Ali and Baba discovered an underground palace and set out to map all the treasure in it. After carefully mapping the interior, they found that the palace had a vault filled with treasure chests. In each chest, they found either 7 gold bars or 11 silver bars. There were 90 bars in total. How many of them were gold bars?

The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

Herein we have a simple harmonic motion model represented by a sinusoidal expression of the form y(t) = A · sin (C · t) + B · cos (C · t), which must be transformed into its canonical form, that is, y(t) = A' · sin (C · t + D). We proceed to perform the procedure by algebraic and trigonometric handling.

The amplitude of the canonical function is determined by the Pythagorean theorem:

A' = √(2² + 5²)

A' = √ 29

The angular frequency C  is the constant within the trigonometric functions from the non-canonical formula:

C = 4π

Then, we find the initial position of the weight in time: (t = 0)

y(0) = 2 · sin (4π · 0) + 5 · cos (4π · 0)

y(0) = 5

And now we calculate the angular phase below: (A' = √ 29, C = 4π, y = 5)

5 = √ 29 · sin (4π · 0 + D)

5 / √ 29 = sin D

D ≈ 0.379π rad

The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .

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The graph that models the pH of this solution is graph A.

It should be noted that a graph is a diagram such as a series of one or more points, lines, line segments, curves, or areas which represents the variation of a variable in comparison with that of one or more other variables.

The pH is a measure of how acidic or basic water is. It should be noted that the range goes from 0 - 14, with 7 being neutral. The pHs of less than 7 indicate acidity, while a pH of greater than 7 indicates a base. The pH is really a measure of the relative amount of free hydrogen and hydroxyl ions that are in the water.

In this case, x represents the concentration of the hydrogen ions. The first graph illustrates this.

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Complete question:

The ph of a particular solution is given by pH=-log(x-2) where x represents the concentration of the hydrogen ions in the solution in moles per liter. Which graph models the ph of this solution?

Answer:

[tex]\{x=\frac{19-\sqrt{409} }{2}\ , \ x=\frac{19+\sqrt{409} }{2}\}[/tex]

Step-by-step explanation:

x² = 19x + 12

⇔ x² - 19x - 12 = 0

Calculating the discriminant :

b² - 4ac = (-19)² - 4×1×(-12) = 409

The discriminant is positive ,then the equation has two solutions.

[tex]x=\frac{19-\sqrt{409} }{2} \ \ or\ \ x=\frac{19+\sqrt{409} }{2}[/tex]

Answer:

-12

Step-by-step explanation:

First, solve in parentheses.

2(-2-4)

=

2(-6)

Next, multiply 2 by -6.

Which equals -12.

So therefore using the distributive property shown above, the answer would be -12.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the distributive formula?}[/tex]

[tex]\mathsf{a(b + c)}[/tex]

[tex]\mathsf{= a(b) + a(c)}[/tex]

[tex]\mathsf{= ab + ac}[/tex]

[tex]\huge\textbf{What is the equation?}[/tex]

[tex]\mathsf{2(-2 - 4)}[/tex]

[tex]\huge\textbf{What are we simplifying?}[/tex]

[tex]\mathsf{2(-2 - 4)}[/tex]

[tex]\mathsf{= 2(-2) + 2(-4)}[/tex]

[tex]\mathsf{= -4 - 8}[/tex]

[tex]\mathsf{= -12}[/tex]

[tex]\huge\textbf{How are you going to translate to}\\\\\huge\textbf{easier terms?}[/tex]

[tex]\mathsf{2(-2 - 4)}[/tex]

[tex]\mathsf{= 2(-6)}[/tex]

[tex]\mathsf{= -12}[/tex]

[tex]\huge\textbf{What is the ANSWER to the question?}[/tex]

[tex]\huge\boxed{\mathsf{-12}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

8 minutes.

Step-by-step explanation:

We work in fractions of the wall they can paint in 1 minute, so

1/12 + 1/24 = 1/x  where x is the time it takes when working together.

Multiplying through by 24x:

2x + 1x = 24

3x = 24

x = 8 minutes.

The midpoint of co-ordinate is (5, 6)

Add both "x" coordinates, and divide by 2.

Add both "y" coordinates, and divide by 2.

Given that;

Coordinates of A = (2,3)

Coordinates of B = (8,9)

Find:

Midpoint of co-ordinate

Computation:

Midpoint of co-ordinate = [(x1 + x2) / 2], [(y1 + y2) / 2]

Midpoint of co-ordinate = [(2 + 8) / 2], [(3 + 9) / 2]

Midpoint of co-ordinate = [10 / 2], [12 / 2]

Midpoint of co-ordinate = (5, 6)

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Answer:

Total cost is $177.50.

