Read each question. Then write the letter of the correct answer on your paper.How many negative solutions does 2|3 x-6| ≥ 6 have? (f) 0 (g) 1 (h) 2 (i) infinitely many

The number required in the word problem given is 4/5

Let the number = n

We can set up the word problem thus :

n ÷ 3/2 = (n * 3/2 - 2/3)

n * 2/3 = 3n/2 - 2/3

2n/3 = 3n/2 - 2/3

2n/3 - 3n/2 = -2/3

(4n - 9n)/6 = -2/3

4n - 9n = -12/3

-5n = -4

divide both sides by -5

n = 4/5

Therefore, the number required is 4/5.

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Answer:

44

Step-by-step explanation:

First, let's sum up the ratio.

Sum the ratios = 6 + 2 + 3 = 11

We can make y the total number of boots sold together last month

If 24 pairs of boots were sold, then the equation would be

6/11 × y = 24

Cross multiply

6 × y = 24 × 11

6y = 264

y = 44

Therefore, total number of boots sold altogether last month were 44

Answer: 775

Step-by-step explanation: $15 for each guest (so you need to multiply 15 by 45) then add the $100 setup fee!

Answer:

19

Step-by-step explanation:

f(x)=2(3^x)+1,

Let x=2

f(2)=2(3^2)+1

Exponents first

    =2 (9) +1

Then multiply

    =18+1

    =19

Answer:

\(\frac{\sqrt[3]{19} }{\sqrt[3]{x} }\)

So A is the answer

Step-by-step explanation:

\(y=\frac{19}{x^3}\\\mathrm{Interchange\:the\:variables}\:x\:\mathrm{and}\:y\\x=\frac{19}{y^3}\\\mathrm{Solve}\:x=\frac{19}{y^3}\:\mathrm{for}\:y\\y=\sqrt[3]{\frac{19}{x}}\\\sqrt[3]{\frac{19}{x}}\\\frac{\sqrt[3]{19} }{\sqrt[3]{x} }\)

Answer:

1200 / 60 = 20 hours

Equation form:

x=2, y=-1

x=0, y=-3

The conversion of the polar equation r = 16cos(θ) + 7sin(θ) to rectangular coordinates results in the equation (x - 8)^2 + (y - 3.5)^2 = 113. This equation represents a circle in the Cartesian coordinate system.

To convert the polar equation r = 16cos(θ) + 7sin(θ) to rectangular coordinates, we can use the following trigonometric identities:

cos(θ) = x/r

sin(θ) = y/r

where x and y represent the rectangular coordinates, and r represents the radial distance from the origin.

Substituting these identities into the given equation, we have:

r = 16(x/r) + 7(y/r)

To eliminate the fraction, we can multiply both sides of the equation by r:

r^2 = 16x + 7y

Now, we need to express r^2 in terms of x and y. In the rectangular coordinate system, r^2 can be written as:

r^2 = x^2 + y^2

Substituting this expression into the equation, we have:

x^2 + y^2 = 16x + 7y

This is the equation in rectangular coordinates that corresponds to the given polar equation.

To simplify this equation further, we can rearrange it:

x^2 - 16x + y^2 - 7y = 0

Completing the square for the x and y terms, we need to add half of the coefficient of x and y, squared, to both sides:

(x^2 - 16x + 64) + (y^2 - 7y + 49) = 64 + 49

(x - 8)^2 + (y - 3.5)^2 = 113

So, the equation in rectangular coordinates, after completing the square, is:

(x - 8)^2 + (y - 3.5)^2 = 113

This equation represents a circle in the Cartesian coordinate system, centered at the point (8, 3.5), with a radius of √113.

In summary, the conversion of the polar equation r = 16cos(θ) + 7sin(θ) to rectangular coordinates results in the equation (x - 8)^2 + (y - 3.5)^2 = 113. This equation represents a circle in the Cartesian coordinate system.

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A) The probability that the chosen ball will be blue or red is 2/3.b) The probability that the chosen ball will be green given that it is not red is 8/15.

a) One ball is chosen at random from the bag. The probability that the ball chosen will be blue or red can be calculated as follows:

We have 19 red balls and 7 blue balls. So, the total number of favourable outcomes is the sum of the number of red balls and blue balls.i.e, the total number of favourable outcomes = 19 + 7 = 26

Also, there are 19 red balls, 7 blue balls and 8 green balls in the bag.

