The solution to an inequality is given in set-builder notation as {x l x >2/3 }. What is another way to represent this solution set?

[tex]_8C_5=\dfrac{8!}{5!3!}=\dfrac{6\cdot7\cdot8}{2\cdot 3}=56[/tex]

[tex]\huge{\boxed{72}}[/tex]

First, find the total number of apples.  [tex]6*1200=7200[/tex]

Now, multiply this by the probability of picking a rotten apple, which is [tex]\frac{1}{100}[/tex].  This is also the same as dividing by [tex]100[/tex], or moving the decimal point two places to the left.  [tex]7200*\frac{1}{100}=72[/tex]

This means that based on the probability given, [tex]72[/tex] rotten apples will be picked.

Number of rotten apple may be picked are 72.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

Given

Probability of picking rotten apple in a box is [tex]\frac{1}{100}[/tex].

There are 6 boxes containing 1200 apples each

Number of rotten apple may be picked to be find.

Total number of apples  = [tex]6 \times 1200 = 7200[/tex]

Number of rotten apple may be picked = [tex]7200 \times \frac{1}{100}[/tex]

= 72

Number of rotten apple may be picked are 72.

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Answer:

cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down

Step-by-step explanation:

* Lets revise the angles in the four quadrants

- If angle x is in the first quadrant, then the equivalent angles to it are

# 180 - x ⇒ second quadrant (sin (180 - x) = sin x , cos (180 - x) = -cos x

  tan (180 - x) = -tan x)

# 180 + x ⇒ third quadrant (sin (180 - x) = -sin x , cos (180 - x) = -cos x

  tan (180 - x) = tan x)

# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x

  tan (180 - x) = -tan x)

# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x

  tan (- x) = -tan x)

* Lets solve the problem

∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)

- From the rules above cos x = cos(-x)

∴ cos x cos (-x) = cos x cos x

∴ cos x cos (-x) = cos² x

- From the rule above sin (-x) = - sin x

∴ sin x sin (-x) = sin x [- sin x]

∴ sin x sin (-x) = - sin² x

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x - (- sin² x)

∴ cos x cos (-x) - sin (x) sin (-x) = cos² x + sin² x

∵ cos² x + sin² x = 1

∴ R.H.S = 1

∴ L.H.S = R.H.S

∴ cos x cos (-x) -sin x sin (-x) = 1

Answer:

The correct option is A

Step-by-step explanation:

The expression is

2y3 - 27 + 5y2 + (25 / 5)

Substitute the value of y=2 in the expression:

=2(2)³-27+5(2)²+(25/5)

We know that 2³ means multiply 2 three times

2³= 2*2*2=8

Likewise 2²=2*2=4

=2(8)-27+5(4)+(25/5)

=16-27+20+25/5

Now take the L.C.M which is 5

=80-135+100+25/5

Solve the values in the numerator:

=70/5

=14

Thus the correct option is A....

Least to greatest:

When ordering decimals from least to greatest, it's crucial to understand place value. When ordering, I usually like to start with whole numbers and put them first and then I think about the numbers after the decimal.

Answer:

h×a²×1/3

Step-by-step explanation:

where h is the vertical height of pyramid a is the length of base ..this formula is applicable for square based pyramid only.

Answer:

1/3 A h.

Step-by-step explanation:

The volume of a pyramid is 1/3 * area of the base * height = 1/3 A h.

So for example the area of a square-based  pyramid = 1/3 s^2 h where s is the length of a side of the square.

Answer:

tan O = √3/ 3.

Step-by-step explanation:

The tangent is  positive in quadrant 3.

The adjacent side has length  √((2^2 - (-1)^2)

= -√3.

So tan O  = -1 / -√3

= 1 / √3

= √3/ 3.

To determine tan(θ) for an angle θ where sin(θ) = -1/2 and θ is in quadrant III, we perform the following steps:
1. **Understand the given information:** When sin(θ) = -1/2, it means the opposite side to angle θ in a right triangle is -1 and the hypotenuse is 2. Since θ lies in the third quadrant, both sine and cosine values are negative, implying that the adjacent side length must also be negative.
2. **Use the Pythagorean theorem:** For a right triangle:
  \[ \text{hypotenuse}^2 = \text{opposite}^2 + \text{adjacent}^2 \]
  Substituting hypotenuse and opposite side values:
  \[ 2^2 = (-1)^2 + \text{adjacent}^2 \]
  Simplify and solve for the adjacent side:
  \[ 4 = 1 + \text{adjacent}^2 \]
  \[ 3 = \text{adjacent}^2 \]
  \[ \text{adjacent} = \sqrt{3} \] or \[ \text{adjacent} = -\sqrt{3} \]
  Since the angle is in the third quadrant where cosine is also negative, we must take the negative square root:
  \[ \text{adjacent} = -\sqrt{3} \]
3. **Calculate tan(θ):** By definition,
  \[ \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} \]
  Substitute the known side lengths:
  \[ \tan(θ) = \frac{-1}{-\sqrt{3}} \]
4. **Simplify the expression:**
  \[ \tan(θ) = \frac{1}{\sqrt{3}} \]
  To rationalize the denominator:
  \[ \tan(θ) = \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \]
  \[ \tan(θ) = \frac{\sqrt{3}}{3} \]
Thus, if sin(θ) = -1/2 and θ is in quadrant III, then tan(θ) = √3/3. Note that in the context of trigonometry, it is often assumed that the angle and the ratios are dimensionless, so a negative 'opposite' simply reflects the direction along the coordinate axis rather than a literal negative length.

