I need help with math work!!

Answer:

  $16,479

Step-by-step explanation:

The table tells you Ed's tax is ...

  14,138.50 + 0.31×(70,000 -62,450) = 16,479 . . . . dollars

ANSWER

Extraneous solution: x=6

Real solution: x=11

EXPLANATION

The given expression is

[tex] \sqrt{x - 2} + 8 = x[/tex]

Add -8 to both sides:

[tex]\sqrt{x - 2} + 8 + - 8= x + - 8[/tex]

[tex] \implies\sqrt{x - 2} = x - 8[/tex]

Square both sides.

[tex]\implies(\sqrt{x - 2} )^{2} =( x - 8)^{2} [/tex]

[tex]x - 2=( x - 8)^{2} [/tex]

We expand the to get

[tex]x - 2 = {x}^{2} - 16x + 64[/tex]

Write in standard quadratic form.

[tex] {x}^{2} - 16x - x + 64 + 2 = 0[/tex]

[tex] {x}^{2} - 17x + 66 = 0[/tex]

Factor to get:

[tex](x - 6)(x - 11) = 0[/tex]

[tex]x = 6 \: or \: \: x = 11[/tex]

We check for extraneous solutions by substituting each value of x into the original equation.

When x=6

[tex]\sqrt{6 - 2} + 8 = 6[/tex]

[tex]\sqrt{4} + 8 =6[/tex]

[tex]2 + 8 = 10 \ne8[/tex]

Hence x=6 is an extraneous solution.

When x=11

[tex]\sqrt{11- 2} + 8 = 11[/tex]

[tex]\sqrt{9} + 8 = 11[/tex]

[tex]3 + 8 = 11[/tex]

This statement is true.

Hence x=11 is the only solution.

Answer:

5 units

Step-by-step explanation:

This is a circle with a center of (0, 0).  The square root of 25 represents the radius of the circle which is 5.  The radius represents the distance that the outside of the circle is from the center.

Answer: The mean and the standard error of the distribution of the sample mean are 200 and 2.

Step-by-step explanation:

Given: Sample size : n= 81

Mean of infinite population : [tex]\mu=200[/tex]

We know that the mean of the distribution of the sample mean is same as the mean of the population.

i.e. [tex]\mu_x=\mu=200[/tex]

The standard error of the distribution of the sample mean is given by :-

[tex]S.E.=\dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\Rightarrow\ S.E.=\dfrac{18}{\sqrt{81}}=\dfrac{18}{9}=2[/tex]

Hence, the mean and the standard error of the distribution of the sample mean are 200 and 2.

The mean of the sample mean distribution for a random sample of size 81 from a population with a mean of 200 and a standard deviation of 18 is 200, and the standard error is 2.

The question is about determining the mean and the standard error of the distribution of the sample mean. According to the Central Limit Theorem, regardless of the distribution of the original population, the distribution of the sample mean tends to form a normal distribution as the sample size increases. In this case, the mean of the sample mean distribution is the same as the population mean, which is 200.

The standard error of the mean is calculated as the population standard deviation divided by the square root of the sample size. So, the standard error in this scenario would be 18/√81 = 2.

Therefore, in a random sample of size 81 taken from an infinite population with a mean of 200 and a standard deviation of 18, the mean of the sample mean distribution is 200, and the standard error is 2.

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Answer:

C. 106

Step-by-step explanation:

Angles 2 and 6 are corresponding angles so they're both 74. So you just subtract 74 from 180 to get 106.

Answer:

C. 106 is the answer

Step-by-step explanation:

angle 3 = angle 2 (vertically opp. angle)

angle 3+ angle 5 = 180

74+ angle 5 = 180

angle 5 = 106

Answer:

D. Incomplete randomization

Step-by-step explanation:

Answer:

  1763 ft²

Step-by-step explanation:

Using the given conversion factor, ...

