sin(90° - x) = sqrt3/2

The value of a is 72.74.

Probability is the study of likeliness of an event to happen.

It is given that

The mean [tex]\rm \mu[/tex] of the distribution is 70

Standard deviation [tex]\rm \sigma[/tex]  is 2

p( x<a) = 0.9147

a = ?

From Z table

For p ( p < 0.9147) , z = 1.37

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

[tex]\rm \rm 1.37 = \dfrac { a - 70}{ 2}[/tex]

a = 70+ 2*1.37

a = 72.74

Therefore the value of a is 72.74.

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Answer:

11) 195312

13) 5461

Step-by-step explanation:

11)

15÷(-3) = -5

(-75)÷15 = -5

375÷(-75) = -5

It’s clear that the common ratio of this geometric sequence is -5

Then using the sum formula for geometric sequences :

[tex]S_{11}=\left( -3\right) \times \frac{1-\left(-5 \right)^{8} }{1-(-5)} =-\frac{1}{2}\times(1-(-5)^8)=195312[/tex]

……………………………………………………

13)

[tex]S_{13}=1\times \frac{1-4^{7}}{1-4} =-\frac{1}{3} \times(1-4^{7})=5461[/tex]

Answer:

210 seconds

Step-by-step explanation:

LCM of 5,6 and 7

Answer:

y=-x+4

Step-by-step explanation:

First use slope formula using 2 points.

(0,3) and (1,2)

[tex]\frac{y2-y1}{x2-x1}[/tex]

[tex]\frac{2-3}{1-0}=\frac{-1}{1} =-1[/tex]

Slope is -1.

Now, use point-slope formula.

y-y1=m(x-x1)

Plug in the information that we have.

y-3=-1(x-0)

Use distributive property.

y-3=-x+1

Add 3 to both sides.

y=-x+4

It is now in slope-intercept form.

Hope this helps!

If not, I am sorry.

Answer:

wait lang yong tppp heheehhehe

Answer:

b is the awancer yw

Step-by-step explanation:

The quadratic inequality represented by the graph is:

y ≤ 2x² - 8x + 3

First, we can see that the shaded region is below the parabola, and the line of the parabola is solid, which means that the points on the parabola are solutions, then the inequality is:

y ≤ quadratic equation.

Now we need to get the quadratic equation.

Now, if you look at the y-intercept, you can see that it happens at y = 3. Then the constant term of the quadratic equation is 3.

The only one that has that (and the  ≤  symbol)  y-intercept is the first option:

y ≤ 2x² - 8x + 3

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The radius will be equal to 7.55 centimeters.

The arc length is the curved length on the circumference of a circle suspended by a small angle.

The radius will be calculated as follows:-

r = [tex]\dfrac{Arc}{Angle}[/tex]

r = [tex]\dfrac{\dfrac{26\pi}{9}}{\dfrac{69\times \pi}{180}}[/tex]

r = [tex]\dfrac{9.07}{1.20}[/tex]

r = 7.55 centimeters

Therefore the radius will be equal to 7.55 centimeters.

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By solving a system of equations, we will see that m measures 12 units.

Notice that we have 3 right triangles.

Then we can write the equations:

cos(a) = 6/m

For the small triangle on the left, where m is the hypotenuse.

cos(a) = m/(6 + 18)

For the larger triangle (the one composed of the two triangles).

Where in both equations, angle "a" is the one in the top left.

Then we have the system of equations:

cos(a) = 6/m

cos(a) = m/(6 + 18)

Then we can write:

6/m = m/(6 + 18)

If we simplify the expression, we get:

6*(6 + 18) = m^2

6*(24) = m^2

144 = m^2

√144 = m = 12

Then we conclude that m measures 12 units.

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Answer:

1st option

Step-by-step explanation:

let y = f(x) and rearrange making x the subject , that is

y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )

y + 2 = [tex]\frac{1}{9}[/tex] x ( multiply both sides by 9 to clear the fraction )

9(y + 2) = x

9y + 18 = x

change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = 9x + 18

Answer: A

Step-by-step explanation:

GOT IT RIGHT ON EDG TEST

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:[tex]x=-\frac{1}{3}, 4[/tex]

Step-by-step explanation:

Graphs intersect the x-axis where y=0, so we can set f(x)=0.

[tex]3x^2 - 11x-4=0 \\ \\ (3x+1)(x-4)=0 \\ \\ x=-\frac{1}{3}, 4[/tex]

Answer:

negative x intercept is at -1/3

positive x intercept 4

Step-by-step explanation:

Answer:

the answer is A K= -2.5

Step-by-step explanation:

i did the problem

The equations;

A linear equation is one in which there is only one solution. In a linear solution, the highest power of x is 1.

If we look at the equations listed, we will discover that they are all linear equations, as such;

Will all have exactly 1 solution.

