The sum of nine times a number and five is one hundred eighty-five

Answer:

vector

Step-by-step explanation:

6x+3y = 15

========================================================

Work Shown:

x = number of touchdowns

y = number of field goals

6x = points only from the touchdowns (ignore the fieldgoals for now)

3y = points only from the field goals (ignore the touchdowns for now)

6x+3y = total number of points from both categories combined

6x+3y = 15 since Kingston scored 15 points overall

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

Extra info (optional section)

We don't have enough info to fully nail down what x and y are in terms of numbers, but let's say he scored y = 1 field goal.

Then x would be,

6x+3y = 15

6x+3(1) = 15

6x+3 = 15

6x = 15-3

6x = 12

x = 12/6

x = 2

This tells us that Kingston scored 2 touchdowns if he scored 1 field goal.

2 touchdowns + 1 field goal = 2*6 + 1*3 = 12 + 3 = 15 points total

The ordered pair (x,y) = (2,1) is one solution to that equation.

Another solution is (x,y) = (1,3) following similar steps as shown above.

The third solution is (x,y) = (0,5). Each time x goes down by 1, y goes up by 2 and vice versa.

We only have 3 solutions in this case because x & y are nonnegative whole numbers. If x and/or y were allowed to be any real number, then we'd have infinitely many solutions.

The required equation is 6x + 3y = 15 which can be used to model the given situation.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We can use the following equation to model the given situation:

6x + 3y = 15

This equation represents the total number of points scored by Kingston.

The term "6x" represents the number of points scored by touchdowns, where x is the number of touchdowns.

The term "3y" represents the number of points scored by field goals, where y is the number of field goals.

The constant 15 on the right side of the equation represents the total number of points scored by Kingston.

Hence, the correct answer would be an option (A).

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The graph of y = x is graph C.

x = 3 is represented by graph E.

The graph that matches x + y = 3 is graph D.

The equation of a graph can be expressed as y = mx + b, in slope-intercept form, where you have m as the slope of the line and b as the y-intercept.

The equation of a vertical line is x = b, where b is the point on the x-axis that the line intercepts.

For a horizontal line, the equation is y = b, where b is the point on the y-axis where the line intercepts.

y = x, has a slope of 1, and is a proportional graph that passes through the origin (0, 0) and rises. Therefore, the graph of y = x is graph C.

x = 3 is a vertical line that intercepts the x-axis at 3. Therefore, x = 3 is represented by graph E.

x + y = 3, can be rewritten as y = -x + 3. The line has a declining slope of -1, and intercepts the y-axis at 3. Therefore, the graph that matches x + y = 3 is graph D.

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From the Conditional probability formula, if events A and B are conditionally independent given event C,

a) Yes, for A and Bᶜ guaranteed to be conditionally independent given C.

b) No, A and B guaranteed to be conditionally independent given Cᶜ.

Conditional probability represented by notation P(A|B) is read as the probability of event A occurring given that event B has occurred. We will use the definition of conditional probability and independent events to prove the required result. In conditional probability, we calculate the probability of an event and it is known that the other event has already occurred. The events A and B are conditionally independent for the given event C such that P( C) > 0 and P( Cᶜ ) > 0.

In case of independent, the probability of one event can't be effect the probability of a 2nd event, that is Probability of intersection of two events is product of individual probabilities

From the definition of conditional probability, for independent events A and B, P( (A∩B)| C) = P( A|C) P( B|C)

a) Using the properties of conditional probability, \(P( ( A∩B^c )| C) = P( A|C) P( B^c |C) \\ \)

so, yes, A and B guaranteed to be conditionally independent given C.

b) Using the properties of conditional probability independent, P( (A∩B)| C) = P( A|C) P( B|C) but \(P( (A∩B)| C^ c ) ≠ P( A|C^c) P( B|C^c) \\ \).

So, A and B are not guaranteed to be conditionally independent given Cᶜ.

Hence, the first statement is right but not second.

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Complete question:

4. suppose that events A and B are conditionally independent given event C. suppose that p(C) > 0 and p(Cᶜ ) > 0. (a) are a and bc guaranteed to be conditionally independent given c? justify your answer. (b) are a and b guaranteed to be conditionally independent given Cᶜ ? justify your answer.

