A = 1/ 7 - 4√3
B = 1/ 7+ 4√3
Find....
A) a² + b²
B) a³ + b³

Answer:

20%

Step-by-step explanation:

Half of 2 = 1

Half of 1.6 = 0.8

1 - 0.8 = 0.2

0.2 × 100 = 20%

Answer:

$26

Step-by-step explanation:

Let blueberry pies = x and lemon pies = y.

4x + 13y = 230

4x + 2y = 76

Using elimination, we see that 11y = 154. Therefore, y = 14.

4x + 2(14) = 76

4x + 28 = 76

4x = 48

x = 12

x + y = 12 + 14 = 26.

$26 is your answer.

Answer:

Step-by-step explanation:

Let B be the price of a blueberry pie.  Let L be the price of a lemon meringue pie.

We are told that Shreya makes a total of $76 by selling 4 blueberry and 2 lemon meringue pies.  This can be made into an equation:

Shreya:  4B + 2L = $76

We also learn that Shanice is doing particularly well:

Shanice:  4B + 13L = $320

We want to determine the prices for each type of pie, B and L.  We have two equations and two unknowns.  That means we should be able to find the answers by substitution.

Rearrange Shreya's equation to isolate B:

Shreya:  4B + 2L = $76

               4B   = $76 - 2L

                 B = ($76-2L)/4

Now use this definition of B in Shanice's equation:

Shanice:  4B + 13L = $320

                4( ($76-2L)/4) + 13L = $320

                     ($76-2L) + 13L = $320

            11L = 244

                L = $22.18

Use L = $22.18 in either equation and solve for B:

4B + 2L = $76

4B + 2*($22.18) = $76

4B = $31.64

B = $7.91

---

Blueberry pies are $7.91 each.

Lemon meringue pies are $22.18 each

=========

CHECK:  Do these prices provide the correct sales for each person?

            Price($/pie)        Shreya     Shanice

Blueberry          7.91               4            4

Lemon Mer.    22.18                2           13

Blueberry Sales ($)                    31.64        31.64

Lemon Mer. Sales ($)               44.3       288.36

Total Sales                              $76        $320

YES - These prices account for each person's sales.

The number of primes less than 190 using the principle of inclusion-exclusion are 42

The principle of inclusion-exclusion is known as a counting technique that computes the number of elements satisfying at least one of several properties and guaranteeing that the numbers are not counted twice.

Prime numbers are numbers only divisible by 1 and itself.

Prime numbers less than 190 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181

They are 42 in number

Therefore, the number of primes less than 190 using the principle of inclusion-exclusion are 42

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Answer:

Part A: The appropriate design would be: 300 male patients chosen should be suffering from ruptured disks in the lumbar region of the back, with similar magnitude of pain (or segregating these 300 as per magnitude of pain)

Part B: If the study consisted of 150 male and 150 female patients instead of 300 malepatients, I would change the study design, because the pain level could endure for femalecould vary compare to male.

Part C:Yes, I could design a double-blind, because it is a very good ways to show theeffect of the therapy because neither the participants nor the researchers knows whichgroups of participants is assigned to which treatment, and who are the groups of participant receiving it.

Answer:

Period = 4 units

Step-by-step explanation:

Standard form of a tangent function:

[tex]f(x)=\sf A \tan(B(x+C))+D[/tex]

The tangent function has a vertical asymptote whenever cos(x) = 0

The tangent function does not have an amplitude because it has no maximum or minimum value.

Given function:

[tex]y=\tan \left(\dfrac{\pi}{4}\left(x-\dfrac{\pi}{3}\right)\right)[/tex]

Therefore:

Answer: 4 units

Step-by-step explanation:

Using the normal distribution, it is found that:

a) The pilot is at the 72th percentile.

b) 19.13% of pilots are unable to fly.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 72.6, \sigma = 2.7[/tex].

Item a:

The percentile is the p-value of Z when X = 74.2, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{74.2 - 72.6}{2.7}[/tex]

Z = 0.59

Z = 0.59 has a p-value of 0.7224.

72th percentile.

Item b:

The proportion that is able to fly is the p-value of Z when X = 78 subtracted by the p-value of Z when X = 70, hence:

X = 78:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{78 - 72.6}{2.7}[/tex]

Z = 2

Z = 2 has a p-value of 0.9772.

X = 70:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 72.6}{2.7}[/tex]

Z = -0.96

Z = -0.96 has a p-value of 0.1685.

0.9772 - 0.1685 = 0.8087 = 80.87%.

Hence the percentage that is unable to fly is:

100 - 80.87 = 19.13%.

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Answer:

r = 5

Step-by-step explanation:

The zeroes ( where the function intersects the x - axis) are equi-distant from the vertex line of symmetry

vertex 2,4      to  get to  -1 , 0    you have to go three units in the negative x direction .....  the other zero is on the OTHER side of the vertex 3 units which would be    5,0       so   r  = 5

Here is a graph to look at:

The option that best describes the experiment is accurate and reproducible.