  (164 m²)(1 ft/(.305 m))² = 165/.093025 ft² ≈ 1763 ft²

_____

The exact conversion factor is 1/0.3048, so the area is closer to 1765 ft². For a 4-significant digit answer, you need to use a conversion factor accurate to 4 significant digits.

To convert square meters to square feet, you must square the feet to meter conversion factor, resulting in approximately 10.764 sq ft/sq m. You then multiply this by the square meter measurement to get the equivalent in square feet. Therefore, the house's area, which was provided as 164 square meters, translates to approximately 1765.736 square feet.

The measure of the area in square feet can be derived using the conversion factor for feet to meters, 1 ft = 0.305 m. However, when you deal with areas, you must square the conversion factor. We then apply the conversion factor to the known area in reference, which in our case is 164 square meters.

So our conversion factor becomes (1/0.305)² sq ft/sq m = 10.764 sq ft/sq m.

To use the conversion factor, we multiply it by the metric unit measurement, like this: 164 m²*(10.764 ft²/m²) = 1765.736 square feet.

So, the house's area is approximately 1765.736 square feet.

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b. An increase in expected inflation, combined with a constant real risk-free rate and a constant market risk premium, would lead to identical increases in the required returns on a riskless asset and on an average stock, other things held constant.

Hope this helps :)

Final answer:

To solve the problem, use the system of inequalities: x + y ≥ 0, x ≥ 0, y ≥ 0, 6x + 6y ≥ 60, and x + y ≤ 12.

Explanation:

To solve the given real-world problem, the system of inequalities you would use is:

These inequalities represent the conditions that need to be met: x and y (representing the number of hours worked as a cashier and as a babysitter, respectively) must be greater than or equal to 0, and the total income from both jobs (6x + 6y) must be greater than or equal to $60, and the total number of hours worked (x + y) must be less than or equal to 12.

Let assume that [tex]\sqrt3[/tex] is rational. Therefore we can express it as [tex]\dfrac{a}{b}[/tex] where [tex]a,b\in \mathbb{Z}[/tex] and [tex]\text{gcd}(a,b)=1[/tex].

[tex]\dfrac{a}{b}=\sqrt3\\\dfrac{a^2}{b^2}=3\\a^2=3b^2[/tex]

It means that [tex]3|a^2[/tex] and so also [tex]3|a[/tex].

Therefore [tex]a=3k[/tex] where [tex]k\in\mathbb{Z}[/tex].

[tex](3k)^2=3b^2\\9k^2=3b^2\\b^2=3k^2[/tex]

It means that [tex]3|b^2[/tex] and so also [tex]3|b[/tex].

If both [tex]a[/tex] and [tex]b[/tex] are divisible by 3, then it contradicts our initial assumption that [tex]\text{gcd}(a,b)=1[/tex]. Therefore [tex]\sqrt3[/tex] must be an irrational number.

The solution to the system of equations is [tex]\(x = -1\) and \(y = 2\)[/tex].

To solve the system of equations:

[tex]\[ \begin{cases} -5x + 2y = 9 \\ 3x + 5y = 7 \end{cases} \][/tex]

We can use either the substitution method or the elimination method. Let's use the elimination method here.

First, let's rewrite the equations in standard form:

Equation 1: [tex]\( -5x + 2y = 9 \)[/tex]

Equation 2: [tex]\( 3x + 5y = 7 \)[/tex]

To eliminate one of the variables, let's multiply Equation 1 by 3 and Equation 2 by 5 to make the coefficients of x the same:

[tex]\[ \begin{cases} -15x + 6y = 27 \\ 15x + 25y = 35 \end{cases} \][/tex]

Now, let's add the two equations:

[tex]\[ (-15x + 6y) + (15x + 25y) = 27 + 35 \]\[ -15x + 6y + 15x + 25y = 62 \]\[ 31y = 62 \][/tex]

Now, let's solve for y:

[tex]\[ y = \frac{62}{31} \][/tex]

y=2

Now that we have found the value of y, let's substitute it back into one of the original equations to find x. Let's use Equation 1:

[tex]\[ -5x + 2(2) = 9 \]\[ -5x + 4 = 9 \]\[ -5x = 9 - 4 \]\[ -5x = 5 \]\[ x = \frac{5}{-5} \][/tex]

[tex]\[ x = -1 \][/tex]

Complete question: Find the solution of the following system of equations

-5x+2y=9

3x+5y=7

\[ x = -\frac{28}{3} \] and \( y = 7 \) are the solutions to the system of equations.

