a student concluded that the solution to the equation startroot 2x+1 endroot +3=0 is x=4 do you agree? explain why or why not.

Answer:

10 yrs old and 35 yrs old

Step-by-step explanation:

I figured it out by trial and error but here's the thinking process.

10 + 35= 45

Son becomes dad's age so 35-10=25, so plus 25 year to each age.

10+25=35

35+25= 60

35+60=95

I hope that makes enough sense!

For the given trigonometric function sin(x/3) = -√3/2 , all the solution for the given interval  [ 0,2π) is given by (x/3) = 4π/3 , 5π/3.

As given in the question,

Given trigonometric function is :

sin(x/3) = -√3/2

sin(x/3) = sin (-π/3)

⇒ x/3 = -π/3

But the interval is given [ 0, 2π)

So valid solution is given by:

π + (π/3) lies in the interval [0,2π)

sin(x/3) = sin (π+π/3)

⇒x/3 = 4π/3

2π -(π/3) lies in the interval [0,2π)

sin(x/3) = sin (2π-π/3)

⇒x/3 = 5π/3

Therefore, for the given trigonometric function sin(x/3) = -√3/2 , all the solution for the given interval  [ 0,2π) is given by (x/3) = 4π/3 , 5π/3.

Learn more about interval here

brainly.com/question/14264237

#SPJ1

Answer:

20/27

Step-by-step explanation:

Answer:

5 would be the answer.

Step-by-step explanation:

13 divided by 3(weeks) = 4.3

4.3 x 5 = 21.

= 5.

By showing that the corresponding sides are not proportional we know that the Triangles △fgh and △jih are not similar.

To prove that triangles △fgh and △jih are not similar, we need to show that at least one pair of corresponding sides is not proportional.
Let's compare the side lengths:

Side fg does not have a corresponding side in △jih.
Side gh in △fgh corresponds to side hi in △jih.
Side fh in △fgh corresponds to side ij in △jih.

By comparing the side lengths, we can see that side gh/hj and side fh/ij are not proportional.

Therefore, triangles △fgh and △jih are not similar.

Know more about Triangles  here:

https://brainly.com/question/1058720

#SPJ11

Triangle FGH (△FGH) is not similar to triangle JIH (△JIH) because their corresponding angles are not congruent and their corresponding sides are not proportional.

To prove that triangle FGH (△FGH) is not similar to triangle JIH (△JIH), we need to show that their corresponding angles and corresponding sides are not proportional.

1. Corresponding angles: In similar triangles, corresponding angles are congruent. If we compare the angles of △FGH and △JIH, we find that angle F in △FGH corresponds to angle J in △JIH, angle G corresponds to angle I, and angle H corresponds to angle H. Since the corresponding angles in both triangles are not congruent, we can conclude that the triangles are not similar.

2. Corresponding sides: In similar triangles, corresponding sides are proportional. Let's compare the sides of △FGH and △JIH. Side FG corresponds to side JI, side GH corresponds to side IH, and side FH corresponds to side HJ. If we measure the lengths of these sides, we can see that they are not proportional. Therefore, the triangles are not similar.

Learn more about corresponding angles :

https://brainly.com/question/28175118

#SPJ11

Answer:

x=4

Step-by-step explanation:

on edge

The extraneous solution to the logarithmic equation log₇(3x²+x)-log₇x=2 is x=16

When you raise a number with an exponent, there comes a result.

Lets say you get\(a^b = c\)

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

\(b = \log_a(c)\)

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We are given the function as;

log₇(3x²+x)-log₇x=2

Domian: 3x²+x>0

x(3x+1)>0

x∈(-∞,-1/3)U(0,∞)

Hence, x∈(0,∞), Thus x∈(0,∞)

In this problem we use the following formula:

 \(\boxed {log_ax-log_ay=log_a\frac{x}{y}}\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\x=16\)

Learn more about logarithm here:

https://brainly.com/question/20835449

#SPJ7

Answer:

x = 6

Step-by-step explanation:

we both know you dont wanna know how you just want the answer

The statement means that when adding or subtracting polynomials, the result is always another polynomial. For example, adding \(2x^2 + 3x - 5\)and \(x^2 - 2x + 1\) yields \(3x^2 + x - 4,\) which is a polynomial. Similarly, subtracting these polynomials gives \(x^2 + 5x - 4\), also a polynomial.