Step-by-step explanation:

Rackets:

Divide the cost for racket by 6 to find the cost per racket.

186÷6=31

Multiply 31 by 5 to find the cost for 5 rackets.

31×5=155

$155

Tubes of balls:

Divide 27 by 6 to find the cost per a tube of balls.

27÷6=4.50

Multiply 4.50 by 5 to find the cost for 5 tubes of balls.

4.50×5=22.50

$22.50

Add the amounts for rackets and tubes of balls to find the total cost.

155+22.50=177.50

The total cost is $177.50.

Hope this helps!

Answer:

x intercepts: (1,0), (-3,0)

the roots are 1 and -3

Step-by-step explanation:

Using the Quadratic Formula:

x=−b±sqrt(b2−4ac)/2a

Substitute:

x= -8±sqrt(8^2-4(4)(-12))/2(4)

x=-8±sqrt((64- -192))/8

x=-8±sqrt(256)/8

Solve two equations (±)

x=-8±16/8

x=8/8  and x=-24/8

x=1 and x=-3

Answer:

x = -3

x = 1

Step-by-step explanation:

Hello!

We can solve the quadratic by Factoring the Equation and using the Zero Product Property.

We want to find two numbers that multiply out to -3, but add up to 2. The numbers that work are -1 and 3. We can expand 2x to -x and 3x and factor by grouping.

Set each factor to 0 and solve for x in both.

Therefore, the x-interecpts are -3 and 1.

Answer:

x=12

Step-by-step explanation:

x^9=12^9

power of 9 cancel eachother at both sides of equation.

so

x=12

Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 6) ← 2 points on the line

m = [tex]\frac{6-0}{0-(-3)}[/tex] = [tex]\frac{6}{0+3}[/tex] = [tex]\frac{6}{3}[/tex] = 2

The amount of money Kim, maneet and Sutopa have is $115.6, $97.6 and $73.2 respectively.

x + (x - 18) + 3/4(x-18) = 286.40

x + x - 18 + 3/4x - 13.5 = 286.40

2 3/4x = 286.40 + 13.5 + 18

11/4x = 317.9

x = 317.9 ÷ 11/4

= 317.9 × 4 / 11

= 1,271.6 / 11

x = $115.6

So,

Kim = x

= $115.6

Maneet = x - 18

= 115.6 -18

= $97.6

Sutopa = 3/4(x-18)

= 3/4(97.6)

= $73.2

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The time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.

We assume the minutes taken by Millie to catch up with Ben to be x minutes.

The number of words Ben has already typed = 180.

The unit rate for Ben for the typing of words = 30 per minute.

Therefore, words typed by Ben in x minutes = 30x words.

Therefore, the total number of words typed by Ben = 180 + 30x words.

The number of words Millie has already typed = 60.

The unit rate for Millie for the typing of words = 50 per minute.

Therefore, words typed by Millie in x minutes = 50x words.

Therefore, the total number of words typed by Millie = 60 + 50x words.

As Millie needs to catch up with Ben after x minutes, the total number of words typed by them needs to be equal, that is, 60 + 50x = 180 + 30x, which is the required linear equation in one variable.

To find the minutes taken by Millie to catch up with Ben, we solve this linear equation in one variable as follows:

60 + 50x = 180 + 30x,

or, 60 + 50x - 30x = 180 + 30x - 30x {Subtracting 30x from both sides},

or, 60 + 20x = 180 {Simplifying},

or, 60 + 20x - 60 = 180 - 60 {Subtracting 60 from both sides},

or, 20x = 120 {Simplifying},

or, 20x/20 = 120/20 {Dividing both sides by 20},

or, x = 6 {Simplifying}.

Thus, the time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.

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The approximate wage of someone with 0 years of experience is -4.64

The dataset of wages is

Wages = 8, 20, 10, 12, 16, 14

The mean is calculated as:

Mean = Sum/Count

This gives

Mean = (8+ 20+ 10+ 12+ 16+ 14)/6

Mean = 13.33

The variance is

Variance = ∑(x- mean)²/n-1

This gives

Variance = [(8 - 13.33)^2 + (20 - 13.33)^2 + (10 - 13.33)^2 + (12 - 13.33)^2 + (16 - 13.33)^2 + (14 - 13.33)^2]/5

Evaluate

Variance = 18.67

The standard deviation is

Standard deviation = √Variance

This gives

Standard deviation = √18.67

Evaluate

Standard deviation = 4.32

The dataset of experience is

Wages = 1, 10, 2, 4, 4, 6

The mean is calculated as:

Mean = Sum/Count

This gives

Mean = (1+ 10+ 2+ 4+ 4+ 6)/6

Mean = 4.5

The variance is

Variance = ∑(x- mean)²/n-1

This gives

Variance = [(1 - 4.5)^2 + (10 - 4.5)^2 + (2 - 4.5)^2 + (4 - 4.5)^2 + (4 - 4.5)^2 + (6 - 4.5)^2]/5

Evaluate

Variance = 10.3

The standard deviation is

Standard deviation = √Variance

This gives

Standard deviation = √10.3

Evaluate

Standard deviation = 3.21

See attachment for the scatter plot and the straight line that best fits the data points.

The equation of the straight line is

y = 0.69x - 4.64

The approximate wage of someone with 0 years of experience is

y = 0.69 * 0 - 4.64

Evaluate

y = -4.64

Hence, the approximate wage of someone with 0 years of experience is -4.64

This is calculated as:

Cov(x,y) = ∑(x - x mean)(y - y mean)/N - 1

So, we have:

Cov(x,y) = [(8 - 13.33) * (1 - 4.5) + (20 - 13.33)*(10 - 4.5) + (10 - 13.33)*(2 - 4.5) + (12 - 13.33)*(4 - 4.5) + (16 - 13.33)*(4 - 4.5) + (14 - 13.33)*(6 - 4.5)]/5

Evaluate

Cov(x,y) = 12.80

Hence, the covariance of wages and experience is 12.80

Is this consistent with the line you drew in part c?

Yes it is

Here, we use a graphing calculator.

From the graphing calculator, we have:

r = 0.9231

Hence, the correlation of wages and experience is 0.9231

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Answer:

Maybe this could help?

Answer:

[tex]T_{23}=-153[/tex]

Step-by-step explanation:

[tex]T_{23}=a+(n-1)d\\[/tex]

[tex]=a+(23-1)d=a+22d[/tex]

Now [tex]a=-21[/tex] and

[tex]d=-27-(-21)\\=-6[/tex]

So [tex]T_{23}==21+((22)6\times-1)[/tex]

[tex]=-153[/tex]

Answer: 7

Step-by-step explanation:

By the triangle proportionality theorem,

[tex]\frac{?}{21}=\frac{3}{9}\\\\?=7[/tex]

The area of the shaded region is 502.4 ft^2

The area of a circle is the space occupied by a circle in a two-dimensional plane. Alternatively, the space taken up inside the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, etc. Area of a circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. It is a special mathematical constant.

It is given that inner diameter is 36 ft and width of the ring is 4 ft

We need to find the area of the shaded region

diameter of outer ring= d1=36+4+4 = 44 ft ,

diameter of inner ring= d2=36 ft,

r1=d1/2= 44/2 = 22 ft , r2=d2/2 = 36/2 = 18 ft

Area of shaded region = Area of Outer circle - Area of inner circle

= π r1^2 - π r2^2

= π ( 22^2 - 18^2 )

= 3.14 * 160

= 502.4 ft^2

Hence the area of the shaded region is 502.4 ft^2

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The area of the shaded region is 502.4 sq. ft.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space.

According to the question,

Diameter of inner circle = 36 ft.

Radius of inner circle = 36/2 ft. =18 ft.

As the width of the ring is 4 ft. , the diameter of the outer circle = 36+4+4= 44 ft.

Radius of outer circle = 22 ft.

Area of the shaded region = Area of outer circle - Area of inner circle

                                              = π(22)(22) - π(18)(18)

                                              = π(484 - 324)

                                              = 3.14 * 160

                                              = 502.4 sq. ft.

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The biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.

The trophic level of an organism is the position it occupies in a food web. The trophic level of an organism is the number of steps it is from the start of the chain.

Below are the list of the trophic levels:

The biotic factors of an ecosystem are arranged in feeding levels known as trophic levels.

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 The range of the function f(x) = 2x² -7 with domain: x = {-4, -2, 0, 3} is y = (25, 1, -7, 11). Option D is the correct answer.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we substitute an x value, this set of values is what the function outputs. The y values are those.

In light of the query

x VS F(x) = 2x² -7

-4     F(4) = [tex]2(-4)^2 -7[/tex] = 25

-2     F(-2) = [tex]2(-2)^2 -7[/tex] = 1

0      F(0) = [tex]2(0)^2 -7[/tex] = -7

3      F(3) = [tex]2(3)^2 - 7[/tex] = 11

∴ Option D, y = (25, 1, -7, 11)

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Answer:

5040 ways

Step-by-step explanation:

here we need to find the number of permutations of the 7 balls :

= 7!