To solve the system of equations:

1. -5 + 2y = 9

2. 3x + 5y = 7

We can start by solving equation 1 for [tex]\( y \):[/tex]

[tex]\[ -5 + 2y = 9 \][/tex]

Add 5 to both sides:

[tex]\[ 2y = 9 + 5 \]\[ 2y = 14 \][/tex]

Divide both sides by 2:

[tex]\[ y = \frac{14}{2} \]\[ y = 7 \][/tex]

Now that we have the value of [tex]\( y \)[/tex], we can substitute it into equation 2 and solve for [tex]\( x \):[/tex]

[tex]\[ 3x + 5(7) = 7 \]\[ 3x + 35 = 7 \][/tex]

Subtract 35 from both sides:

[tex]\[ 3x = 7 - 35 \]\[ 3x = -28 \][/tex]

Divide both sides by 3:

[tex]\[ x = \frac{-28}{3} \][/tex]

So, the solution to the system of equations is [tex]\( x = -\frac{28}{3} \) and \( y = 7 \).[/tex]

Answer:

(a)Two lines parallel to a third line are parallel.

(c) Two planes parallel to a third plane are parallel.

(f) Two lines perpendicular to a plane are parallel.

(h) Two planes perpendicular to a line are parallel.

(i) Two planes either intersect or are parallel.

(k) A plane and a line either intersect or are parallel

Step-by-step explanation:

(b) Two lines perpendicular to a third line are parallel. -- No. The y-, and z-axes are perpendicular to the x-axis, but are not parallel.

(d) Two planes perpendicular to a third plane are parallel. -- No. The x-y and y-z coordinate planes are both perpendicular to the x-z coordinate plane, but are at right angles to each other.

(e) Two lines parallel to a plane are parallel. -- No. Two intersecting lines in the plane z=0 are both parallel to the plane z=1, but are not parallel to each other.

(g) Two planes parallel to a line are parallel. -- No. Both the x-z plane and the y-z plane are parallel to the line (x, y, z) = (1, 1, z), but those coordinate planes are perpendicular to each other.

(j) Two lines either intersect or are parallel. -- No. The lines may be skew, running different directions in parallel panes.

Final answer:

The student's inquiry into the truth of various geometric statements has been addressed, confirming the true relationships and correcting the false ones, based on the principles of Euclidean geometry which govern lines and planes.

Explanation:

When it comes to geometry in the context of Euclidean space, which is the setting for high school mathematics, the rules governing the behavior of lines and planes can be understood through the principles of parallel and perpendicular relationships. Now, let's assess each of the statements given by the student:

These principles form the basis for understanding the complex relations of geometric shapes and objects which are important for most geometrical problems and real-world applications.

Answer:

A

Step-by-step explanation:

Volume varies directly with the square of the radius, so:

V = k r²

When V = 80, r = 4.

80 = k (4)²

k = 5

V = 5r²

When r = 3:

V = 5 (3)²

V = 45

The flow is 45 L/min.

Answer: 0.2420

Step-by-step explanation:

Given: Mean : [tex]\mu = 250 \text{ feet}[/tex]

Standard deviation : [tex]\sigma =50\text{ inch}[/tex]

Sample size : [tex]n=49[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x= 245

[tex]z=\dfrac{245-250}{\dfrac{50}{\sqrt{49}}}=-0.7[/tex]

The P Value =[tex]P(Z<245)=P(z<-0.7)=0.2419637\approx0.2420[/tex]

Hence, the probability that the 49 touchdowns traveled an average of less than 245 feet= 0.2420

The probability that the 49 touchdowns traveled an average of less than 245 feet is approximately 0.2438, or 24.38%.