Answer:

When a matrix is multiplied by its inverse the result will be the identity matrix. If we multiply two matrix with the same size, the resulting matrix will have the same dimension.

Therefore, if we multiply the matrices X and Y we will get a 2x2 identity matrix, as follows:

[tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

Answer:

[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]

Step-by-step explanation:

We are asked find the matrix that represent the product of matrices X and Y both measures [tex]2\times 2[/tex] and inverse of each other.

For a matrix multiplication to be defined, the number of columns in the first matrix must be equal to number of rows in the second matrix.

Since the both matrices are [tex]2\times 2[/tex] (same number of column and row), then the product of both matrices would result in [tex]2\times 2[/tex] matrices.

We also know that the multiplication of a matrix with its inverse results in identity matrix.

Therefore, our matrix would be a [tex]2\times 2[/tex] identity matrix as:

[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex].

Answer:

Rounded to nearest hundredths is 8.75.

Rounded to nearest tenths is 8.7.

Step-by-step explanation:

Law of sines:

[tex]\frac{\sin(A)}{\text{ side opposite to }A}=\frac{\sin(B)}{ \text{ side opposite to }B}[/tex]

Measure of angle [tex]A[/tex] is 28 and the side opposite to it is [tex]x[/tex].

Measure of angle [tex]B[/tex] is 105 and the side opposite to it is 18.

Plug in to the formula giving:

[tex]\frac{\sin(28)}{x}=\frac{\sin(105)}{18}[/tex]

Cross multiply:

[tex]18 \sin(28)=x \sin(105)[/tex]

Divide both sides by sin(105):

[tex]\frac{18 \sin(28)}{\sin(105)}=x[/tex] is the exact answer.

I'm going to type it in my calculator now:

18*sin(28) / sin(105) is what is going in there.

The output is 8.748589074.

Rounded to nearest hundredths is 8.75.

Rounded to nearest tenths is 8.7.

Answer:

y = 4x

Step-by-step explanation:

Let x = length of the side = independent variable

Let y = perimeter of the square = dependent variable

y = 4x

Answer: 85 pounds,

Step-by-step explanation: Americans don't use the other things to measure weight.

Answer:

The scale factor is 1 because it has not increased or decreased and therefore are congruent

Answer:

Something close to (1.8,2.6)

Step-by-step explanation:

y=2x-1

y=-1/4 x+3

Since y=2x-1 and y=-1/4 x +3 then 2x-1=-1/4 x +3.

I'm going to multiply both sides by 4 to get rid of the fraction:

8x-4=-x+12

Add x on both sides:

9x-4=12

Add 4 on both sides:

9x=16

Divide both sides by 9:

x=16/9 is approximately 1.8 when put into calculator.

Now if x=16/9 and y=2x-1, then y=2(16/9)-1=32/9-1=32/9-9/9=(32-9)/9=23/9.

y=23/9 is approximately 2.6 when put into calculator.

So we are looking for an ordered pair pretty close to (1.8,2.6).

The graph is shown to you so I will put one here as well:

Answer:

A. 1 3/4, 2 1/2

Step-by-step explanation:

Answer:

A. y+8=2(x-4)

Step-by-step explanation:

A line perpendicular to y=-1/2x+11 would have slope +2, which is the negative reciprocal of -1/2.

Starting with the slope-intercept form of the equation of a straight line, find the y-intercept based upon this new line's passing through (4, -8):

y = mx + b becomes  -8 = 2(4) + b.  Then b = -16, and the desired new line is

y = 2x - 16.  

Eliminate answer choices B and C, because 1/2 is not the correct slope.

Choice A is correct.  Note that the result of subbing 4 for x and -8 for y into A:  y + 8 = 2(x - 4) is a true equation:  -8 + 8 = 2(4 - 4)

Also note that y + 8 = 2(x - 4) can be written in slope-intercept form:

y = -8 + 2x - 8, or y = 2x - 16 (same as obtained earlier)

Answer:Y+8=2(x-4)

Step-by-step explanation:

it’s correct I promise

Answer:

A large pizza costs $5 and a small pizza costs $3.