To find the second solution of the given differential equation x²y" - 3xy' + 3y = 2x²ex, we can use the method of variation of parameters. Assuming the second solution in the form of y₂ = u(x)ex, we differentiate y₂ to find y₂' and y₂", substitute them into the original differential equation, and simplify. This leads to a differential equation for u(x), which can be solved using appropriate methods. Once we find u(x), the second solution y₂ is determined as y₂ = u(x)ex.

To find the second solution, we can use the method of variation of parameters. Since y₁ = ex is a solution of the homogeneous equation y" - y = 0, we assume a second solution in the form of y₂ = u(x)ex, where u(x) is an unknown function to be determined. We differentiate y₂ to find y₂' and y₂":

y₂' = u'(x)ex + u(x)ex

y₂" = u''(x)ex + 2u'(x)ex + u(x)ex

Substituting y₂, y₂', and y₂" into the original differential equation, we obtain:

x²(u''(x)ex + 2u'(x)ex + u(x)ex) - 3x(u'(x)ex + u(x)ex) + 3u(x)ex = 2x²ex

Simplifying and rearranging terms, we have:

x²u''(x)ex + (2x² + 2x)u'(x)ex + (x² - 3x + 3)u(x)ex = 2x²ex

To find u(x), we equate the coefficient of ex on both sides of the equation. We obtain the following differential equation for u(x):

x²u''(x) + (2x² + 2x)u'(x) + (x² - 3x + 3)u(x) = 2x²

We can now solve this second-order linear non-homogeneous differential equation for u(x) using appropriate methods such as the method of undetermined coefficients or variation of parameters. Once we find u(x), the second solution y₂ can be determined as y₂ = u(x)ex.

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The statement "The Taylor series centered at 0 (aka MacLaurin Series) for f(x) = \(x^{11}\) sin x has only even powers of x" is false.

The Taylor series centered at 0 (or MacLaurin series) for the function f(x) = \(x^{11}\) sin(x) includes terms with both even and odd powers of x. The general form of the Taylor series for this function is:

f(x) = f(0) + f'(0)x + f''(0)\(x^{2}\)/2! + f'''(0)\(x^{3}\)/3! + ...

The derivative of f(x) = \(x^{11}\) sin(x) involves both the derivative of \(x^{11}\) (which has only even powers) and the derivative of sin(x) (which has both even and odd powers). Therefore, when the Taylor series is expanded, terms with both even and odd powers of x will be present.

Hence, the statement is false.

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Answer: $50,750

Step-by-step explanation: To get the percentage of a number, you need to turn the percent into a decimal, then multiply it with the number you need the percentage of. 35% translates into 0.35. Then you would multiply 145,000 by 0.35, getting 50,750 as your answer!

The calculated t-value (2.82) is greater than the critical value of 1.812. So we reject the null hypothesis and conclude that there is evidence at the 0.1 level that the mean door height is either too long or too short.

The null hypothesis is The mean door height is equal to 2058.0 millimeters. An alternative hypothesis is The mean door height is not equal to 2058.0 millimeters. The level of significance is 0.1 or 10%.

Calculate the test statistic:

Since the alternative hypothesis is two-sided and the level of significance is 0.1, we will use a two-tailed t-test with 10 degrees of freedom. From a t-distribution table with 10 degrees of freedom and a level of significance of 0.1, the critical values are ±1.812.

The calculated t-value (2.82) is greater than the critical value of 1.812. Therefore, we reject the null hypothesis and conclude that there is evidence at the 0.1 level that the mean door height is either too long or too short.

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Answer:

y = -1/4(x-1)

Step-by-step explanation:

y - \(y_{1}\) = m(x - \(x_{1}\))  From the point given \(y_{1}\) = 0 and \(x_{1}\) = 1

m = slope -1/4  Plug these in and get

y - 0 = -1/4(x - 1)       y-0 is just y

Answer:

18 and 6

Step-by-step explanation:

The sum of two numbers is twice their difference: 18 + 6 = 24, 18 - 6 = 12. 24 is twice of 12.

The larger number is 5 more than twice the smaller. Twice of 6 is 12. 5 more than 12 is 18.

