An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 3 tan(3θ) − 1 = 0 (b) Find the solutions in the interval [0, 2π).

Answer:

  3y - 5 + 2y = 7

Step-by-step explanation:

Subtracting 5 from the second equation gives ...

  x = 3y -5

Using the expression on the right for x in the first equation gives ...

  x + 2y = 7 . . . . . . . . first equation

  (3y -5) +2y = 7 . . . . with expression substituted for x

  3y - 5 + 2y = 7 . . . . with parentheses removed

let's say "x" is the whole lot and thus the 100%.

we know 12 is 60%, how much is "x" or 100%?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 12&60 \end{array}\implies \cfrac{x}{12}=\cfrac{100}{60}\implies \cfrac{x}{12}=\cfrac{5}{3} \\\\\\ 3x=60\implies x=\cfrac{60}{3}\implies x=20[/tex]

Answer:

no solutions

Step-by-step explanation:

-2x+3y=8

 2x-3y=10

We can use elimination to solve for x and y

Add the two equations together

-2x+3y=8

 2x-3y=10

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

0 = 18

Since this is never true, there are no solutions to this system of equations

The domain of all three functions is all real numbers. The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The statements that accurately compare the domain and range of the functions are:

For the functions f(x) = 3x^2, g(x) = 1/3x, and h(x) = 3x:

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Answer:c and d

Step-by-step explanation:

i got it right

Expand:

[tex]n(n-1)-(n+3)(n+2)=(n^2-n)-(n^2+5n+6)=-6n-6[/tex]

Then we can write

[tex]n(n-1)-(n+3)(n+2)=6\boxed{(-n-1)}[/tex]

which means [tex]6\mid n(n-1)-(n+3)(n+2)[/tex] as required.

Answer:

b

Step-by-step explanation:

To find the distance between two points on a coordinate system, we can use the distance formula, which is derived from the Pythagorean theorem.

To find the distance between two points on a coordinate system, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the given points (-3,4) and (8,-7), we can plug in the coordinates into the formula:

d = sqrt((8 - (-3))^2 + (-7 - 4)^2)

Simplifying the equation, we get:

d = sqrt(11^2 + (-11)^2)

Finally, calculating the square root, we find that the distance between the two points is sqrt(242), which is approximately 15.56 units.

Thus, the distance on the coordinate system from the point (-3,4)to the point (8,-7) is fond to be 15.56 units.

Answer:

No. Anna is incorrect.

Step-by-step explanation:

In order to find if the answer is right, just find the diagonals using the pythogorean theorem.

a² + b² = c²

For the rectangle, the base is 14 and the height is 7. We will have to find the hypotenuse.

14² + 7² = c²

196 + 49 = c²

245 = c²

c = √245

c = √49 × √5

c = 7√5

For the square, the base is 7 and the height is 7. We will have to find the hypotenuse.

7² + 7² = c²

49 + 49 = c²

98 = c²

c = √98

c = √49 × √2

c = 7√2

Now compare :

7√5 and 7√2

Clearly, 7√5 is not the double of 7√2

Answer:

c. {(4, -12)}

Step-by-step explanation:

It is convenient to rearrange the equation to standard form:

5x +y = 8

Then check the offered points.

(6, -11): 5·6 -11 = 19 ≠ 8

(4, -12): 5·4 -12 = 8 . . . . . . this is in the solution set

(5, -9): 5·5 -9 = 16 ≠ 8

(3, -14): 5·3 -14 = 1 ≠ 8

To find the solution set, substitute the x and y values into the equation and check if it is true.

To find the solution set for the equation, we need to check which coordinates from the replacement set satisfy the equation y = -5x + 8.

The solution set for the equation, given the replacement set, is {(3, -14)}.

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Explanation:

Multiply it out, collect terms, and look for a factor of 7:

  n(n +2) -(n -7)(n -5) = n² +2n -(n² -12n +35)

  = 14n -35

  = 7(2n -5)

The expression has a factor of 7, so is divisible by 7 with a resulting quotient of 2n-5.

