

Answer: 61

Step-by-step explanation:

explination in image

Answer:

3 packages

Step-by-step explanation:

61 - 20 * 2 (small grain sandpaper) = $21 remain. The largest grain costs $7, so 21/7 = 3 packages of the largest grain sandpaper was bought.

Hope this helped!

The value of sec A as required to be determined in the task content is; -√13 / 2.

As evident from the task content; it follows that the terminal ray of angle A, drawn in standard position, passes through the point (-4, -6).

Therefore, the length that the line from the origin to A has length;

L = √((-4)² + (-6)²)

L = √52.

On this note, it follows that the value of sec A which is represented by; hypothenuse/ adjacent is;

sec (A) = -√52 / 4

sec (A) = -√13 / 2.

Ultimately, the value of sec (A) as required is; -√13 / 2.

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Answer:

25 computers per hour

Step-by-step explanation:

look ate the point 2 hours corresponding to 50 computers

50/2 = 25/1 or 25 computers per hour

Answer:

x=1

Step-by-step explanation:

2.5+x=3.5

3.5-2.5=x

1=x

x=1

The null hypothesis is rejected whenever "there is a low probability that the obtained results could be due to random error." The correct answer is Option B.

The null hypothesis is a statistical hypothesis used to test the difference between two sample data groups. The null hypothesis is the hypothesis that the sample statistics are not significantly different. Any significant differences between the sample data are seen as supporting the alternative hypothesis.

A null hypothesis is often expressed as "no difference," "no correlation," or "no significant effect." For example, the null hypothesis for an experiment comparing two groups of people could be "there is no difference between the two groups." When the null hypothesis is rejected, it means that the results of the experiment are statistically significant, and the alternative hypothesis is supported.

Therefore, the null hypothesis is rejected whenever there is a low probability that the obtained results could be due to random error.

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Length of the median of the triangle is b. 18

How to find the length of the median of a triangle?
Given that the centroid of a triangle is located 12 units from one of the vertices of a triangle. We need to find the length of the median of the triangle drawn from that same vertex.

Let ABC be a triangle.

Let AD be median of the triangle.

Let E be centroid of ΔABC

Length of the median of triangle = AD

AD = Length of AE + Length of ED

But,

AE = 12

ED = x

So,

AD = 12 + x

Since, centroid divides median in 2:1 ratio.

Then,

[tex]12 : x = 2 : 1\\12/x = 2/1\\\\12= 2x\\[/tex]

Divide by 2 each side

[tex]x = 6[/tex]

So,  AD = 12 + x = 12 + 6 = 18

Thus, Length of the median of triangle is 18.

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Answer:

[tex]\large\boxed{\mathtt{C) \ 12x^{2}-5x-3}}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to multiply 2 Binomials.}[/tex]

[tex]\textsf{We should use the FOIL Method.}[/tex]

[tex]\large\underline{\textsf{FOIL Broken Down;}}[/tex]

[tex]\textsf{F - Fronts}[/tex]

[tex]\textsf{O - Outers}[/tex]

[tex]\textsf{I - Inners}[/tex]

[tex]\textsf{L - Last}[/tex]

[tex]\large\underline{\textsf{For Example.}}[/tex]

[tex]\mathtt{(2x+2y)(3x+3y)}[/tex]

[tex]\mathtt{(F) \ 2x \times 3x = 6x^{2}}[/tex]

[tex]\mathtt{(O) \ 2x \times 3y = 6xy}[/tex]

[tex]\mathtt{(I) \ 2y \times 3x = 6xy}[/tex]

[tex]\mathtt{(L) \ 2y \times 3y = 6y^{2}}[/tex]

[tex]\textsf{Let's use the FOIL Method for our problem.}[/tex]

[tex]\large\underline{\textsf{FOIL;}}[/tex]

[tex]\mathtt{(4x-3)(3x+1)}[/tex]

[tex]\mathtt{(F) \ 4x \times 3x = 12x^{2}}[/tex]

[tex]\mathtt{(O) \ 4x \times 1 = 4x}[/tex]

[tex]\mathtt{(I) \ -3 \times 3x = -9x}[/tex]

[tex]\mathtt{(L) \ -3 \times 1 = -3}[/tex]

[tex]\large\underline{\textsf{We should have;}}[/tex]

[tex]\mathtt{12x^{2}+4x-9x-3}[/tex]

[tex]\large\underline{\textsf{Combine Like Terms;}}[/tex]

[tex]\large\boxed{\mathtt{C) \ 12x^{2}-5x-3}}[/tex]

ANSWER

Jules paid $0.70 for one pencil

STEPS

Cost of One Pencil.