All the values from the experiment are close in value to the accepted value. This indicates that the experiment is accurate. Two experiments yield the same values. This indicates that the experiment is reproducible.

Here is the table used in answering the question:

Accepted Value: 130

Experiment 1 129

Experiment 2 131

Experiment 3 129

Experiment 4 132

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Answer:

(A)They are precise and reproducible

Step-by-step explanation:

Answer:

Given:

Let, the slope of the line passing through the point ( m) = -2

The line passing through the point M(-1,-3)= (x1 , y1)

The equation of the line passing through the point M(-1,-3) is

y-y1 = m (x-x1)

or, y-(-3) = -2 (x-(-1))

or, y+3 = -2 (x+1)

or, y+3 = -2x-2

or, 2x+y = -2-3

Hence, 2x+y =-5 is the required equation.

(a) is the correct answer .

Answer:

d = 15

Step-by-step explanation:

8 - 10 - 28 + 7 is equal to -23

8 + d - 10 - 36 is equal to -38 + d

if -23 = -38 +d

15 = d

The solution of the equation is d = 15

Two or more expressions with an Equal sign is called as Equation.

The given equation is 8-10-28+7=8+d-10-36

In the equation d is the variable

We have to solve for d

8-10-28+7=8+d-10-36

-23 = -38+d

Add 38 on both sides

-23+38=d

15=d

Hence, the solution of the equation is d = 15

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Answer:

x = - 6 , x = 4

Step-by-step explanation:

the absolute value function always gives a positive value but the expression inside can be positive or negative , that is

2x + 2 = 10 or - (2x + 2) = 10

solving both

2x + 2 = 10 ( subtract 2 from both sides )

2x = 8 ( divide both sides by 2 )

x = 4

or

- (2x + 2) = 10

- 2x - 2 = 10 ( add 2 to both sides )

- 2x = 12 ( divide both sides by - 2 )

x = - 6

Answer+Step-by-step explanation:

[tex]f^{-1}\left( x\right) =\frac{1}{7} x^{2}+3 \ ,\text{where}\ x\geq 0[/tex]

Answer:

false

Step-by-step explanation:

so D(2) is equal to how much money he has after 2 years while D(7) is after 7 years. since he earns 3% interest each year he will have more money after 7 years than 2 years

Answer:

[tex]\boxed {\frac{dy}{dx}= 2x}[/tex]

Step-by-step explanation:

Solving :

⇒ log y = log (x²)

⇒ log y = 2 log x

⇒ [tex]\mathsf {\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} \times 2}[/tex]

⇒ [tex]\mathsf {\frac{dy}{dx}= 2x}[/tex]

Answer:

y’ = 2x

Step-by-step explanation:

Let y = f (x), take the natural logarithm of both sides ln (y) = ln (f (x))

ln (y) = ln (x²)

Differentiate the expression using the chain rule, keeping in mind that y is a function of x.

Differentiate the left hand side ln (y) using the chain rule.

y’/y = 2 In (x)

Differentiate the right hand side.

Differentiate 2 ln (x)

y’/y = d/dx = [ 2 In (x) ]

Since 2 is constant with respect to xx, the derivative of 2 ln (x) with respect to x is 2 d/dx [ln (x)]

y’/y = 2 d/dx [In (x)]

The derivative of ln (x) with respect to x is 1/x.

y’/y = 2 1/x

Combine 2 and 1/x

y’/y = 2/x

Isolate y' and substitute the original function for y in the right hand side.

y’ = [tex]\frac{2}{x}[/tex] x²

Factor x out of x².

y’ = [tex]\frac{2}{x}[/tex] (x * x)

Cancel the common factor.

y’ = [tex]\frac{2}{x}[/tex] (x * x)                     (The x that is under 2 and the other x that I have underlined are the ones that cancel out)  

Rewrite the expression.

y’ = 2x

So therefore, the answer would be 2x.

Answer:

the first equation could be something along the lines of [tex]y=3x^{2}[/tex] then the second is [tex]y=3x^{2} -3\\[/tex]

Step-by-step explanation:

this is how shifting works

Answers:

height = 4.46 units

area = 26.73 square units

Both values are approximate

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

Explanation:

h = height of the triangle

Focus on the smaller triangle on the left.

Use the cosine ratio to find h

cos(angle) = adjacent/hypotenuse

cos(27) = h/5

h = 5*cos(27)

h = 4.4550326 approximately

Your calculator needs to be in degree mode.

We can now find the area of the overall largest triangle.

area = 0.5*base*height

area = 0.5*12*4.4550326

area = 26.7301956

area = 26.73

Answer with a step-by-step explanation:

1) First, let us find the height of the triangle.

For that let us use cos theta to find the triangle's height.

Let us use the below formula to find it.

Let the height (adjacent ) be h.

Let us find it now.

cos Θ = Adjacent ÷ hypotenuse

cos 27° = h ÷ 5

0.8910 = h ÷ 5

0.8910 × 5 = h

4.455 = h

Therefore the height of the triangle is 4.455 units.