If both Bob and Fred make $20 less a week than twice John's weekly salary, then

[tex]B+F+20 = 2*J[/tex],

where B, F, and J are Bob's, Fred's, and John's salaries, respectively.

We want to find F, Fred's salary. Plugging in Bob's and John's salaries, we obtain

[tex]140+F+20 = 2*110[/tex]

[tex]F+160 = 220[/tex]

[tex]F = 60[/tex]

So Fred makes $60 a week.

Answer:

Fred makes $60/week.

Step-by-step explanation:

Fred makes f dollars per week, john j dollars and bob b dollars.

Then b = $140/week; j = $110/week; and b + f = 2j - 20.

Substitute $140/week for b in this equation; also substitute $110/week for j.  Then:  

    $140/week + f = 2($110) - $20.  There's only one variable here, f, so we're ready to solve for f:

    $140/week + f = $220/week - $20/week,   or:

     $140/week + f = $200/week

Subtract $140 from both sides, obtaining:

f = $60

Fred makes $60/week.

The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.

What is a point Estimate?

A) In order to find the point estimate of the mean, we will add up the data and divide it by the number of values.

Here,

∑x = 57 + 61 + 86 + 74 + 72 + 73 + 20 + 57 + 80 + 79 + 83 + 74

    = 816

n = 12 numbers

Thus;

Mean = ∑x/n

         = 816/12

Mean = 68

B) In order to find the estimate of the standard deviation, we have the formula;

s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]

∑x² = 57² + 61² + 86² + ... + 74²

     = 59,010

s = √[ (12*(59,010) - (816)²)/(12)(11)]

s = 17.6

Hence, The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.

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Answer:

a) starting height: 5.5 ft

b) hang time: 5.562 seconds

c) maximum height: 126.5 ft

d) time to maximum height: 2.75 seconds

Step-by-step explanation:

a) The starting height is the height at t=0.

h(0) = -16·0 +88·0 +5.5

h(0) = 5.5

The starting height is 5.5 feet.

__

b) The ball is in the air between t=0 and the non-zero time when h(t) = 0. We can find the latter by solving ...

-16t^2 + 8t +5.5 = 0

t^2 -(11/2)t = 5.5/16 . . . . . subtract 5.5, then divide by -16

t^2 -(11/2)t +(11/4)^2 = (5.5/16) +(11/4)^2 . . . . complete the square

(t -11/4)^2 = 126.5/16 . . . . . . . . . . . . . . . . . . . . call this [eq1] for later use

t -11/4 = √7.90625

t = 2.75 +√7.90625 ≈ 5.562

The ball will be in the air about 5.562 seconds.

__

c) If we multiply [eq1] above by -16 and add the constant on the right, we get the vertex form of the height equation:

h(t) = -16(t -11/4) +126.5

The vertex at (2.75, 126.5) tells us ...

The maximum height of the ball is 126.5 feet.

__

d) That same vertex point tells us ...

The maximum height will be reached at t = 2.75 seconds.

_____

If you really need answers fast, a graphing calculator can give them to you in very short order (less than a minute).

Answer:

y = 2x+3

Step-by-step explanation:

The slope is "what happens to the graph when you move one unit to the right in x-direction". As you can check, if you move 1 to the right, the y value increases by 2. Therefore the slope is 2.

The intercept is the graph's y value when x=0, ie., when it passes the y axis. This is at y=3.