The statement "Polynomials are closed under the operations of addition and subtraction" means that when we add or subtract two polynomials, the result is always another polynomial. In other words, the sum or difference of two polynomials will still be a polynomial.

An addition example:

Let's consider two polynomials:

p(x) =\(2x^2 + 3x - 5\)

q(x) = \(x^2 - 2x + 1\)

To add these two polynomials, we simply combine like terms:

p(x) + q(x) = \((2x^2 + x^2) + (3x - 2x) + (-5 + 1)\)

= \(3x^2 + x - 4\)

The result, \(3x^2 + x - 4\), is also a polynomial.

A subtraction example:

Using the same polynomials, p(x) and q(x), we can subtract them:

p(x) - q(x) =\((2x^2 - x^2) + (3x - (-2x)) + (-5 - 1)\)

= \(x^2 + 5x - 4\)

Again, the result,\(x^2 + 5x - 4\), is a polynomial.

In both examples, the addition and subtraction of polynomials resulted in another polynomial, demonstrating that polynomials are closed under these operations.

for such more question on polynomial

https://brainly.com/question/7297047

#SPJ11

We can do this by halving the coefficient of the x-term (-34/2 = -17) and squaring it to get the constant term (17^2 = 289). Thus, the constant term needed to complete the square is k = 289 - 10 = 279.

To complete the square of the quadratic equation x^2 - 34x + k = 10, we need to find the constant term that will make the quadratic a perfect square trinomial. Therefore, the answer is not listed in the given options. We can verify this by completing the square and writing the equation in vertex form: (x - 17)^2 = 289 - 10, which simplifies to (x - 17)^2 = 279. Thus, the constant term that should be used to complete the square is 279.

To know more about Constant visit:

https://brainly.com/question/17550734

#SPJ11

Answer:

(14, - 3 )

Step-by-step explanation:

Under the translation < 6, 0 >

Add 6 to the x- coordinate and 0 to the y- coordinate, that is

B(8, - 3 ) → B'(8 + 6, - 3 + 0 ) → B'(14, - 3 )

The following can be shown about the diagonals of parallelogram PQRS to compare the proof that diagonals of a parallelogram bisect each other: B. PR and SQ have the same midpoint.

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel opposite sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:

(Line segment PR)/2 = (Line segment SQ)/2

Line segment PR = Line segment SQ

Read more on a parallelogram here: brainly.com/question/31416609

#SPJ1

Answer:

29.87 metros cuadrados

Step-by-step explanation:

Dados los siguientes datos;

Área de tierra = 35.72 yardas cuadradas

Para encontrar el área del terreno en metros cuadrados;

Para hacer esto, tendríamos que convertir el valor en yardas cuadradas a metros cuadrados.

Conversión:

1 yarda cuadrada = 0.8361 metros cuadrados

35.72 yardas cuadradas = X metros cuadrados

Multiplicación cruzada, tenemos;

X = 35.72 * 0.8361

X = 29.87 metros cuadrados

Por lo tanto, el área del terreno en metros cuadrados es 29,87.

Answer:

SO THE VALUE OF FG IS 13

Step-by-step explanation:

we can find FG by subtracting EF FROM EG

FG=EG-EF

FG=25-12

FG=13

I HOPE IT WILL HELP YOU :)

Answer:

\(given \\ EG = 25 \\ EF = 12 \\ FG=? = \\ EF+ FG= EG\\ or \: 12 + FG= 25 \\ or \: FG = 25 - 12 \\ FG = 13\)

hope this helps..

Good luck on your assignment...

The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

Learn more about harvest here:

brainly.com/question/16953777

#SPJ11

The solution to the initial value problem y'=2y^2, y(0)=y0 will have a vertical asymptote at t=3 and a t-interval of existence\((-∞, 3)\) for y0 = -1/6.