2) And now let us find the area of the triangle.

The formula to find the area of a triangle is:

Let us find it now.

A =  [tex]\frac{1}{2}[/tex] × base × height

A =  [tex]\frac{1}{2}[/tex] × 12 × 4.455

A =  [tex]\frac{1}{2}[/tex] × 53.46

A = 26.73 units²

Answer:

putting the values of coordinates in equation to check for the solution.

For A

2x + y < 10

2(-5) + 4 < 10.

-10 - 4 < 10

-14 < 10 ( true)

2x - 4y > 8

2(-5) - 4(4) > 8

-10 - 16 > 8

-26 > 8

false..

it is not the solution of the equation.

similarly we can find for other coordinates.

E is the solution

Answer: A. The function has two distinct real zeros.

Answer:

C. The function has four distinct real zeros.

Step-by-step explanation:

The function intersects y=0 at x=1/2, 4, and 6 twice. It has two solutions at 6 twice as it is a behavior of polynomial or rational functions

Answer: [tex]2x^2+2x-4-\frac{4}{x+1}[/tex]

Not a factor because there is a remainder.

Step-by-step explanation:

Let's use synthetic division to solve this..

-1  ║ 2 | 4 | -2 | -8

   ║    | -2| -2 |  4

   ║ 2 | 2|  -4 |  -4

[tex]2x^2+2x-4-\frac{4}{x+1}[/tex]

PS: if anyone knows a better way to do a synthetic division chart please let me know.

Answer:

50

Step-by-step explanation:

if last year 100% of the tomatoes were produced and this year 40% less were produced then that would mean 60% of tomatoes were produced this year.

if 60% = 30 then

100% = ?

100x30÷60

The value of cos θ is 3/5.

Trigonometric ratios can be used to determine the ratios of any two sides out of a total of three sides of a right-angled triangle in terms of the respective angles.

Here, given point on circle is (0.6, 0.8) or (3/5 , 4/5)

x - axis (base) = 3/5

y - axis (Perpendicular) = 4/5

Radius (Hypotenuse) = 1

Now, we know

cos θ = Base / Hypotenuse

cos θ = 3/5

Thus, the value of cos θ is 3/5.

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negative number taken to an odd power gives a negative result (because, after cancelling, there will be one minus sign left over).

the answer is always. negative numbers raised to odd powers remain negative. negative numbers raised to even powers become positive.

The graph is increasing for x > -5

y = x⁴- 5x² + 4 represents the first graph.

y = x(x + 3)(x - 2) represents the second graph.

1) The first polynomial is;

y = x⁴- 5x² + 4

Simplifying this gives us;

y = x⁴- 4x² - x² + 4

y = x²(x² - 4) - 1(x²- 4)

y = (x² - 1)(x² - 4)

y = (x - 1)(x + 1)(x - 2)(x + 2)

Thus, the zeros of this polynomial are; x = -2, -1, 1, 2

From the given graphs attached, first graph has the zeros (x-intercepts) as x = -2, -1, 1, 2.

So graph (1) represents the polynomial  y = x⁴- 5x² + 4

2). The second graph shows the x-intercepts at x = -3, 0, 2

Since, y = x(x + 3)(x - 2) is the polynomial with x-intercepts at x = -3, 0, 2

Therefore, y = x(x + 3)(x - 2) represents the second graph.

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Answer:

estimated gpa:  2.85

Step-by-step explanation:

Evaluate y=0.14x+0.75 at x = 15 (hours):

y = 0.14(15 hours) + 0.75

  = 2.1 + 0.75

y  =  2.85  =  estimated gpa corresponding to 15 houirs of study

Answer:

c is the answer. I hope that helps

Answer: 0.68 or 13.92

Step-by-step explanation:

If the height is 47 meters, then the height, h, is equal to 47.

[tex]47=73t-5t^2\\\\5t^2 - 73t+47=0[/tex]

Using the quadratic formula,

[tex]t=\frac{-(-73) \pm \sqrt{(-73)^{2}-4(5)(47)}}{2(5)}\\\\\\t=\frac{73 \pm \sqrt{4389}}{10}\\\\\\ t=\frac{73+\sqrt{4389}}{10}, \frac{73-\sqrt{4389}}{10}\\\\\boxed{t \approx 0.68, 13.92}[/tex]

[tex]3x ^{2} \: + \: {6x}^{3} \: - \: 9 {x}^{2} y[/tex]

[tex] \boxed{ \bold{3 {x}^{2} \: \times \: (1 \: + \: 2x \: - \: 3y)}}[/tex]

Answer:

[tex]\boxed{3x²(1 + 2x - 3y)}[/tex]

Step-by-step explanation:

3x squared + 6 x cube - 9x squared y

To factor

Solution:

A process when algebraic expression is expressed as a product of two or more expressions is factorisation.

ATP,

Square = a²

Cube = a³

We can see that 3x^2 is common in this expression.

So rewrite as:

Done!

Answer:

a = 11, b = 7

Step-by-step explanation:

See picture