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There are 2 blue blocks in a bag of 9 blocks. You pick 4 without replacement. What is the probability that you get at least 1 blue block?

For this problem, we are given a triangle with a line that bisects its base BC on point D. We need to determine DB using the fact that CB is equal to 6.8.

A bisector divides a segment in two equal parts. Since the line I bisects the segment CB, then it divides this segment in two equal parts such as:

Since the value of CB is equal to 6.8, we have:

The value of DB is equal to 3.4 cm.

Solution

where:

F=future value = 45000

P=present value

r=rate (as a decimal) = 7%=0.07

n=number of compounding periods per year = 1

t=number of years = 6

Therefore the present value deposited today = $29,985.40

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:6

Step-by-step explanation:

The number of hours when the amount Andrew and dave pay for the rentals be equal will be 6 hours.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

\(\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\)

From the equation, the two points of Dave's line will be (0, 6) and (2, 9). Then the equation is given as,

(y - 6)[(9 - 6) / (2 - 0)](x - 0)

y = 1.5x + 6

From the equation, the two points of Andrew's line will be (0, 3) and (1, 5). Then the equation is given as,

(y - 3) = [(5 - 3) / (1 - 0)](x - 0)

y = 2x + 3

The number of hours when the amount Andrew and dave pay for the rentals be equal will be calculated as,

2x + 3 = 1.5x + 6

0.5x = 3

x = 6 hours

The number of hours when the sum Andrew and dave pay for the rentals be equivalent will be 6 hours.

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The simplified expression of 4/x is at most 3 is 3x ≥ 4

The statement is given as:

4/x is at most 3

Express as inequality: (at most means ≤)

So, we have:

4/x ≤ 3

Multiply both sides by x

4 ≤ 3x

Rewrite as:

3x ≥ 4

See attachment for the graph of the inequality

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Answer:

53°

Step-by-step explanation:

As we can see that ∠3 and ∠7 are corresponding angles. Therefore,

Now calculate the angles of ∠3 and ∠7.

Now we can see that ∠3 and ∠1 are alternate angles and ∠7 and ∠1 are alternate exterior angles. Thus, we can say that

Hence the measure of ∠1 is 53°.

♦♦♦♦♦Hope it helps♦♦♦♦♦

Answer:

1,080 meters squared.

Step-by-step explanation:

Let's say the breadth of the rectangle is x. That means the length of it is 6/5x.

The perimeter is 132 meters. The formula for the perimeter is 2 times the breadth plus two times the length.

2(x) + 2(6/5x) = 132

2x + 12/5x = 132

10/5x + 12/5x = 132

22/5x = 132

22x = 660

x = 30.

That means that the breadth of the rectangle is 30 meters, and the length is (6/5) * 30 = 6 * 6 = 36 meters.

The formula for the area of the rectangle is the breadth times the length, so the area is 36 * 30 = 1,080 meters squared.

Hope this helps!

The correct option is option (C) .

Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .

Sampling :

Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.

Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.

There are two main types of sampling:

i) probability sampling

ii) Non-probability sampling

A) probability sampling:

It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.

The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.

Probability Samples:

1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.

2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.

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Answer: 21

Step-by-step explanation:

Answer:

x = 8

y = 21

Step-by-step explanation:

The angle (7x + 12)° and the angle (12x-28)° are alternate interior angles and so has got the same measurement

7x + 12 = 12x - 28

12 + 28 = 12x - 7x

40 = 5x divide both sides by 5

8 = x

The sum of angle (12x - 28)° and (9y - 77)° must be equal because they make a straight line with the measure of 180°

12x - 28 + 9y - 77 = 180 we already found the value of x as 8 so let's rewrite the equation

12 × 8 - 28 + 9y - 77 = 180

96 - 28 - 77 = 180 add like terms

9y - 9 = 180

9y = 189 divide both sides by 9

y = 21

Answer:

-15

Step-by-step explanation:

We proceed as follows;

In this question, we want to fill in the blank so that we can have the resulting expression expressed as the product of two different linear expressions.