So, the total number of possible outcomes = 19 + 7 + 8 = 34

Therefore, the probability that the ball chosen will be blue or red is given by:

Probability of blue or red ball = (Number of favourable outcomes) / (Total number of possible outcomes)

Probability of blue or red ball = (26) / (34)

Simplifying the above fraction gives us the probability that the chosen ball will be blue or red as a fraction i.e.2/3

b) One ball is chosen at random from the bag. Given that the chosen ball is not red, we have only 7 blue balls and 8 green balls left in the bag.So, the total number of favourable outcomes is the number of green balls left in the bag, which is 8.

Therefore, the probability that the chosen ball is green given that it is not red is given by:

Probability of green ball = (Number of favourable outcomes) / (Total number of possible outcomes)

Probability of green ball = 8 / 15

Simplifying the above fraction gives us the probability that the chosen ball will be green as a fraction i.e.8/15.

The final answers for the question are:a) The probability that the chosen ball will be blue or red is 2/3.b) The probability that the chosen ball will be green given that it is not red is 8/15.

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Answer:

Step-by-step explanation:

Given quadratic function:

Points on the graph:

Substitute values of x and y and solve the system of equations:

Subtract eq 2 from eq 1:

Subtract eq 2 from eq 3:

Compare eq 4 and eq 5, solve for a:

Find the value of b using eq 4:

Find the value of c using eq 2:

We now have a, b and c:, the function is:

Answer:

y = -3x² + 7x - 9

Step-by-step explanation:

Given quadratic function:

y = ax² + bx + c

Points on the graph:

(-2,-35), (1,-5), (3,- 15)

Substitute values of x and y and solve the system of equations:

-35 = a(-2)² + b(-2) + c ⇒ -35 = 4a - 2b + c   ⇔ eq 1

-5 = a(1)² + b(1) + c ⇒ -5 = a + b + c               ⇔ eq 2

-15 = a(3)² + b(3) + c ⇒ -15 = 9a + 3b + c       ⇔ eq 3

Subtract eq 2 from eq 1:

-35 - (-5) = 4a - 2b + c - a - b - c

-30 = 3a - 3b

b = a + 10                                                         ⇔ eq 4

Subtract eq 2 from eq 3:

-15 - (-5) = 9a + 3b + c - a - b - c

-10 = 8a + 2b

b = -4a - 5                                                       ⇔ eq 5

Compare eq 4 and eq 5, solve for a:

a + 10 = -4a - 5

a + 4a = -5 - 10

5a = -15

a = -3

Find the value of b using eq 4:

b = -3 + 10

b = 7

Find the value of c using eq 2:

-5 = -3 + 7 + c

c = -5 - 4

c = -9

We now have a, b and c:, the function is:

y = -3x² + 7x - 9

Answer:

■ y = m x

m = slope

Here m = 4/3

,*,slope is 4/3

The degree of polynomial 3x^4-0x^3+0x^5 is 4

Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).

Therefore, inx^3+3x+5, the degree of the polynomial is 3 as the highest power in its terms is 3. (power and exponent are same thing);

Given in the question;

Polynomial= 3x^4-0x^3+0x^5

The highest degree from observation is of 3x that is equal to 4

Hence, the correct degree will be 4

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To calculate the probability that a 0.270 hitter in baseball will not get a hit on his next at-bat, we need to know the hitter's batting average.

A batting average of 0.270 means that the hitter gets a hit in 27 out of every 100 at-bats. Therefore, the probability of getting a hit on any given at-bat is 0.270.

The probability of not getting a hit on a single at-bat can be calculated as 1 minus the probability of getting a hit. So, the probability of not getting a hit on a single at-bat for a 0.270 hitter is:

Probability of not getting a hit = 1 - Probability of getting a hit

Probability of not getting a hit = 1 - 0.270

Probability of not getting a hit = 0.730

Therefore, the probability that a 0.270 hitter in baseball will not get a hit on his next at-bat is 0.730 or 73.0%.

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Answer:

x>12-(2y)/(3)

y>18-(3x)/(2)

Step-by-step explanation:

Answer:

The solution is:

x = 5

y = 11

Step-by-step explanation:

15x+10y>180

Since I know 15 + 10 = 25, I subtracted 25 from 180.