Step 1:

To find the probability that the 49 touchdowns traveled an average of less than 245 feet, we can use the Central Limit Theorem (CLT) since we have a large enough sample size (49) to assume that the sample mean follows a normal distribution.

The CLT states that the distribution of sample means of a sufficiently large sample size will be approximately normal, regardless of the distribution of the original population, as long as the sample size is large enough.

Given:

- Population mean mu = 250 feet

- Population standard deviation [tex](\( \sigma \))[/tex] = 50 feet

- Sample size n = 49

Step 2:

The standard error of the sample mean SE is given by:

[tex]\[SE = \frac{\sigma}{\sqrt{n}}\][/tex]

Substituting the given values:

[tex]\[SE = \frac{50}{\sqrt{49}} = \frac{50}{7} \approx 7.14\][/tex]

Step 3:

Now, we can calculate the z-score for the sample mean of 245 feet using the formula:

[tex]\[z = \frac{\bar{x} - \mu}{SE}\][/tex]

Where:

- [tex]\( \bar{x} \)[/tex] is the sample mean

- [tex]\( \mu \)[/tex] is the population mean

- [tex]\( SE \)[/tex] is the standard error of the sample mean

Step 4:

Substituting the given values:

[tex]\[z = \frac{245 - 250}{7.14} \approx -0.6993\][/tex]

Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to this z-score.

The probability that the sample mean is less than 245 feet can be found by finding the area to the left of the z-score on the standard normal distribution curve.

From the standard normal distribution table, we find that the probability corresponding to a z-score of -0.6993 is approximately 0.2438.

Therefore, the probability that the 49 touchdowns travelled an average of less than 245 feet is approximately 0.2438, or 24.38%.

The probability that exactly one customer dines on the first floor is:

                     0.26337  

We need to use the binomial theorem to find the probability.

The probability of k success in n experiments is given by:

       [tex]P(X=k)=n_C_k\cdot p^k\cdot (1-p)^{n-k}[/tex]

where p is the probability of success.

Here p=1/3

( It represents the probability of choosing first floor)

k=1 ( since only one customer has to chose first floor)

n=6 since there are a total of 6 customers.

This means that:

[tex]P(X=1)=6_C_1\times (\dfrac{1}{3})^1\times (1-\dfrac{1}{3})^{6-1}\\\\\\P(X=1)=6\times (\dfrac{1}{3})\times (\dfrac{2}{3})^5\\\\\\P(X=1)=0.26337[/tex]

Using the binomial distribution, it is found that there is a 0.2634 = 26.34% probability that exactly one customer dines on the first floor.

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

For each customer, there are only two possible outcomes, either they dine on the first floor, or they do not. The probability of a customer dining on the first floor is independent of any other customer, which means that the binomial probability distribution is used to solve this question.

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

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of a success on a single trial.

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

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

The probability that exactly one customer dines on the first floor is P(X = 1), thus:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{6,1}.(0.3333)^{1}.(0.6667)^{5} = 0.2634[/tex]

0.2634 = 26.34% probability that exactly one customer dines on the first floor.

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Answer:

3/5

Step-by-step explanation:

Total tossed : 30

# of times landed on tails : 18

Experimental probability of tails = 18/30 = 3/5

Answer:

i cant see the picture

Step-by-step explanation:

Answer:

10,000

Step-by-step explanation:

With a bike lock, you can usually use the same number more than one... you can have them the same (7777) if you want.

So, you have 10 possibilities for the first digit, 10 again for the second digit, 10 for the third digit... and also 10 for the last digit.  So...

10 * 10 * 10 * 10 = 10,000

These combinations range from 0000 to 9999

Final answer:

The total number of possible combinations for a 4-digit bike lock with each digit ranging from 0-9 is 10,000, as determined by the fundamental counting principle and calculated by multiplying 10 choices for each digit.