Let 'x' be the number of large pizzas and 'y' the number of small pizzas. We have that:

x + y = 150

5x + 3y = 570

Solving the system of equations:

x + y = 150 → 3x + 3y = 450 → 3y = 450 - 3x

5x + 3y = 570 → 5x + 450 - 3x = 570

2x = 120

x = 60

y = 150 - 60 = 90

Therefore. Carmen y Carlos will make 60 large pizzas and 90 small pizzas.

Answer:

49 minutes

Step-by-step explanation:

It would take 49 minutes for 9 people to paint 7 walls.

4 walls need 262 people/minutes (7)(36)

9 people could do that in 49 minutes (441/9)

Answer:

49 minutes

Step-by-step explanation:

first we need to find the rate at which a person paints the walls :

it takes 36 minutes  to paint 4 walls   by 7 people :

so for 7 people the rate at which they paint the walls is : [tex]\frac{4}{36}[/tex] walls/minute

if we simplify we get  [tex]\frac{1}{9}[/tex]

now that was for 7 people , for 1 person the rate is : [tex]\frac{1}{9} \frac{1}{7}[/tex] which is [tex]\frac{1}{63} walls / minute[/tex]

now we have the rate for one person

so for 9 people they will paint [tex]\frac{9}{63} =\frac{1}{7}[/tex] walls/minute

so it takes them 7 minute to paint 1 wall

which means it takes them 7 x7 = 49 minutes to paint 7 walls

Answer:

[tex]a_n=2.(3)^{n-1}[/tex]

Step-by-step explanation:

Given sequence is:

2,6,18,54,162

So the common ratio can be found by dividing the second term by first term:

r = 6/2 = 3

The standard formula for geometric sequence is:

[tex]a_n=a_1r^{n-1}[/tex]

Putting the value of r

[tex]a_n=2.(3)^{n-1}[/tex]

So,

[tex]a_1=2.(3)^{1-1} => 2.3^0 = 2*1 = 2\\a_2=2.(3)^{2-1} => 2.3^1 = 2*3 = 6\\a_3=2.(3)^{3-1} => 2.3^2 = 2*9 = 18\\a_4=2.(3)^{4-1} => 2.3^3 = 2*27 = 54\\a_5=2.(3)^{5-1} => 2.3^4 = 2*81 = 162[/tex]

The equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].

The general equation of the circle is [tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex].

Where, (h, k) is the center and r is the radius of the circle.

Let the equation of the circle be

[tex](x-h)^{2} +(y-k)^{2} =r^{2}..(i)[/tex]

According to the given question.

The center of the circle is (-8, 15).

⇒ (h, k) = (-8, 15)

And, the circle is passing through origin i.e. (0, 0).

Since, the center of the circle is (-8, 15).

So, the equation (i) can be written as

[tex](x-(-8))^{2} +(y - 15)^{2} = r^{2}[/tex]

Also, the circle is passing through (0, 0).

Therefore,

[tex](0+8)^{2} +(0-15)^{2} = r^{2}[/tex]

[tex]\implies 64+ 225 = r^{2} \\\implies 289 = r^{2} \\\implies r=\sqrt{289} \\\implies r = 17[/tex]

So, the radius of the circle is 17 unit and its center is (-8, 15).

Therefore, the equation of the circle is

[tex](x+8)^{2} +(y-15)^{2} = 289[/tex]

Hence, the equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].

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Answer:

The correct option is B

Step-by-step explanation:

Lets put the values in the given function one by one: You will get the answer

f(x)=-(x - 20)(x - 100)

The first option is 20. Substitute the value in the function:

f(x)=-(20-20)(20-100)

f(x)=(- 0)(-80)

f(x)= 0

Second option is 60.

Substitute the value in the function

f(x)=-(x - 20)(x - 100)

f(x)=-(60 - 20)(60 - 100)

f(x)=(-40)(-40)

f(x)=160

Third option is 80:

Substitute the value in the function

f(x)=-(x - 20)(x - 100)

f(x)=-(80 - 20)(80 - 100)

f(x)=(-60)(-20)

f(x)=120

Fourth option is 100:

Substitute the value in the function

f(x)=-(x - 20)(x - 100)

f(x)=-(100 - 20)(100 - 100)

f(x)=(-80)(0)

f(x)= 0

Therefore the values we got are 0, 160, 120, 0

The greatest value is 160.

Thus the correct option is B....