Now we have our two ingredients, so y = slope * x + intercept, so 2x+3

Answer:

Last option

−1 • f(x)

Step-by-step explanation:

The function [tex]f(x) = (0.5) ^ x[/tex] passes through point (-1, 2) because:

[tex]f(-1) = (0.5) ^ {-1}= \frac{1}{(0.5)} = 2[/tex]

and also goes through the point (0, 1)

Because:

[tex]f(0) = (0.5)^0 = 1[/tex]

Then, if the transformed function passes through the point (0, -1) and passes through the point (-1, -2) then this means that the graph of [tex]f(x) = (0.5) ^ x[/tex] reflected on the axis x. This means that if the point [tex](x_0, y_0)[/tex] belongs to f(x), then the point [tex](x_0, -y_0)[/tex] belongs to the transformed function

The transformation that reflects the graph of a function on the x-axis is.

[tex]y = cf(x)[/tex]

Where c is a negative number. In this case [tex]c = -1[/tex]

Then the transformation is:

[tex]y = -1*f(x)[/tex]

and the transformed function is:

[tex]f (x) = - (0.5) ^ x[/tex]

Answer:

f(x) -2 is the correct answer.

Step-by-step explanation:

Just took the test!

Answer:

9

Step-by-step explanation:

If n is the number of tablets, the maximum value it can have is given by ...

0.25n = 2.25

Dividing by the coefficient of n gives ...

n = 2.25/0.25 = 9

The patient can take a total of 9 tablets through the day.

Answer:

The answer is 2:9

Step-by-step explanation:

On plato

Answer:

  x ∈ {-26, 22}

Step-by-step explanation:

A graph shows that the points (-26, -27) and (22, -27) lie on a circle of radius 40 centered at (-2, 5). That is, if Q is either one of these points, the vector PQ will have a length of 40:

You can call it -40 if you like, but you have to define what negative length means when you do that.

For this case we have the following equation:

[tex]x ^ 3 = 375[/tex]

We must find the value of "x":

We apply cube root on both sides of the equation to eliminate the exponent:

[tex]x = \sqrt [3] {375}[/tex]

We can write 375 as [tex]5 ^ 3 * 3[/tex]

So:

[tex]x = \sqrt [3] {5 ^ 3 * 3}\\x = 5 \sqrt [3] {3}[/tex]

Then, the correct options are:

[tex]x = \sqrt [3] {375}\\x = 5 \sqrt [3] {3}[/tex]

Answer:

Option A and B

Step 4

The numerator of this fraction is right because there are 5 shaded sections, but the denominator is incorrect because there are 6 total boxes, not 5.

Hope this helps!!

Answer:

the answer is C step 3

Step-by-step explanation:

because out side the box said 1/2 when its 3/6 and the question sais

In which step did her first error occur? so thats the firt the second one

its 1/3 when its 2/6. Hope it helps :)

Answer:

x = 0

Step-by-step explanation:

Since the product is not equal zero, we need to multiply both parenthesis first:

[tex](x-3)(x+9) =-27[/tex]

[tex]x*x+x*9+(-3)*x+(-3)*9=27[/tex]

[tex]x^2+9x-3x-27=27[/tex]

[tex]x^2+6x-27=27[/tex]

Add 27 from both sides:

[tex]x^2+6x-27+27=-27+27[/tex]

[tex]x^2-6x=0[/tex]

Factor [tex]x[/tex] out:

[tex]x(x+6)=0[/tex]

Apply the zero product:

[tex]x=0,x+6=0[/tex]

[tex]x=0,x=-6[/tex]

The solutions of the equation are [tex]x=0[/tex] and [tex]x=-6[/tex].

We can conclude that the correct answer is x = 0.

Answer:

C: x = 0

There is no solution.

For this case we have the following inequality:[tex]d> 11[/tex]

Assuming that "d" is the variable that represents the number of hours worked by Mo during this week, we have that the hours were greater than 11, according to the inequality sign.

So, the correct option is:

Mo worked more than 11 hours this week.

