You got an A on 6 of your last 8 quizzes in Algebra 2. What is the experimental probability that you will get an A on your next quiz? (Simplify the fraction).

Answer:

120x

Have a great day and night!!!!

Answer:

0.571

Step-by-step explanation:

Answer:

0.571

Step-by-step explanation:

divide 4 and 7

Answer:

2 real solutions

Step-by-step explanation:

\(y=x^2+3x-2\)

\(y=4x-1\)

\(x^2+3x-2=4x-1\)

\(x^2-x-2=-1\)

\(x^2-x-1=0\)

\(x=\frac{1 +-\sqrt{1-4*1*(-1)} }{2}\)

\(x=\frac{1+-\sqrt{5}}{2}\)

If a certain regular polygon is rotated 30° about its center, which carries the figure onto itself, this regular polygon could be: A. dodecagon.

In Mathematics and Geometry, the measure of the angle at the center of a regular polygon is equal to 360 degrees. Therefore, the smallest angle of rotation that maps (carries) a regular polygon onto itself can be calculated by using this formula:

α = 360/n

α = 360/30

α = 12°

Since the other angles that would map a regular polygon onto itself must be a multiple of the smallest angle of rotation, we have:

α = 12°, 24°, 48°, 96°, 192°, etc.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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a) Using Newton's method, the root of √15 to the nearest thousandth is 3.873.

b) Using Newton's method, the root of ∛121 to the nearest thousandth is 4.983.

Newton's method for approximating roots: Newton's method is used to approximate the roots of a function f(x) by successive approximations. Newton's method is an iterative numerical technique that is used to locate the roots of a function. It uses the idea that if the value of a function is equal to zero at point c, then its derivative will be zero at that point. Newton's method can be used to approximate the square root of a number. The square root of a number and the cube root of a number can be approximated using Newton's method by setting the function equal to zero and finding the derivative of that function.

To find: a) \(\sqrt{15} \)  

             b) \( \sqrt[3]{121} \)

1: For the given function f(x), we need to determine the derivative f'(x).

Let's begin with finding the function and its derivative for a) and b) respectively.

a) Let f(x) = \(x^2 - 15\) be the function

f'(x) = 2x be the derivative function.

b) Let f(x) = \(x^3 - 121\) be the function

f'(x) = 3\(x^2\) be the derivative function.

2: Choose a starting point x₀ and compute the first approximation, x₁ using the formula below:

\[x_{n+1} = x_n - \frac{{f'(x_n)}}{{f(x_n)}}\]

x₁ = 5 - \(\frac{(5^3 - 121)}{3(5^2)}\)

For a) let x₀ = 5, then x₁ = 5 - \(\frac{(5^2 - 15)}{2(5)}\)

= 3.5.

For b) let x₀ = 5, then x₁ = 5 - \(\frac{(5^3 - 121)}{3(5^2)}\)

= 4.6667.

3: Use the following formula to find x₂:

For a) x₂ = 3.5 - \(\frac{(3.5^2 - 15)}{2(3.5)}\)

              = 3.87179 ≈ 3.873

For b) x₂ = 4.6667 - \(\frac{(4.6667^3 - 121)}{3(4.6667^2)}\)

              = 4.983 (rounded to the nearest thousandth).

Thus the roots to the nearest thousandth of a) \(\sqrt{15}\) and b) \(\sqrt[3]{121}\) are 3.873 and 4.983 respectively.

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Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

Null hypothesis (H0): The population mean weight of all employees is equal to or greater than 200 lb. Alternative hypothesis (H1): The population mean weight of all employees is less than 200 lb.

The test statistic used in this case is the z-score, which can be calculated using the formula:

z = (x - μ) / (σ / \(\sqrt{n}\)) where:

x = sample mean weight = 183.9 lb

μ = population mean weight (claimed) = 200 lb

σ = known standard deviation = 121.2 lb

n = sample size = 54

By substituting the given values into the formula, we can calculate the z-score. The critical value for a 0.10 significance level (α) is -1.28 (obtained from the z-table). If the calculated z-score is less than -1.28, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

After calculating the z-score and comparing it to the critical value, we find that the z-score is -3.093, which is less than -1.28. Therefore, we reject the null hypothesis. Based on the analysis, there is sufficient evidence to support the claim that the population mean weight of all employees is less than 200 lb.

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Recall the definition of each concept to check if it fits the figure.

A) Square: A square is a quadrilateral whose sides all have the same length.

B) Polygon: A polygon is a 2D shape formed by non-intersecting straight segments.

C) Triangle: A triangle is a polygon with exactly 3 sides.