= 7×6×5×4×3×2×1

= 5 040

Answer:

Shark

Step-by-step explanation:

They have gills,scales,swim bladders to float,most produce eggs and also in ectothermic.

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

Further explanation:

Answer:

[tex]a=\sqrt{40.768}[/tex]

Step-by-step explanation:

Given a leg and a hypotenuse we can find the third side by substituting the known values using Pythagorean theorem, let the unknown be a.

[tex]a^2+3.24^2=7.16^2[/tex]

Now all we must do is solve for a:

[tex]a^2+3.24^2=7.16^2\\a^2+10.4976=51.2656\\a^2=40.768\\a=\sqrt{40.768}[/tex]

Answer:

Gavin has 19 nickels & 114 quarters

Step-by-step explanation:

N : D : Q

1 : 3 : 6 = 57

x : 57 : y

57 / 3 = 19

1 x 19 : 3 x 19 : 6 x 19

19 : 57 : 114

Answer:

The equation is ×=-3

Step-by-step explanation:

Let x be the number

Difference between a number tines 3 and 6 is 9

3x-6x=9

-3x=9

x=-3

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The values of x is 1 and 6.

According to the statement

we have two tangents which are represented by x+5 and x+1 then

we have to find the value of x to get the perfect value of tangent

so, due to interior values of tangent they are equal to each other but in opposite sign.

But here we have to find the value of x one by one.

It means

Here we take interior value of tangent and exterior value of tangent equal to each other

So, the equations become are written below

X+5= 6 then x = 1

X+1= 7 then x = 6

So, The values of x is 1 and 6.

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The mean height of plants is 44.07cm.

Given that a raj measures the height of 70 plants which is shown in the table in the image attached below.

The mean is defined as the mean value equal to the ratio of the total number of a given set of values ​​to the total number of values ​​contained in that set.

Firstly, we will find the midpoint of the height by using the formula

(upper limit +lower limit)/2

When h is 10<h<20 then the midpoint is

x₁=(10+20)/2

x₁=15

When h is 20<h<0 then the midpoint is

x₂=(20+40)/2

x₂=30

When h is 40<h<50 then the midpoint is

x₃(40+50)/2

x₃=45

When h is 50<h<60 then the midpoint is

x₄=(50+60)/2

x₄=55

When h is 60<h<90 then the midpoint is

x₅=(60+90)/2

x₅=75

Now, we will find the mean height by using the formula

x=(f₁x₁+f₂x₂+f₃x₃+f₄x₄+f₅x₅)/(Σfi)

Here, f₁=7,f₂=15,f₃=27,f₄=13,f₅=8

and Σfi=7+15+27+12+8=70

Substitute these values in the formula, we get

x=(7×15+15×30+27×45+12×55+8×75)/70

x=(105+450+1215+715+600)/70

x=(3085)/70

x=44.07

Hence,  the estimate of the mean height of the plants when raj measures the height of 70 plants is 44.07cm.

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Answer:

2.78%

Step-by-step explanation:

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

We are told that the six-sided dice is fair. This means that each of the faces has the same probability of being rolled.

Therefore, the probability of rolling one is:

[tex]\implies \sf P(x = 1)=\dfrac{1}{6}[/tex]

The probability of rolling six is:

[tex]\implies \sf P(x = 6)=\dfrac{1}{6}[/tex]

Therefore, the probability of rolling one and then six is:

[tex]\begin{aligned}\implies \sf P(x=1)\:and\:P(x=6) & = \sf \dfrac{1}{6} \times \dfrac{1}{6}\\& =\sf \dfrac{1}{36}\\& = \sf 0.0278\:(3\:s.f.)\\& = \sf 2.78\%\:(3\:s.f.)\end{aligned}[/tex]

Total elements in sample space=6

P(1)

P(6)

P(1 and 6)

Using translation concepts, the equations are given as follows:

a) [tex]y = \sqrt{16 - 4x^2}[/tex]

b) [tex]y = 3\sqrt{16 - x^2}[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent function is:

[tex]y = \sqrt{16 - x^2}[/tex]

In item a, when it is horizontally compressed by a factor of 2, it means that x -> 2x, hence:

[tex]y = \sqrt{16 - (2x)^2} = \sqrt{16 - 4x^2}[/tex]

In item b, the transformations are given as follows:

Then:

[tex]y = 3\sqrt{16 -(-x)^2} = 3\sqrt{16 - x^2}[/tex]

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Answer:its b

Step-by-step explanation:

trust me its b