To find the solution of the initial value problem\(y'=2y^2, y(0)=y0\), we can use separation of variables and integrate both sides to get:

\(∫1/y^2 dy = ∫2 dt\)

This simplifies to:

\(-y^-1 = 2t + C\)
Where C is the constant of integration. Solving for y, we get:

y = -1/(2t + C)

To find the value(s) of y0 that will result in a vertical asymptote at t=3, we need to set C=6. This is because the denominator of y becomes 0 when 2t + C = 0, or when t = -C/2. Therefore, we want t=3 to be equal to -C/2, or C=-6.

Substituting C=-6 into our expression for y, we get:

y = -1/(2t - 6)

This function has a vertical asymptote at t=3, since the denominator becomes 0 when 2t - 6 = 0, or when t=3.

To find the interval of existence of this solution, we need to check when the denominator of y becomes 0 again. This happens when 2t - 6 = 0, or when t=3. Therefore, the interval of existence of the solution is (-∞, 3) or t < 3.

In summary, the solution to the initial value problem \(y'=2y^2, y(0)=y0\) will have a vertical asymptote at t=3 and a t-interval of existence \((-∞, 3)\) for y0 = -1/6.

To learn more about asymptote, refer below:

https://brainly.com/question/4084552

#SPJ11

Answer:

31.4

Step-by-step explanation:

Answer:

523.33 cubic inches

Step-by-step explanation:

the probability that 50 or more requests are made for pop songs is  0.0967, or about 9.67%.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

We can use the binomial distribution to model this situation, where the number of trials is 120 (the number of people at the party), and the probability of success (making a request for a pop song) is 0.37. Let X be the number of requests for pop songs. Then:

The mean of X is μ = np = 120 x 0.37 = 44.4

The standard deviation of X is σ = sqrt(np(1-p)) = sqrt(120 x 0.37 x 0.63) = 4.32

To find the probability that 50 or more requests are made for pop songs, we can use the normal approximation to the binomial distribution, which applies when np >= 10 and n(1-p) >= 10.

Let Z be a standard normal random variable, then:

P(X >= 50) = P((X - μ)/σ >= (50 - μ)/σ)

= P(Z >= (50 - 44.4)/4.32)

= P(Z >= 1.2963)

= 1 - P(Z < 1.2963)

= 1 - 0.9033

= 0.0967

Therefore, the probability that 50 or more requests are made for pop songs is approximately 0.0967, or about 9.67%.

To know more about variables, visit:

https://brainly.com/question/17344045

#SPJ1

If the city worker released the statement that 60% of dairy city's 3,000 homes are in violation of city codes , then the City Worker's statement is an example of : (d) Statistical Inference .

The Statistical Inference involves making generalizations about a population based on a sample.

In this case, the city worker has taken a sample of 200 homes out of the total 3,000 homes in Dairy City, and based on that sample, the City Worker is making an inference about the proportion of homes in violation of city codes for the entire population of Dairy City.

The statement is not a census as a census would involve collecting data from every single unit in the population, in this case every single home in Dairy City.

The given question is incomplete , the complete question is

A city worker inspected 200 homes in dairy city. during that inspection, 120 homes were found to violate one or more city codes. the city worker released a statement that 60% of dairy city's 3,000 homes are in violation of city codes.

The City Worker's statement is an example of :

(a) Census

(b) An experiment

(c) Descriptive Statistics

(d) Statistical Inference

Learn more about Statistical Inference here

https://brainly.com/question/13752289

#SPJ4

(a) Since S is nonempty and bounded below, then B, the set of lower bounds of S, is also nonempty.

(b) To prove that sup(B) is a lower bound of S, we can use the fact that sup(B) is the smallest upper bound of B.

(c) Finally, we can conclude that sup(B) is the greatest lower bound of S (i.e. sup(B)=inf(S)) because for any lower bound L of S, we have sup(B) >= L.

Since S is nonempty, B, the set of lower bounds of S, is also nonempty. This is because any real number that is less than or equal to all elements of S is a lower bound of S.

Furthermore, B is bounded above because any upper bound of S is also an upper bound of B. This is because if M is an upper bound of S, then for any element b in B, we have b <= M.

To prove that sup(B) is a lower bound of S, we can use the fact that sup(B) is the smallest upper bound of B. This means that for any lower bound L of S, we must have sup(B) >= L.