D) Polyhedron: A polyhedron is a 3D shape formed by flat polygonal shapes.

E) Pyramid: A pyramid is a polyhedron formed by a simple polygon whose lateral faces are triangles that converge in a common vertex.

F) Prism: A prism is a polyhedron formed by two parallel and equal polygonal faces, whose lateral faces are parallelograms.

The given object is a 3D shape formed by flat polygonal shapes, with a base that is a quadrilateral and whose lateral faces are triangles that converge in a common vertex.

Therefore, the only two terms that correcty describe the given object are:

D) Polyhedron

E) Pyramid

Answer:

26r^2 + 36r.

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Recall the triple angle identity for cosine:

cos(3x) = cos³(x) - 3 sin²(x) cos(x)

… = cos³(x) - 3 (1 - cos²(x)) cos(x)

… = 4 cos³(x) - 3 cos(x)

and the definition of secant,

sec(x) = 1/cos(x)

So we have

sec(x) cos(3x) = 0

(4 cos³(x) - 3 cos(x))/cos(x) = 0

cos(x) (4 cos²(x) - 3)/cos(x) = 0

If cos(x) ≠ 0 (this happens at the endpoints of the interval [-π/2, π/2]), we can simplify this to

4 cos²(x) - 3 = 0

cos²(x) = 3/4

cos(x) = ±√3/2

But since -π/2 < x < π/2, we know cos(x) > 0, so we ignore the negative case:

cos(x) = √3/2

==>   x = π/6 and x = -π/6

The solution of the given trigonometric equation by using trigonometric identities is \(\frac{\pi }{6} \ and \frac{-\pi }{6}\).

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

\(cos(3x) = 4cos^{3}(x) -3cos(x)\)

According to the given question.

We have an equation

\(sec(x)cos(3x) = 0\)

Since, the above equation can be written as by using trigonometric identities

\(sec(x)cos(3x) = 0\\\implies \frac{1}{cos(x)} (4cos^{3} x-3cos(x))=0\)

Solve the above equation for x.

\(\implies 4cos^{2} x -3= 0\)

\(\implies 4cos^{2}x = 3\\ \implies cos^{2} x = \frac{3}{4} \\\implies cos x = \sqrt{\frac{3}{4} } \\\implies cos x = \pm\frac{\sqrt{3} }{2}\)

In the given domain \([\frac{-\pi }{2}, \frac{\pi }{2} ]\) we know that cosx > 0. Therefore, we take only positive part

\(\implies cosx = \frac{\sqrt{3} }{2} \\\implies x = cos^{-1} \frac{\sqrt{3} }{2} \\\implies x = \frac{\pi }{6}, and \frac{-\pi }{6}\)

Hence, the solution of the given trigonometric equation by using trigonometric identities is \(\frac{\pi }{6} \ and \frac{-\pi }{6}\).

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Answer:

Hello, I solved it out for you and I did an example.

Step-by-step explanation:

From the problem, we have :

Using distributive property, multiply 3 to the expression inside the parenthesis.

This will be :

The answer is 27x - 3

The dot product of vectors u and v is -24.

Given the vectors u = (8,0) and v = (-3,-3), the following steps will be followed to solve the problem:Step 1: Sketch the vectors u and v on the same graph paper. Step 2: Find the angle between the vectors. Step 3: Compute the dot product of vectors using the definition of the dot product. Sketch the vectorsThe sketch of vectors u and v is shown below. From the graph, the following observations can be made about the vectors:vector u lies entirely in the positive x-axis directionvector v lies in the second quadrant between the angles 135° and 180°Consider the vectors u = (8,0) and v = (-3,-3)Find the angle between the vectorsThe angle between vectors can be found using the dot product of vectors. For two non-zero vectors u and v, the dot product is given as follows:u . v = |u| |v| cos θwhere, θ is the angle between the vectors u and v.To find θ, rearrange the equation above as:cos θ = (u . v) / (|u| |v|)cos θ = [(8 x -3) + (0 x -3)] / [(sqrt(8^2 + 0^2) x sqrt(-3^2 + (-3)^2))]cos θ = -24 / (8 x 3)cos θ = -1/3θ = arccos(-1/3)θ = 109.47°θ = (109.47 x pi) / 180θ = 0.7854 x 3.1416θ ≈ 2.3562 radiantheta = 3pi/4What is the dot product? (8,0).(-3,-3) = 8 x -3 + 0 x -3= -24Hence, the dot product of vectors u and v is -24.

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Answer:

x=4, y=-11. (4, -11).