Answer:

24

Step-by-step explanation:

√64 ×∛27

√64=√8²=8

∛27 = √3³=3

8*3=24

Answer:

then answer it

Step-by-step explanation:

Answer:

4.5 inches long by 2.5 inches wide

Step-by-step explanation:

If the first scale drawing is 1:8, and the second is 1:16, the dimensions are divided into two to get their drawn lengths.

Hope this helps :)

(Brainliest, please? I only need one more to level up)

The statement that the real price growth of gadgets is less than inflation is correct. Thus, option A is correct.

To calculate the inflation rate, we use the formula:

Inflation Rate = (CPI₂ - CPI₁) / CPI₁ x 100%,

where CPI₁ is the Consumer Price Index in the base year and CPI₂ is the Consumer Price Index in the current year.

Given that the CPI in year 1 is 100 and the CPI in year 2 is 115, we can substitute these values into the formula:

Inflation Rate = (115 - 100) / 100 x 100% = 15%.

Now, to calculate the price of a year 2 gadget in year 1 dollars (real price), we use the formula:

Real Price = Nominal Price / (CPI / 100),

where CPI is the Consumer Price Index.

We are given that the nominal price of the gadget in year 2 is $2. Substituting this value along with the CPI of 115 into the formula:

Real Price = $2 / (115 / 100) = $2 / 1.15 = $1.7391 ≈ $1.74.

Therefore, the price of a year 2 gadget in year 1 dollars is approximately $1.74.

Regarding the statement about real price growth, it is stated that the real price growth of gadgets is less than inflation. This conclusion is based on the comparison between the nominal price and the real price.

In this case, the nominal price of the gadget increased from $1 in year 1 to $2 in year 2, which is a 100% increase. However, when considering the real price in year 1 dollars, it increased from $1 to approximately $1.74, which is a 74% increase.

Since the inflation rate is 15%, we can observe that the real price growth of gadgets (74%) is indeed less than the inflation rate (15%). Therefore, the statement that the real price growth of gadgets is less than inflation is correct.

Thus, option A is correct

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There is no sufficient evidence that we can use in order to substantiate the claim of the publisher,

The null hypothesis H0: p = 0.47

The alternative hypothesis is H1: p > 0.47

The question requires us to test the fact that more than 47 percent of the readers have their own personal computer. This is therefore the claim that is to be tested here.

There is no sufficient evidence to substantiate the claim because of the lack of certain details that would have been used to carry out the hypothesis test.

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A list of dependent quantities from a table would include only those variables that are changing in response to the independent variable.

An explanation of independent and dependent variables in a table.

The independent variable is the variable that is changed or manipulated by the experimenter.

It is usually placed in the first column of the table.

The dependent variable on the other hand is the variable that changes in response to the independent variable.

It is usually placed in the second column of the table.

Let's say we are conducting an experiment to see how the time spent exercising affects the number of calories burned.

The independent variable would be the time spent exercising and the dependent variable would be the number of calories burned.

Our table might look something like this:

Time Spent Exercising (minutes) Calories Burned

10 100

20 200

30 300

40 400

"Time Spent Exercising" is the independent variable as it is the variable that we are changing.

"Calories Burned" is the dependent variable as it is the variable that is changing in response to the time spent exercising.

A list of dependent quantities from a table would include only those variables that are changing in response to the independent variable. Without seeing the specific table mentioned I cannot give an answer with complete accuracy but I hope this explanation helps clarify the concept of dependent and independent variables in a table.

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Changing the coefficient of x to 6 changes the meaning of expression as 5 is added to 6 times x

Solution:

Given that number 2 in the expression 5 + 2x is called the coefficient of x

We are asked to find what happens when changing the coefficient to 6 change the meaning of the expression

In the expression,

5 + 2x

This means 5 is added to 2 times x or 5 is added to twice of x

Number 2 is called coefficient of x

When we change this coefficient to 6, the expression becomes,

5 + 6x

So now the meaning of expression becomes,

5 is added to 6 times x

So changing the coefficient of x changes the meaning of expressionStep-by-step explanation:

Answer: Where is the table?