Answer:

Option A

Answer: a

Step-by-step explanation:

Answer:

20 ft out from the wall by 40 ft parallel to the wall

Step-by-step explanation:

Let x represent the length of fence in the direction parallel to the wall. Then the other dimension of the rectangular pen is (80 -x)/2. The area is the product of these dimensions:

area = x(80 -x)/2

This function describes a downward-opening parabola with zeros at x=0 and x=80. The vertex (maximum) is halfway between the zeros, at x=40.

The dimensions are 40 ft parallel to the wall and 20 ft out from the wall.

Length l=40 and Breadth b=20 will maximize the area of the pen.

let us take 'l' as the length of the rectangular pen.

'b' as the width of the rectangular pen.

let us assume that the barn will be built opposite to length.

so, according to the given condition

l +b+b=80

l+2b=80......(1)

area of the rectangular pen = lb= (80-2b)b

f(b)= (80-2b)b.......(2)

to get local maxima, differentiate the function and equate to zero, get the point say it 'x'

again check double derivative if its value is negative the point 'x' will give the maximum value of the function.

to maximize the area

let us derivate the f(b)= (80-2b)b

f'(b)= 80-4b=0

b=20

f"(b)= -4(-ve)

means we will have local maxima at b=20

it means at b=20, we will get maximum area.

l = 80-2b=80-2*20=40

therefore, l=40 and b=20 will maximize the area of the pen.

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Answer:

f(x) = 9(x -1/3)^2 -3

Step-by-step explanation:

In vertex form the equation of a quadratic with vertical scale factor "a" and vertex (h, k) is ...

y = a(x -h)^2 +k

To make the equation have (1, 1) as a solution, we need to find the value of "a". We can put the point coordinates in the equation and solve for "a":

1 = a(1 -1/3)^2 -3 . . . . . for (h, k) = (1/3, -3) as given

1 = (4/9)a -3 . . . . simplify

4 = (4/9)a . . . . . . add 3

9 = a . . . . . . . . . . multiply by 9/4

The quadratic function you desire is ...

f(x) = 9(x -1/3)^2 -3

Answer:

  3.5 years

Step-by-step explanation:

Each year, Louis earned

  $1500×0.035 = $52.50

in interest.

The amount of interest that had been credited to his account at the time of withdrawal was ...

  $1683.75 -1500.00 = $183.75

Then the length of time the money had been in the account was ...

  $183.75/($52.50/yr) = 3.5 yr

_____

Comment on the problem

We have assumed the account earned simple interest. Given the neatness of the answer, we believe that to be a correct assumption.

Answer:

Already in standard form

Step-by-step explanation:

-4y=10

-4y= by

10= c

And in this case ax=0x, so it will not show up in the equation

0x-4y=10, which is already in standward form

-4y=10 divide both sides by -2, so 2y=5 subtract 5 from both sides,

2y-5=0

Find the points of Midtown and Downtown then use the midpoint formula.

Midtown = (6,12)

Downtown = (12,4)

Midpoint = X2+X1 /2 , Y2+Y1 /2

Midpoint = 12+6 /2 , 4+12 /2

Midpoint = 18/2 , 16,2

Midpoint = (9,8)

Answer:

68

Step-by-step explanation:

∠DPG and ∠EPF are vertical angles, so they are equal.

7x = 4x + 48

3x = 48

x = 16

So ∠DPG is:

∠DPG = 7x

∠DPG = 112

∠DPE and ∠DPG are supplementary, so they add up to 180:

∠DPE + ∠DPG = 180

∠DPE + 112 = 180

∠DPE = 68

Area of rectangles = Length x width.

Area of triangles = 1/2 x base x height.

1 face is 12 x 10 = 120 square units

1 face is 12 x 8 = 96 square units

1 face is 12 x 6 = 72 square units

And 2 faces are 1/2 x 8 x 6  = 24 square units

Answers are 24 , 72 and 96 square units.

Answer:

A.24 Square units

C.72 Square units

D.96 Square units

Step-by-step explanation:

I got it right edge 2020.