Let's assume the cost of one notebook be x and one pencil be y.

According to the given information,

Shanika bought 1 notebook and 5 pencils at a cost of $10.00. Therefore,

1x + 5y = 10 --- equation 1

Jules paid $14.90 for 1 Notebook and 12 pencils. Therefore,

1x + 12y = 14.9 --- equation 2

We need to find the cost of one pencil, i.e., y.

We can solve the above equations simultaneously to find the value of y.

Multiplying equation 1 by 12 and equation 2 by 5, we get:

12x + 60y = 120 --- equation 3

5x + 60y = 74.5 --- equation 4

Subtracting equation 4 from equation 3, we get:

7x = 45.5

x = 6.5

Substituting the value of x in equation 1, we get:

1(6.5) + 5y = 10

5y = 3.5

y = 0.7

Therefore, Jules paid $0.70 for one pencil.

ChatGPT

Answer:

Jules pay:

$0.7

Step-by-step explanation:

1n + 5p = 10                  Eq. 1

1n + 12p = 14.9              Eq. 2

n = cost of one notebook

p = cost of one pencil

From Eq. 1

n = 10 - 5p               Eq. 3

From Eq. 2

n = 14.9 - 12p            Eq. 4

Equalizing Eq. 3 and Eq. 4:

10 - 5p = 14.9 - 12p

12p - 5p = 14.9 - 10

7p = 4.9

p = 4.9 / 7

p = 0.7

From Eq. 3:

n = 10 - 5p

n = 10 - 5*0.7

n = 10 - 3.5

n = 6.5

Check:

From Eq. 2:

n + 12p = 14.9

6.5 + 12*0.7 = 14.9

6.5 + 8.4 = 14.9

Then:

1 pencil = $0.7

The solution to the logarithmic equation [tex]2log12(-8x) = 6[/tex] is [tex]x = -9/32[/tex] .

What are logarithmic properties ?

Logarithmic properties are the rules that govern the behavior of logarithmic functions. These properties are important in simplifying logarithmic expressions and solving logarithmic equations. Some of the commonly used logarithmic properties include:

Product property: [tex]logb(xy) = logb(x) + logb(y)[/tex]

This property allows us to simplify the logarithm of a product of two numbers into the sum of logarithms of the individual numbers.

Quotient property: [tex]logb(x/y) = logb(x) - logb(y)[/tex]

This property allows us to simplify the logarithm of a quotient of two numbers into the difference of logarithms of the individual numbers.

Power property:[tex]logb(x^y) = ylogb(x)[/tex]

This property allows us to simplify the logarithm of a power of a number by bringing the exponent outside of the logarithm and multiplying it with the logarithm of the base.

Change of base formula: [tex]logb(x) = logc(x) / logc(b)[/tex]

This property allows us to change the base of a logarithm by dividing the logarithm of the number by the logarithm of the base in a different base.

Solving the given logarithmic equation :

The equation can be solved by using logarithmic properties and basic algebraic manipulation.

We can begin by using the property that states [tex]loga(b^n) = nloga(b)[/tex] for any base a and any positive real number b. Applying this property, we can rewrite the left side of the equation as:

[tex]log12((-8x)^2) = log12(64x^2)[/tex]

Next, we can use the property that states [tex]loga(b) = c[/tex] is equivalent to [tex]a^c = b[/tex]. Applying this property, we can rewrite the equation as:

[tex]12^{2log12(64x^2)} = 12^6[/tex]

Simplifying the left side, we get:

[tex]64x^2 = 12^6 / 12^2[/tex]

[tex]64x^2 = 144[/tex]

Dividing both sides by 64, we get:

[tex]x^2 = 144/64[/tex]

[tex]x^2 = 9/4[/tex]

Taking the square root of both sides, we get:

[tex]x=\pm 3/2[/tex]

However, we need to check the solutions for extraneous roots since the original equation has a logarithm with a negative argument. We can see that the solution x = 3/2 is extraneous since it results in a negative argument for the logarithm. Therefore, the only valid solution is x = -9/32.

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