Explanation:

To find the total number of possible combinations for a 4-digit bike lock where each digit can range from 0-9, you apply the fundamental counting principle. This principle states that if there are n ways to perform one task and m ways to perform another task, then there are n × m ways to perform both tasks in sequence.

For the bike lock, each of the 4 digits can be chosen in 10 ways (0 through 9). Since the choice of each digit is independent of the others, you multiply the number of choices for each digit together:

Therefore, the total number of combinations is 10 × 10 × 10 × 10 = 10,000.

Answer:

The probability of the sample mean foot length less than 23 cm is 0.120

Step-by-step explanation:

* Lets explain the information in the problem

- The eighth-graders asked to measure the length of their right foot at

  the beginning of the school year, as part of a science project

- The foot length is approximately Normally distributed, with a mean of

 23.4 cm

∴ μ = 23.4 cm

- The standard deviation of 1.7

∴ σ = 1.7 cm

- 25 eighth-graders from this population are randomly selected

∴ n  = 25

- To find the probability of the sample mean foot length less than 23

∴ The sample mean x = 23, find the standard deviation σx

- The rule to find σx is σx = σ/√n

∵ σ = 1.7 and n = 25

∴ σx = 1.7/√25 = 1.7/5 = 0.34

- Now lets find the z-score using the rule z-score = (x - μ)/σx

∵ x = 23 , μ = 23.4 , σx = 0.34

∴ z-score = (23 - 23.4)/0.34 = -1.17647 ≅ -1.18

- Use the table of the normal distribution to find P(x < 23)

- We will search in the raw of -1.1 and look to the column of 0.08

∴ P(X < 23) = 0.119 ≅ 0.120

* The probability of the sample mean foot length less than 23 cm is 0.120

Answer: the answer to this question is B

Step-by-step explanation: Hope This Helps

Formula to find the margin of error :

[tex]E=z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where n= sample size  , [tex]\hat{p}[/tex] is the sample proportion and z*= critical z-value.

Let p be the proportion of 19-year-olds had a driver’s license.

A) As per given , In 1983

[tex]\hat{p}=0.87[/tex]

n=  1200

Critical value for 95% confidence level is 1.96 (By z-table)

So ,Margin of error : [tex]E=(1.96)\sqrt{\dfrac{0.87(1-0.87)}{1200}}\approx0.019[/tex]

Interval : [tex](\hat{p}-E , \ \hat{p}+E)=(0.87-0.019 ,\ 0.87+0.019)[/tex]

[tex]=(0.851,\ 0.889)[/tex]

B) In 2008 ,

[tex]\hat{p}=0.75[/tex]

Margin of error :    [tex]E=(1.96)\sqrt{\dfrac{0.75(1-0.75)}{1200}}\approx0.0245[/tex]

Interval : [tex](\hat{p}-E, \hat{p}+E)=(0.75-0.0245,\ 0.75+0.0245)[/tex]

[tex]=(0.7255,\ 0.7745)[/tex]

c. The margin of error is not the same in parts (a) and (b) because the sample proportion of 19-year-olds had a driver’s license are not same in both parts.

Answer:

  175

Step-by-step explanation:

The rate of change of the goose population is a function of the population:

  G'(x) = (x/5)(350 -x)

This function describes a downward-opening parabola with zeros at x=0 and x=350. The value of x halfway between these zeros, at x = 175, is where the maximum value of G'(x), hence the maximum rate of change, is located.

The goose population is increasing most rapidly when it is 175.

Answer:

b. (-1,3)

Step-by-step explanation:

the  image of the point (x ; y)  by symmetry about x-axis is : ( x ;-  y)

so the answer "b" : (-1,3)

Answer: (a) 0.37

Step-by-step explanation:

Given: The speed of cars on a stretch of road is normally distributed with an average 48 miles per hour with a standard deviation of 5.9 miles per hour.

i.e. Mean : [tex]\mu = 48\text{ miles per hour} [/tex]

Standard deviation : [tex]\sigma = 5.9\text{ miles per hour}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For the probability that a randomly selected car is violating the speed limit of 50 miles per hour (X≥ 50).