Answer:

B.) 60

Step-by-step explanation:

Answer:

x = 1/2

Step-by-step explanation:

Plug in 0 for y

8x + 2(0) = 4

Simplify

8x + 0 = 4

8x = 4

Divide both sides

8x/8 = x

4/8 = 1/2

Simplify

x = 1/2

Answer

x = 1/2

Answer:

X=1/2

Step-by-step explanation:

The equation for the situation where Carla withdraws $7 and is left with an $89 balance is: B - $7 = $89. So Carla's initial balance was $96.

When writing an equation based on the statement that after withdrawing $7 from a checking account, Carla’s balance was $89, we are essentially working out what Carla's balance was before she made the withdrawal.

If we let the variable B represent Carla's initial balance, then after she withdraws $7, her new balance is B - $7.

Since it's given that her balance after the withdrawal is $89, we can write the following equation to represent the situation:

B - $7 = $89

To find the value of B, we would add $7 to both sides of the equation, which would give us:

B = $89 + $7

B = $96

So, Carla's initial balance before the withdrawal was $96.

An isosceles triangle is the following options, acute and isosceles, which is B and D. Remember that an isosceles triangle has 2 sides that are the same, so its D and every isosceles triangles are acute, not obtuse, so its B.

Hope this helped!

Nate

Answer:

Acute triangle

Step-by-step explanation:

A isosceles triangle is a triangle that has two equal sides.

It would not be a scalene triangle because in scalene triangles all the sides have different lengths.

It might be an acute triangles because all the angles in an acute triangle would be acute angles.

it wouldn't be an obtuse triangle because in an obtuse triangle there is at least one obtuse angle and the other 2 angles would be either acute, right, or obtuse.

It could be an isosceles triangle but that wouldn't make sense since its already an isosceles triangle.

Hope This Helps!!!

Answer: [tex]m=\frac{y-b}{x}[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

To solve for the slope "m", you can follow these steps:

- Subtract "b" from both sides of the equation:

[tex]y-b=mx+b-b\\\\y-b=mx[/tex]

- Divide both sides of the equation by "x". Then:

[tex]\frac{y-b}{x}=\frac{mx}{x}\\\\m=\frac{y-b}{x}[/tex]

Answer:

V = 64 ft^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length of the cube

V = (4)^3

V = 64 ft^3

Answer:

64 ft

Step-by-step explanation:

Volume=Height*Length*Base

=4*4*4

=16*4

=64 ft

Answer:

x=2

Step-by-step explanation:

2(5x+3)=4x+18                       Remove the brackets

10x + 6 = 4x + 18                   Subtract 4x from both sides.

10x - 4x + 6 = 4x-4x + 18      Combine

6x + 6 = 18                            Subtract 6 from both sides

6x + 6 - 6 = 18 - 6                 Combine

6x = 12                                  Divide by 6

6x/6 = 12/6                           Do the division

x = 2

Answer:

20 ≤ f(x) ≤ 28.14

Step-by-step explanation:

Answer:

3x[x² - 6][2x - 3]

Step-by-step explanation:

Group each term carefully [two-by-two], and you will arrive at your answer.

Answer:

[tex]\frac{f(x)}{g(x)}=3x^2+6x-2-\frac{12}{3x+1}[/tex]

Step-by-step explanation:

The first function is [tex]f(x)=9x^3+21x^2-14[/tex]

The second function is [tex]g(x)=3x+1[/tex].

[tex]\frac{f(x)}{g(x)}=\frac{9x^3+21x^2-14}{3x+1}[/tex]

We perform the long division as shown in the attachment to obtain the quotient as: [tex]Q(x)=3x^2+6x-2[/tex] and remainder [tex]R=-12[/tex].

Therefore:

[tex]\frac{f(x)}{g(x)}=3x^2+6x-2-\frac{12}{3x+1}[/tex]

where [tex]x\ne -\frac{1}{3}[/tex]

Answer:

on the flvs test it is option A

Step-by-step explanation:

Answer:

  1.7% compounded continuously

Step-by-step explanation:

The model used for continuous compounding is ...

  f(t) = Pe^(rt)

where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have ...

  f(t) = 1000·e^(0.017t)

Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.

The balance grows at a continuous rate of 1.7%.

To find the growth rate of the account balance in the given function, we differentiate it to obtain [tex]f'(t) = 1000 × 0.017e^(0.017t)[/tex], which shows that the balance grows at a continuous compound rate of 1.7% per year.

The student's question refers to a savings account where the money is compounded continuously. We are given the function [tex]f(t) = 1000e^{0.017t,[/tex]that models the account balance over time t. To find the rate at which the balance grows, we can differentiate this function concerning time.

The derivative of the function[tex]f(t) = 1000e^{0.017t[/tex] concerning t gives us [tex]f'(t) = 1000 × 0.017e^{0.017t[/tex]. This represents the rate of change of the account balance at any time t, which is also the growth rate. Therefore, the rate at which the balance grows is 0.017 or 1.7% per year.