To see this, suppose that sup(B) < L for some lower bound L of S. Then there would exist an element b in B such that b < L. But this contradicts the fact that sup(B) is the smallest upper bound of B.

Therefore, we must have sup(B) >= L for all lower bounds L of S. This means that sup(B) is the greatest lower bound of S.

Learn more about element here: brainly.com/question/31950312

#SPJ11

Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.

A bell curve is a form of graph that is used to show how a collection of selected values are distributed; it often has a peak at the centre that tends to be normal, with low and high extremes tapering out rather symmetrically on either side.

Given that:

Mean = 42 with standard deviation of 4.

Now,

If mean = 42,

1 standard deviation (+1σ) above that mean = 42 + 4  =48

1 standard deviation (-1σ) below that mean = 42 - 4 = 38

By the empirical rule  68-95-99.7 rule:

68% of the given normal distribution data lies between -1σ and +1σ:  That is between 38 - 48  requests.

And,

In the range 42 - 50  requests (between that mean and +1σ) is half of the given 68% : 68/2 = 34%

Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.

Know more about the bell-shaped curve:

https://brainly.com/question/24182600

#SPJ1

Correct question:

the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 4. using the empirical rule  68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 50?

The sketch of (A∪C)×(B∩D) represents the region where the elements from the union of sets A and C intersect with the elements from the intersection of sets B and D.

To sketch (A∪C)×(B∩D), we consider the two sets separately. First, we examine A∪C, which represents the union of sets A and C. This union encompasses all the elements that are present in either set A or set C, or in both. On the sketch, we can denote this union on one axis by marking the points that belong to either A or C or both.

Next, we consider B∩D, which represents the intersection of sets B and D. This intersection includes all the elements that are common to both sets B and D. On the sketch, we can denote this intersection on another axis by marking the points that belong to both B and D.

Finally, to obtain (A∪C)×(B∩D), we find the pairs formed by taking one element from the union A∪C and one element from the intersection B∩D. We can represent these pairs as points in the resulting region on the sketch. The region will encompass all the possible combinations of elements from A∪C and B∩D, illustrating the Cartesian product of the two sets.

To learn more about intersection click here

brainly.com/question/32797114

#SPJ11

The probability that a randomly selected person will have an IQ score of less than 80 is approximately 0.0918, or 9.18%

To find the probability that a randomly selected person will have an IQ score of less than 80, we need to consider the properties of the normal distribution, as IQ scores typically follow a normal distribution with a mean (μ) of 100 and a standard deviation (σ) of 15.

1. Calculate the z-score: The z-score represents the number of standard deviations a data point is from the mean. Use the formula:

z = (X - μ) / σ

where X is the IQ score, μ is the mean, and σ is the standard deviation.

z = (80 - 100) / 15
z = -20 / 15
z = -1.3333

2. Look up the z-score in a standard normal distribution table or use a calculator to find the corresponding probability. In this case, the probability is 0.0918.

Therefore, the probability that a randomly selected person will have an IQ score of less than 80 is approximately 0.0918, or 9.18% when rounded to four decimal places.

To know more about Probability refer here:

https://brainly.com/question/30034780

#SPJ11

The drums of sealant will be needed if each drum covers 150 sa yd are 5.

The total area of the four driveways is 84.8 sq yd + 124.1 sq yd + 98.9 sq yd + 344.7 sq yd = 652.5 sq yd.

So, the number of drums of sealant needed is given by the total area divided by the area covered by each drum:

652.5 sq yd / 150 sq yd/drum = 4.35 drums (rounded up to the nearest whole number, 5 drums will be needed).

Therefore, 5 drums of sealant will be needed if each drum covers 150 sa yd.

To know more about total area, here

https://brainly.com/question/28124425

#SPJ4

Answer:

B- hope this helps:)

Step-by-step explanation:

The total cost to paint 864.5 square feet of wall is $2,048.87.

It is given that the cost to paint one square foot of wall is $2.37.

We are asked to find the total cost to paint 864.5 square feet of wall.

If we have a number that has a decimal point then we have two parts.

The whole number part and the fractional part.

After the decimal point, we will count the place value as tenths, hundredths, thousandths, and so on.

You can also see the given figure below.

We know that,

One square foot = $2.37.