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Function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we know, when x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.

a) y=6x

The above function is a linear function

b) y=3/x

or

xy = 3

The above function shows an inverse variation.

c) y=1/3x

or

y = (1/3)x

The above function is a linear function

d) y= -.07x

The above function is a linear function

e) y= 2/x+4

or

y = (2+4x)/x

xy = 2 + 4x

The above function shows an inverse variation.

f) xy=-3

The above function shows an inverse variation.

Thus, function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.

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Answer:

b = 0 and b = 4

Step-by-step explanation:

[tex]\frac{5}{3b^3-2b^2-5}[/tex] = [tex]\frac{2}{b^3-2}[/tex] ( cross- multiply )

2(3b³ - 2b² - 5) = 5(b³ - 2) ← distribute parenthesis on both sides

6b³ - 4b² - 10 = 5b³ - 10 ( subtract 5b³ from both sides )

b³ - 4b² - 10 = - 10 ( add 10 to both sides )

b³ - 4b² = 0 ← factor out b² from each term on the left side

b²(b - 4) = 0

equate each factor to zero and solve for b

b² = 0 ⇒ b = 0

b - 4 = 0 ⇒ b = 4

Subtraction is a mathematical operation that reflects the removal of things from a collection. Supplier B would cost $625 more than supplier A. Thus, the correct option is A.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The cost of 500 bushels from supplier A will be,

Cost = ($5.25 × 500) + ($3 × 500)

        = $4,125

The cost 500 bushes from supplier B will be,

Cost = $1,500 + ($6.250×500)

        = $4,750

Now, the difference between the two suppliers' costs for 500 bushels will be,

Difference = $4,625 - $4,125 = $500

Hence, Supplier B would cost $625 more than supplier A. Thus, the correct option is A.

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Answer:

9

Step-by-step explanation:

0

Answer:

4/9 of the students chose summer.

Step-by-step explanation:

Think about it this way. There are 9 students being asked what their favorite season is. 1 chose spring, 3 chose summer. Add those together, and you have 4 people that chose either spring or summer. That number goes on top of the fraction. The total amount of people that were asked goes on the bottom, which is 9.

the first definition of an element was made by

The correct answer will be option B which is the ends of the graph will extend in the opposite direction.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given equation is as follows:-

y = 2x⁶ + 9x⁵ -7x³ -1

When the term -3x⁶ is added the equation will be reduced in the following form.

y = -3x⁶+2x⁶ + 9x⁵ -7x³ -1

y =-x⁶+9x⁵ -7x³ -1

When we plot the graph of the above equation we will see that the graph will be reduced to the form in which both the ends of the graph lie opposite to each other.

The graph of the equation is attached with the answer below.

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Answer:

B is the correct answer

Step-by-step explanation:

Answer:

The answer is -4×3 or -3×4 or -6×2 or -2×6 or -1×12 or -12×1

Step-by-step explanation:

Answer:

Use Calculator:

Approximately. 1429.411

Step-by-step explanation:

Hope it Helps!!!

Answer:

(i) x-intercepts: (2, 0), (6, 0)

(ii) vertex : (4, -4)

Explanation:

y = x² - 8x + 12

To find x intercepts, [set y = 0]

x-intercepts: (2, 0), (6, 0)

To find vertex:

x = -b/2a

  = -(-8)/2(1)

  = 4

y = x² - 8x + 12

  = 4² - 8(4) + 12

  = -4

Vertex : (4, -4)

Solve the equation for y=0

X inetercepts (2,0) and (6,0)

Vertex :-

x coordinate

Y coordinate

Verted at (4,-4)

The numbers should be 2, 2, 5, 9 and 12.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Let us take numbers 2, 2, 5, 9 and 12.

mean = 30/5

mean= 6

range = 10.

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Answer:

B = an event that in the second turn it will land on Lose a Turn. Based from the given wheel, there are 24 equal parts with three $500 and one Lose a Turn. Thus, the probability of landing on $500 then lose a turn is 1921 .

this is possible IF thewheele consists of 24 parts

The chance of landing on $500 and then Lose A Turn will be 1/192. Then the correct option is C.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

The diagram is given below.

The total number of the events will be

Total events = 24

Then the chance of landing on $500 will be

The number of favorable events will be

Favorable events = 3

⇒ 3/24

⇒ 1/8

Then the chance of the Lose A Turn will be

Favorable event = 1

⇒ 1/24

The chance of landing on $500 and then Lose A Turn will be

P = (1/24)(1/8)

P = 1/192

The chance of landing on $500 and then Lose A Turn will be 1/192.

Then the correct option is C.

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Answer:

x=8

Step-by-step explanation:

You cross multiply, 6 times 4 is 24, so what times 3 is 24. 8 times 3 is 24.