For x= 80

[tex]z=\dfrac{50-48}{5.9}=0.338983050847\approx0.34[/tex]

The P Value =[tex]P(z>0.34)=1-P(z<0.34)=1-0.6330717\approx0.3669283\approx0.37[/tex]

Hence,  the probability that a randomly selected car is violating the speed limit of 50 miles per hour =0.37

Answer:

[tex]F(x)=(x-11)(x-3)[/tex]

Step-by-step explanation:

we have

[tex]F(x)=x^{2} -14x+33[/tex]

Find the zeros of the function

F(x)=0

[tex]0=x^{2} -14x+33[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]-33=x^{2} -14x[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]-33+49=x^{2} -14x+49[/tex]

[tex]16=x^{2} -14x+49[/tex]

Rewrite as perfect squares

[tex]16=(x-7)^{2}[/tex]

square root both sides

[tex](x-7)=(+/-)4[/tex]

[tex]x=(+/-)4+7[/tex]

[tex]x=(+)4+7=11[/tex]

[tex]x=(-)4+7=3[/tex]

so

The factors are

(x-11) and (x-3)

therefore

[tex]F(x)=(x-11)(x-3)[/tex]

Answer: 0.1093

Step-by-step explanation:

Given: Mean : [tex]\mu=93[/tex]

Standard deviation : [tex]\sigma = 22[/tex]

Sample size : [tex]n=30[/tex]

The formula to calculate z-score is given by :_

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x= 97.95, we have

[tex]z=\dfrac{97.95-93}{\dfrac{22}{\sqrt{30}}}\approx1.23[/tex]

The P-value = [tex]P(z>1.23)=1-P(z<1.23)=1-0.8906514=0.1093486\approx0.1093[/tex]

Hence, the  probability that the sample mean would be greater than 97.95 WPM =0.1093

The functions F(x) and G(x) are not inverses of each other.

The correct answer is B. No, because the functions contain different operations.

Given are composition of functions, F(x) = √(x) -6G(x) = (x+6)²

We need to determine if the two functions are inverses of each other.

To determine if the functions F(x) = √(x) - 6 and G(x) = (x + 6)² are inverses of each other using composition of functions, we need to check if their compositions result in the identity function.

Let's calculate the composition:

F(G(x)) = F((x + 6)²) = √((x + 6)²) - 6 = |x + 6| - 6

Now, let's calculate the composition in the reverse order:

G(F(x)) = G(√(x) - 6) = (√(x) - 6 + 6)² = (√(x))² = x

Since F(G(x)) = |x + 6| - 6 and G(F(x)) = x, we can see that they are not equal for all values of x.

Therefore, the functions F(x) and G(x) are not inverses of each other.

The correct answer is B. No, because the functions contain different operations.

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Two functions are inverses if both (f o g)(x) and (g o f)(x) are equal to x. If they are, their composition will yield x, indicating that the two functions are indeed inverses.

To determine if two functions are inverses of each other using composition of functions, you should perform the operation (f o g)(x) and (g o f)(x). If f and g are inverse functions, both of these compositions will yield x.

Let's take the example of functions f(x) = 2x + 3 and g(x) = (x - 3) / 2. To check if they are inverses:

Since both (f o g)(x) and (g o f)(x) equals x, so f(x) and g(x) are inverses of each other.

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Answer:

Step-by-step explanation:

The 2 numbers that are not in the domain of the function are the 2 numbers that cause the denominator of the function to equal 0.  In order to find those 2 numbers, we have to factor the quadratic that is in the denominator. When you factor, you get x = 2.79 and x = -1.79

Those are the values of x that cause the denominator to equal 0, which of course is NEVER allowed in math!