Answer:

Step-by-step explanation:

So we need to balance two things here.  The overall volume, and the amount of hydrochloric acid.

Let's say x is the volume of the 12% solution and y is the volume of the 6% solution.

The sum of the volumes equals the total volume:

x + y = 24

And the sum of the amounts is the total amount:

0.12 x + 0.06 y = 0.09 (24)

We now have two equations and two variables.  We can solve this system of equations with either substitution or elimination.  Using substitution:

x = 24 - y

0.12 (24 - y) + 0.06 y = 0.09 (24)

2.88 - 0.12 y + 0.06 y = 2.16

0.72 = 0.06 y

y = 12

x = 24 - 12 = 12

So she needs to mix 12 ounces of 12% solution with 12 ounces of 6% solution to get 24 ounces of 9% solution.

The amount of 12% solution and the amount of 6% solution Doreen Schmidt should mix to obtain 9% hydrochloric acid solution is 12 ounces each.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the amount of 12% solution needed to be mixed be represented by x, while the amount of 6% solution needed to be mixed be represented by y.

Now, since the total amount of solution needed to be made is 24 ounces, therefore, an equation can be formed as,

x+y=24

Solve the equation of x,

x=24 - y

Also, the total concentration of the combined should be 9%, therefore, we can write,

(12% of x) + (6% of y) = 9% of 24

0.12x + 0.06y = (0.09×24)

Substitute the value of x,

0.12(24-y) + 0.06y = 2.16

2.88 - 0.12y + 0.06y = 2.16

y = 12 ounces

substitute the value of y in the equation of x,

x = 24 - y

x = 24 - 12

x = 12

Hence, the amount of 12% solution and the amount of 6% solution Doreen Schmidt should mix to obtain 9% hydrochloric acid solution is 12 ounces each.

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The p-value is 0.0768. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

- Decision regarding H0: Reject H0

- p-value: 0.0768.

The null hypothesis (H0) states that the mean waiting time is 3 minutes or more, while the alternate hypothesis (H1) states that the mean waiting time is less than 3 minutes.

- Null hypothesis (H0): μ ≥ 3

- Alternate hypothesis (H1): μ < 3

The decision rule is to reject H0 if the test statistic (z-score) is less than -1.645.

To compute the test statistic (z-score), we use the formula:

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

Where:

- [tex]\(\bar{x}\)[/tex] is the sample mean waiting time (2.75 minutes)

- [tex]\(\mu\)[/tex] is the population mean waiting time (3 minutes)

- [tex]\(\sigma\)[/tex] is the population standard deviation (1 minute)

- [tex]\(n\)[/tex] is the sample size (50)

Substituting the given values:

[tex]\[ z = \frac{{2.75 - 3}}{{\frac{1}{\sqrt{50}}}} \][/tex]

[tex]\[ z = \frac{{-0.25}}{{0.1414}} \][/tex]

[tex]\[ z ≈ -1.768 \][/tex]

Since -1.768 is less than -1.645, we reject the null hypothesis.

To find the p-value, we look up the z-score (-1.768) in the standard normal distribution table. The corresponding area to the left of -1.768 is approximately 0.0384. Since this is a one-tailed test, we multiply by 2 to get the total probability of both tails:

[tex]\[ p-value ≈ 2 \times 0.0384 = 0.0768 \][/tex]

Thus, the p-value is 0.0768. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

Complete questions:

The waiting time for customers at MacBurger Restaurants follows a normal distribution with a population standard deviation of 1 minute. At the Warren Road MacBurger, the quality-assurance department sampled 50 customers and found that the mean waiting time was 2.75 minutes. At the 0.05 significance level, can we conclude that the mean waiting time is less than 3 minutes? State the null hypothesis and the alternate hypothesis. State whether the decision rule is true or false: Reject H0 if z < −1.645. True False Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? Reject H0 Do not reject H0 What is the p-value? (Round your answer to 4 decimal places.)