Step-by-step explanation: i wish i could help but im afraid there isnt a table

Answer:

The missing coordinate, D = (7, 1)

Answer:

A

Step-by-step explanation:

3x - 2 = 10x - 12

3x - 10x = -12 - 2

-7x = -14

x=2

Answer:

45 men

Step-by-step explanation:

A job takes 30 men for 15 days to complete so it takes x men to do the same job in 10 days

30(15) = x(10)

450 = 10x

x = 450/10

x = 45

Answer:

45 days

Step-by-step explanation:

30men=15days

1man=15×30

1man=450days

10men=450÷10

10men=45days

I think that's it

Answer:

1296

Step-by-step explanation:

Answer:

what i dont understand the word

Answer:

x = - 7.5

Step-by-step explanation:

given y is inversely proportional to x² then the equation relating them is

y = \(\frac{k}{x^2}\) ← k is the constant of proportion

to find k use the condition y = 8 when x = 2.5

8 = \(\frac{k}{2.5^2}\) = \(\frac{k}{6.25}\) ( multiply both sides by 6.25

50 = k

y = \(\frac{50}{x^2}\) ← equation of proportion

when y = \(\frac{8}{9}\) , then

\(\frac{8}{9}\) = \(\frac{50}{x^2}\) ( multiply both sides by x² )

\(\frac{8}{9}\) x² = 50 ( multiply both sides by \(\frac{9}{8}\) to clear the fraction )

x² = 50 × \(\frac{9}{8}\) = \(\frac{450}{8}\) = 56.25 ( take square root of both sides )

x = ±\(\sqrt{56.25}\) = ± 7.5

the negative value of x = - 7.5

Here, we need to perform a hypothesis test at the 0.025 level of significance to see if the mean installation time has changed.

The null and alternate hypotheses are as follows:

Null Hypothesis H0: µ = 6 (mean installation time is equal to 6 minutes)

Alternate Hypothesis H1: µ ≠ 6 (mean installation time is not equal to 6 minutes)

The level of significance (α) is given as 0.025. The sample size is 41. The sample mean is 5.4 minutes and the sample standard deviation is 1.3 minutes.

To perform the hypothesis test, we need to compute the test statistic and compare it with the critical value of the t-distribution at the given level of significance.

Step 1: Specify the level of significance. The level of significance is α = 0.025.

Step 2: Formulate the null and alternate hypothesis. The null and alternate hypothesis are given above.

Step 3: Determine the test statistic

Step 4: Determine the critical value - The critical value of the t-distribution can be found using a t-table or a calculator. Since this is a two-tailed test, the critical values will be tα/2, n-1 and -tα/2, n-1 where α/2 = 0.025/2 = 0.0125.The degrees of freedom are given by (n - 1) = (41 - 1) = 40.

Using the t-distribution table or a calculator, the critical values are:

t0.0125,40 = -2.704 and t0.9875,40 = 2.704

Step 5: Make the decision - Based on the computed test statistic and critical values, we can make the decision whether to reject or fail to reject the null hypothesis. Since this is a two-tailed test, we need to compare the absolute value of the test statistic with the absolute value of the critical value.t > t0.0125,40 or t < -t0.0125,40 => Reject the null hypothesis or fail to reject the null hypothesis

Substituting the values, we get:

|-2.2977| < 2.704. Hence, we fail to reject the null hypothesis.

Step 6: Draw a conclusion and interpret the decision - At a significance level of 0.025, there is not enough evidence to conclude that the new mean installation time is different from 6 minutes. Therefore, we fail to reject the null hypothesis. We can conclude that RodeTech's most popular computer program installation time has not changed significantly. Therefore, there is no need for RodeTech to change its advertising.

Thus, the main answer is D. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance that the new mean installation time is different from 6 minutes and that RodeTech may need to change its advertising.

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Answer:

1/2

Step-by-step explanation:

The selling price for the given cost price and profit percentage is ₹420.5.

The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.

Given that, the cost price of a bag of almonds is ₹290 and it is sold with a profit of 45%.

We know that, Selling price = (100+Profit%)/100 ×CP

Here, Selling price = (100+45)/100 ×290

= 145/100 ×290

= 1.45×290

= 420.5

Therefore, the selling price is ₹420.5.