180 - 25 = 155

Therefore, we know that x and y multiplied by 15 and 10 must equal anything more than 180. Therefore, there are a variety of solutions. However, this is the one that I chose.

15(5)+10(11)>180

75+110>180

185>180 <----- This is a true statement.

Hope this helps! :D

False.

While a Pearson correlation coefficient of +1.00 or -1.00 indicates a strong linear relationship between two variables, it does not necessarily mean that all data points will fit perfectly on a straight line. The correlation coefficient measures the strength and direction of the linear relationship, but it does not guarantee that the data points will fall exactly on a straight line.

Scatter plots with a perfect linear relationship will have all data points lying precisely on a straight line, but this is not always the case even when the correlation coefficient is +1.00 or -1.00. There can still be some degree of scatter or variation around the line, depending on other factors such as measurement errors, outliers, or the presence of other nonlinear relationships in the data.

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The Cartesian coordinate form of the polar equation \(\(r = 2(1 - \cos x)^{-1}\)\) is:

\(\(x = \frac{2 \cos \theta}{1 - \cos \theta}\ , \ y = \frac{2 \sin \theta}{1 - \cos \theta}\)\)

To convert the polar equation \(\(r = 2(1 - \cos x)^{-1}\)\) to Cartesian coordinates, we can use the following relationships between polar and Cartesian coordinates:

\(\(x = r \cos \theta\)\\\(y = r \sin \theta\)\)

In this case, the provided polar equation is \(\(r = 2(1 - \cos x)^{-1}\)\).

We can substitute x with \(\(\theta\)\) to maintain consistency between the variables.

Therefore, we have:

\(\(r = 2(1 - \cos \theta)^{-1}\)\)

To convert this to Cartesian coordinates, we substitute the values of r and \(\(\theta\)\) into the Cartesian coordinate equations:

\(\(x = r \cos \theta\)\(y = r \sin \theta\)\)

Substituting the provided r into the equations:

\(\(x = 2(1 - \cos \theta)^{-1} \cos \theta\)\\\(y = 2(1 - \cos \theta)^{-1} \sin \theta\)\\\)

Simplifying these equations, we obtain the Cartesian coordinate form of the provided polar equation:

\(\(x = \frac{2 \cos \theta}{1 - \cos \theta}\)\\\(y = \frac{2 \sin \theta}{1 - \cos \theta}\)\)

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Answer:

Associative Property

Step-by-step explanation:

The associative property lets us change the grouping, or move grouping symbols (parentheses).

Answer:

1) 1+3

2) c

...............

Answer:

1.) first, second and third

2.) D

Answer:

The GCF is 4

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

look at a Multiplication chart find all factors and find the highest number for 28 and 44

The area of the trapezoid is 140√3 square inches, in simplest radical form.

To find the area of a trapezoid, we can use the formula:

Area = (1/2) * (a + b) * h,

where "a" and "b" are the lengths of the parallel sides and "h" is the height of the trapezoid.

In this case, the lengths of the parallel sides are 20 + 6 = 26 inches and 14 inches, and the height of the trapezoid is not given. However, we can find the height by using the given angle of 60 degrees.

To find the height, we can draw a perpendicular line from one of the parallel sides to the other, forming a right triangle. The given angle of 60 degrees is opposite the side with length 14 inches. Using trigonometry, we can determine the height:

height = 14 * sin(60) = 14 * (√3/2) = 7√3 inches.

Now we can substitute the values into the area formula:

Area = (1/2) * (26 + 14) * (7√3)

= (1/2) * 40 * (7√3)

= 20 * (7√3)

= 140√3 square inches.

Therefore, the area of the trapezoid is 140√3 square inches, in simplest radical form.

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The null and alternative hypotheses for the medical trial can be stated as follows:

The null hypothesis assumes that there is no difference in the mean cholesterol levels, i.e., μ - μ' = 0, while the alternative hypothesis states that there is a reduction of 25%, i.e., μ - μ' = 0.25μ.

To perform the hypothesis test, we would collect a sample of individuals who have taken the supplement, measure their cholesterol levels before and after, and then analyze the data using appropriate statistical methods. Depending on the specifics of the study, we could use techniques such as a paired t-test or a confidence interval for the difference in means.