Step-by-step explanation:

3x+2y=-10

5x+y=9

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

3x+2y=-10

-2(5x+y)=-2(9)

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

3x+2y=-10

-10x-2y=-18

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

-7x=-28

7x=28

x=28/7=4

5(4)+y=9

20+y=9

y=9-20=-11

Answer:

6). 7 years , 29 members ; 7). $5 is the price of the child movie ticket, $15 is the price of the adult movie ticket.

Step-by-step explanation:

6). y = 50 - 3x

    y = 15 + 2x

15 + 2x = 50 - 3x

5x = 35

x = 7 years

y = 15 +2(7)

y = 29 members

In 7 years game club and sport club will have 29 members.

7). 2a + 3c = 45 ......... (1)

    2a + 2c = 40 ......... (2)

(1) - (2)

c = $5 is the price of the child movie ticket

2a + 2(5) = 40

a = $15 is the price of the adult movie ticket

Answer:

Step-by-step explanation:

The difference:

Correct choice:

Answer:

a.) 14.5 minutes longer

Step-by-step explanation:

the average travel time for New Yorkers compare to the United States

= 40.0 - 25.5

= 14.5 min. longer

Answer:

a

Step-by-step explanation:

Answer:

(0, - 5 ) and (2, - 1 )

Step-by-step explanation:

Given the 2 equations

y = 2x - 5 → (1)

y = x² - 5 → (2)

Substitute y = x² - 5 into (1)

x² - 5 = 2x - 5 ( subtract 2x - 5 from both sides )

x² - 2x = 0 ← factor out x from each term

x(x - 2) = 0

Equate each factor to zero and solve for x

x = 0

x - 2 = 0 ⇒ x = 2

Substitute these values into (1) for corresponding values of y

x = 0 : y = 2(0) - 5 = 0 - 5 = - 5 ⇒ (0, - 5 )

x = 2 : y = 2(2) - 5 = 4 - 5 = - 1 ⇒ (2, - 1 )

Answer:

y=2x-5 ......... 1

y = x² - 5 ......... 2

Substitute equation 1 into equation 2

You'll get

2x - 5 = x ² - 5

x² - 2x = -5 + 5

x² - 2x = 0

Factorize

x ( x - 2 ) = 0

x = 0 x = 2

Now put the values of x into any of the equation

When x = 0

y = 2(0) - 5

y = 5

When x = 2

y = 2(2) - 5

y = 4 - 5

y = -1

When x = 0 y = - 5

When x = 2 y = - 1

Hope this helps

Answer:

comparing given quadratic eqn 4x²+15x+9=0 with ax²+bx+C=0,we get

a=4,b=15 and c=9

Now,sum of roots=-b/a=-15/4

and, product of roots=c/a=9/4

Answer:

The sum of its root is -15/4 and the product of its root is 9/4

STEP BY STEP EXPLANATION :

To find the sum of the root -b/a gonna help us

so let's substitute the numbers.

4x^2+15x+9, from the equation

then -b/a => -15/4.

to find the product of the root we use c/a then,

c/a => 9/4.

I hope it help you a lot thank you guys

The inequality given by (x/3) + 5 ≥ 1/6 has the solution x ≥ -29/2 or [-29/2 , +∞).

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.

Given the inequality (x/3) + 5 ≥ 1/6, subtract 5 from both sides.

(x/3) + 5 - 5 ≥ 1/6 - 5

x/3 ≥ -29/6

Multiply both sides by 3.

3(x/3) ≥ 3(-29/6)

x ≥ -29/2

To check, let x = -29/2

x = -29/2 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

(-29/2)/3 + 5 ≥ 1/6

1/6 ≥ 1/6

let x = -14,

x = -14 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

-14/3 + 5 ≥ 1/6

1/3 ≥ 1/6

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Answer:

The Answer is 24 square inches

Step-by-step explanation:

The area of a triangle is 5 because (5x2)/2 =5

Then times that by four because there are four triangles, which gives you 20

Then the square is 2x2 which gives 4

20+4 =24

The surface area equals 24

Answer:

1 3/100

21-24squareroot7/100

21

=24squareroot7/100

Step-by-step explanation:

Answer: d or 21+24square root 7 over 100

Step-by-step explanation:

Answer:

X= − x ^3 + 2 x^2 − 3 x − 2 x ^3 ( x + 2 ) ( x − 2 ) = 0

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

all squares are rhombuses but not all rhombuses are squares

Answer:

What is the optimal value of the function y = - ( x - 5)² - 4?(c.y=4)

Step-by-step explanation:

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Answer:

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