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Answer:

Step-by-step explanation:

Parabola:

   \(\sf f(x) =\dfrac{-1}{2}x^2+7x - 5\\\\a = \dfrac{-1}{2} \ ; b = 7 \ ; \ c = -5\)

\(\sf x = \dfrac{-b}{2a}\\\\x =\dfrac{-7}{2*\dfrac{-1}{2}}\\\\ = \dfrac{-7}{-1}\)

x = 7

Now, to find the y-value substitute this in the equation

               \(\sf f(x) = \dfrac{-1}{2}*7^2+7*7-5\\\\ =\dfrac{-49}{2}+49-5\\\\ = \dfrac{-49}{2}+44\\\\ = \dfrac{-49}{2}+\dfrac{88}{2}\\\\= \dfrac{39}{2}\)

\(\boxed{Vertex(7 ,\dfrac{39}{2})}\)

b) The value of a is negative. So, the parabola is open down words and the maximum value is given by the y-coordinate of the Vertex.

             \(\sf \boxed{Maximum \ value= \dfrac{39}{2}}\)

\(\sf c) Range = [\dfrac{39}{2}, -infinity)\)

Answer:

(a) (7,39/2)

(b) Maximum, 39/2

(c) y ≤ 39/2

(d) Increase when x < 7 and decrease when x > 7

Step-by-step explanation:

Given the parabola:

\(\displaystyle \large{f(x)=-\dfrac{1}{2}x^2+7x-5}\)

( A ) Find the vertex

In order to find the vertex, let’s use calculus for this one. Recall the power rules for differentiation:

Power Rules

\(\displaystyle \large{f(x)=x^n \to f'(x)=nx^{n-1}}\\\\\displaystyle \large{f(x)=kx^n \to f'(x)=knx^{n-1} \quad \tt{(k \ \ is \ \ constant)}}\\\\\displaystyle \large{f(x)=k \to f'(x)=0 \quad \tt{(k \ \ is \ \ constant)}}\)

Derivative Definition

Derive the parabola:

\(\displaystyle \large{f'(x)=-\dfrac{1}{2}(2)x^{2-1} + 7(1)x^{1-1} -0}\\\\\displaystyle \large{f'(x)=-x+7}\)

Since vertex has slope = 0 —> e.g f'(x) = 0:

\(\displaystyle \large{0=-x+7}\\\\\displaystyle \large{-x=-7}\\\\\displaystyle \large{x=7}\)

Substitute x = 7 in f(x):

\(\displaystyle \large{f(7)=-\dfrac{1}{2}(7)^2+7(7)-5}\\\\\displaystyle \large{f(7)=-\dfrac{1}{2}(49)+49-5}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+44}\\\\\displaystyle \large{f(7)=-\dfrac{49}{2}+\dfrac{88}{2}}\\\\\displaystyle \large{f(7)=\dfrac{39}{2}}\)

Therefore, the vertex is at (7,39/2)

( B ) Determine if max or min then find the value

Since the parabola opens downward then there only exists maximum value. The maximum value is the y-value of vertex at x-value of vertex. Henceforth:

( C ) Find range

For parabola, range is minimum value </≤ y </≤ maximum value. We know that parabola has maximum value of 39/2 but no minimum value so we can just ignore it then we’d have:

[Note: < and > are for open-dot meaning the value will not be included —> e.g x > 4 means 4 isn’t included in.]

( D ) Find the interval when function is increasing and when it’s decreasing

For parabola, the function will increase only if f'(x) or slope > 0 and will decrease only f'(x) < 0.

We know, from part A that the derivative is:

\(\displaystyle \large{f'(x)=-x+7}\)

Therefore, when f'(x) > 0 —> e.g -x + 7 > 0:

\(\displaystyle \large{-x+7 > 0}\\\\\displaystyle \large{-x > -7}\\\\\displaystyle \large{x < 7}\)

When f'(x) < 0 —> e.g -x + 7 < 0:

\(\displaystyle \large{-x+7 < 0}\\\\\displaystyle \large{-x < -7}\\\\\displaystyle \large{x > 7}\)

Therefore, the function will increase when x < 7 and will decrease when x > 7.