Answer:

  x = 8

Step-by-step explanation:

There are several ways you can solve a proportion like this. Most of the algebraic solutions involve what amounts to multiplying both sides by (4x/3). There are also graphical solutions and solutions that rely on relations that make fractions be equal.

__

The method of solution usually recommended is to "clear fractions" and then solve the resulting one-step linear equation. To "clear fractions," multiply both sides of the equation by the least common denominator: 4x.

  [tex](4x)\dfrac{3}{4}=(4x)\dfrac{6}{x}\\\\3\cdot x=4\cdot6\qquad\text{looks like "cross multiplication"}[/tex]

We describe this as "cross-multiplication" because it looks like each numerator has been multiplied by the opposite denominator.

This "one-step" linear equation is solved by dividing by the coefficient of x, which is 3:

  [tex]\dfrac{3x}{3}=\dfrac{4\cdot6}{3}\\\\\boxed{x=8}\qquad\text{simplify}[/tex]

Note that we could have done these operations in one step. The two steps, multiply by 4x and divide by 3, are identical to the one step, multiply by (4x/3).

  [tex]\left(\dfrac{4x}{3}\right)\cdot\dfrac{3}{4}=\left(\dfrac{4x}{3}\right)\cdot\dfrac{6}{x}\\\\\boxed{x=8}\qquad\text{simplify}[/tex]

__

We can see the solution almost immediately if we rewrite the fractions so they have the same numerator.

  [tex]\dfrac{3}{4}=\dfrac{6}{x}\\\\\dfrac{3\cdot2}{4\cdot2}=\dfrac{6}{x}\\\\\dfrac{6}{8}=\dfrac{6}{x}\ \Longrightarrow\ \boxed{x=8}[/tex]

The same thing happens if we multiply the equation by the inverse of either side.

  [tex]\dfrac{3}{4}=\dfrac{6}{x}\ \Longrightarrow\ \left(\dfrac{4}{3}\right)\dfrac{3}{4}=\left(\dfrac{4}{3}\right)\dfrac{6}{x}\ \Longrightarrow\ 1=\dfrac{8}{x}\ \Longrightarrow\ \boxed{x=8}\\\\\textsf{ or ...}\\\\\dfrac{3}{4}=\dfrac{6}{x}\ \Longrightarrow\ \left(\dfrac{x}{6}\right)\dfrac{3}{4}=\left(\dfrac{x}{6}\right)\dfrac{6}{x}\ \Longrightarrow\ \dfrac{x}{8}=1\ \Longrightarrow\ \boxed{x=8}[/tex]

__

If the equation is rewritten to a form that has a value of 0 at the solution, then the x-intercept of the graph will be the solution to the equation.

  3/4 = 6/x . . . . . . . . original equation

  6/x -3/4 = 0   ⇒   f(x) = 0

  f(x) = 6/x -3/4

The graph shows the solution to f(x) = 0 is x=8.

Answer:

The value of [tex]x_{2}[/tex] from inverse variation is (-35).

Step-by-step explanation:

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases. While direct variation describes a linear relationship between two variables, inverse variation describes another kind of relationship.

An inverse variation can be represented by the equation

xy=k .

That is y varies inversely as x if there is some nonzero constant k.

Here, the product is given by :

x1y1=x2y2

21 x (-15)=x2 x 9

(-315) / 9 = x2

x2=(-35)

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The number of balloons needed to fill the classroom are  46240 balloons (approx)

Concept: Fermi process is the technique that helps to formulate an answer to a problem based on a series of logical assumptions.

No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)

Given: The classroom is a rectangular prism with a length of 38 ft, a width of 52 ft, and a height of 12 ft, and the balloons are spheres with a radius of 0.35 ft.

No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)

No. of Balloons = 38*52*12/3.14*0.35*0.35*(4/3)

No. of Balloons = 23712/0.5128 = 46240 balloons (approx)

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Answer:

A line traveling to the left with an open dot on x=1.

Explanation:

The inequality x < 1 basically means "less than 1." On number lines, the further left you go, the smaller the number becomes, and the further right you go, the larger the number becomes. So we know that because it's less or smaller than 1, then the line will be to the left. On the other hand, the inequality does not have a line under it to indicate a "less than or equal to 1," just "less than." Therefore, the dot is open. If there were a line under the inequality, then it would indicate "less than or equal to 1" and the dot would be closed.

Answer: Choice C

[tex]x < -2 \text{ or } x \ge 4[/tex]

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

Reason:

The portion on the left represents [tex]x < -2[/tex] because of the open circle at -2 and shading pointing to the left. This represents all numbers smaller than -2.

The portion on the right represents all values that are 4 or larger; hence [tex]x \ge 4[/tex]. Note the use of a closed circle at 4 to include this value.

We connect those two inequalities with the keyword "or" because x can only pick one of those options, but not both at the same time.