Remember that Feet is the plural form of the foot.

We can write,

864.5 square feet = 864.5 x  one square foot

Because in 864.5 square feet we have 864.5 one square foot.

And since one square foot cost $2.37.

864.5 square feet will cost 864.5 x 2.37 dollars.

Now,

864.5 x 2.37 = $2048.865.

Rounding to the nearest hundredth.

6 is in the hundredth place so we will round 86 to 87 since the number in the thousandth place is greater than 4.

Thus the total cost to paint a wall of 864.5 square feet is $2,048.87.

Learn more about rounding decimal numbers here:

https://brainly.com/question/15482780

#SPJ2

Answer:

I'm pretty sure it's c and d

Pua will use 13, 1/4 cups of oatmeal.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Pua needs 3\(\frac{1}{4}\) cups of oatmeal.

The number of 1/4 cups of oatmeal,

she will use,

= 13/4 ÷ 1/4

= 13

Therefore, she will use 13 cups.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ1

Using the least common factor, it is found that it would take 90 minutes for both boys to return to the starting point at the same time.

To find the least common factor, we factor the numbers by prime factors, and then multiply these factors.

The lcm represents the periodicy, that is, when two periodic amounts will be at the same value.

In this problem, the periods are of 15 minutes and 18 minutes, hence:

15 - 18|2

15 - 9|3

5 - 3|3

5 - 1|5

1 - 1

Hence:

lcm(15,18) = 2 x 3 x 3 x 5 = 90.

It would take 90 minutes for both boys to return to the starting point at the same time.

More can be learned about the least common factor at https://brainly.com/question/24873870

The amount spent on each visit to the smoothie shop is $4,000.

Each time someone visits the smoothie shop, they spend $4,000 on average. This amount represents the average expenditure per customer during their visit.

It is important to note that this figure may vary depending on individual preferences and choices made at the shop. Some customers may spend more or less than the average amount.

Factors such as the size of the smoothie, additional toppings or ingredients, and any promotional discounts offered can influence the final cost. Understanding the average spending per visit can help the smoothie shop evaluate its pricing strategy, assess customer preferences, and make informed business decisions.

Learn more about smoothie shop

brainly.com/question/20494276

#SPJ11

The p-value for the claim is 0.0576.

We must run a hypothesis test to find the p-value for the assertion. Here are descriptions of the null and competing hypotheses:

Null Hypothesis (H₀): Young adults in the city share the same smoking patterns as young adults in general in the United States.

Alternative Hypothesis (H₁): The percentage of young adults in the city who smoke differs from the percentage of young adults in the U.S.

To analyse the data, we can perform a hypothesis test for a single proportion, more precisely a one-sample proportion test. Let's use this method to determine the p-value.

We must first calculate the sample proportion's standard error:

SE = \(\sqrt{\frac{p_{0} \times (1 - p_{0})}{n}}\)

where:

p₀ = proportion of young adults who reported smoking at least twice a week or more in the last month (given as 0.16)

n = sample size (given as 75)

SE = sqrt((0.16 * (1 - 0.16)) / 75) ≈ 0.0421

Next, we calculate the test statistic (z-score) using the observed sample proportion:

z = (\(\hat{p}\) - p₀) / SE

where:

\(\hat{p}\) = observed sample proportion (6 out of 75)

p₀ = proportion of young adults who reported smoking at least twice a week or more in the last month (given as 0.16)

SE = standard error of the sample proportion (0.0421)

\(\hat{p}\) = 6/75

\(\hat{p}\) = 0.08

z = (0.08 - 0.16)/0.0421

z ≈ -1.897

Now that we have the probability of seeing a test statistic with either tail as severe as -1.897, we can calculate the p-value.

p-value ≈ P(Z ≤ -1.897) + P(Z ≥ 1.897)

The p-value is about 0.0576, according to a standard normal distribution table or statistical software.

As a result, the claim's p-value is roughly 0.0576.

To learn more about p-value link is here

brainly.com/question/30078820

#SPJ4

Answer:

15

Step-by-step explanation:

you will add each set of number together:

13+0+14+36+18+9=90

Then you will take 90 and divide it by how many numbers are in the number set:

90÷6=15