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Answer:

a. Yes it's correct, reasons;

I) let x=1, f(1)=2^1=2, g(x)=1^2=1 this proves that when a higher number is used the value of f(x) will be higher than g(x).

ii) As x approaches zero f(x) approaches 1, but g(x) approaches 0. Which will make the rate at which the graph of f(x) increase be faster than g(x)

b. f(x) has an infinite degree but g(x) has a finite degree of 2.

Mandy's home computer system is expected to be worth $1,576.11.

Mandy's home computer system is expected to depreciate at a rate of 10% per year. After 1 year, the value of the computer system will be 90% of its original value.

After 2 years, it will be worth 90% of that value, or 0.9 × 0.9 = 0.81 times the original value. Continuing in this way, we can write the value of the computer system after n years as \(0.9^n\) times its original value. Thus, after 9 years, the computer system will be worth \(0.9^n\) times its original value:

Value after 9 years = 4995 × \(0.9^n\)

Using a calculator, we find that the value is approximately $1,576.11 when rounded to the nearest hundredth. Therefore, after 9 years, Mandy's home computer system is expected to be worth $1,576.11.

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The solutions to the quadratic equation x² = -7x - 8 are x equals  \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Given the quadratic equation in the question:

x² = -7x - 8

To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.

x² = -7x - 8

x² + 7x + 8 = 0

a = 1, b = 7 and c = 8

Plug these into the quadratic formula: ±

\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)

Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

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The solution of the recurrence relation is \(a_n=3.2^n\)

For given question,

We have been given a recurrence relation \(a_n = 2a_{n-1}\) for n ≥ 1

and an initial condition \(a_0=3\)

Let \(a_n\) = m², \(a_{n-1}\) = m and \(a_{n-2}\) = 1

So from given recurrence relation we get an characteristic equation,

⇒ m² = 2m

⇒ m² - 2m = 0                     .........( Subtract 2m from each side)

⇒ m(m - 2) = 0                     .........(Factorize)

⇒ m = 0    or  m - 2 = 0

⇒ m = 0   or   m = 2

We know that the solution of the recurrence relation is then of the form

\(a_n=\alpha_1 {m_1}^n + \alpha_2 {m_2}^n\)  where \(m_1,m_2\) are the roots of the characteristic equation.

Let, \(m_1\) = 0   and \(m_2\) = 2

From above roots,

\(\Rightarrow a_n=\alpha_1 {0}^n + \alpha_2 {2}^n\\\\\Rightarrow a_n=0+\alpha_2 {2}^n\\\\\Rightarrow a_n=\alpha_2 {2}^n\)

For n = 0,

\(\Rightarrow a_0=\alpha_2 {2}^0\\\\\Rightarrow a_0=\alpha_2 \times 1\\\\\Rightarrow a_0=\alpha_2\)

But  \(a_0=3\)

This means \(\alpha_2=3\)

so, the solution of the recurrence relation would be \(a_n=3.2^n\)

Therefore, the solution of the recurrence relation is \(a_n=3.2^n\)

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Answer:

At the given rate, the hot air balloon can travel 9/2 or 4.5 miles in 3/4 of an hour

Step-by-step explanation:

We can solve this problem one of two ways:  

The first ways seems the most straight forward, while the second ways helps you confirm your answer, as I'll show at the end:

\(\frac{18}{3}=\frac{d}{3/4} \\\\27/2=3d\\9/2=d\\4.5=d\)

We can check our answer by first finding the rate at which the hot air balloon travelled 18 miles using the distance-rate-time formula, which is

d = rt, where d is the distance, r is the rate, and t is the time:

18 = 3r

6 = r

Now, we can check whether the product of the rate (6 mph) and the second time (3/4 hr) equals the second distance (9/2 mi)

9/2 = 6 * 3/4

9/2 = 9/4

9/2 = 9/2

Answer:

OPTION A

SEE IMAGE FOR SOLUTION

Hope it helps

Have a great day

Answer:

People surveyed: 79

a) p(s) = 46/79

b) p(snv) = 13/79

c) p(suv) = 96/79

hope this helps, and tell me if you get it right! It's prob wrong though, im bad at venn diagrams (×_×)⌒☆

Step-by-step explanation:

Factor of 54

\( = 2 \times 3 \times 3 \times 3\)

Factor of 81

\( = 3 \times 3 \times 3 \times 3\)

Now ...

Common factor = 3 × 3 × 3

= 27

LCM = common factor × remaining factors..

= 27 × 2 × 3

= 162