Now, what to do here is that, when we factor the first two expressions, we need the same kind of expression to be present in the second bracket.

Thus, we have;

2a(b-3) + 5b + _

Now, putting -15 will give us the same expression in the first bracket and this gives us the following;

2a(b-3) + 5b-15

2a(b-3) + 5(b-3)

So we can have ; (2a+5)(b-3)

Hence the constant used is -15

Answer:

x = 5

Answer:

\(3x + 2 = 17 \\ 3x = 15 \\ \boxed{x = 5}\)

Because we know what x is, we plug in 7 to the expression.

7+3<9

Since 7+3 is 10, then the new expression is 10<9.

I have no idea if this is a true/false question, because this statement is false.

---

sorry if this doesn't help

Answer:

Step-by-step explanation:

Let width be x

Let lenght be 25 + x

Total ax = (25+x) * x

Square with 5in long are cut from the four corner formed = 750in

(25+x-10) * (x-10) * 5 = 750

(15+x) (x-10) = 150

15x-150+x^2-10x =150

15x -150-150+x^2-10x+0

x^2+15x-300=0

(ax^2+bx+c=0)

Answer: it’s square root(72) and no the length is not a rational number

Step-by-step explanation:

The median of X is 1;  P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and  the value of q such that P(X < q) = 0.95 is 1.9.

(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.

Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.

For 0 < x < 2, the CDF is:

F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x

Setting (1/2) * x = 0.5 and solving for x:

(1/2) * x = 0.5;  x = 1

Therefore, the median of X is 1.

(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.

For x > 2, the PDF is 0, so P(X > x) = 0.

Therefore, P(X > 2) = 0.

(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.

P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)

Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.

Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.

(d) The variance of X can be calculated using the formula:

Var(X) = E(X²) - [E(X)]²

To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:

E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3

To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:

E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Now we can calculate the variance:

Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33

Therefore, Var(X) is approximately 0.33.

(e) The expected value of X, E(X), is given by:

E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Therefore, E(X) is 1.

(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:

∫(0 to q) f(x) dx = 0.95

Since the PDF is constant at 1/2 for 0 < x < 2, we have:

(1/2) * (x) | (0 to q) = 0.95

(1/2) * q = 0.95

q = 0.95 * 2 = 1.9

Therefore, the value of q such that P(X < q) = 0.95 is 1.9.

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Answer:

sorry I don't know this answer

Answer:

C. 6.02sec

Step-by-step explanation:

Given

\(h(t) = -16t\² +96t + 2\)

Required

Time to hit the ground

When the turtle shell hits the ground, \(h(t) = 0\)

So:

\(0 = -16t\² +96t + 2.\)

Solving using quadratic formula:

\(t = \frac{-b\±\sqrt{b^2-fac}}{2a}\)

Where:

\(a = -16; b =96; c = 2\)

So:

\(t = \frac{-96\±\sqrt{96^2-4 * -16 * 2}}{2*-16}\)

\(t = \frac{-96\±\sqrt{9344}}{-32}\)

\(t = \frac{-96\±96.66}{-32}\)

Split:

\(t = \frac{-96+96.66}{-32}\) or \(t = \frac{-96-96.66}{-32}\)

\(t = \frac{0.66}{-32}\) or  \(t = \frac{-192.66}{-32}\)

\(t = -0.020625\) or  \(t = 6.020625\)

So time can't be negative, we have:

\(t = 6.020625\)

Option C answers the question

Answer:

A. x=6 ; y=3 radical 3

Step-by-step explanation:

30-60-90 triangle theorem

The correct value of \(f'(t) = -5sin(t)(cos(t))^4/(1 - 2sin(t))^5 + (cos(t))^2/(1 - 2sin(t))^2\)

\(dy/dx = -(2x + y)/(3y^2), d^2y/dx^2 = (2 + 2x)/(3y) - (2 - 3x)/(3y^3)\)

To find f'(t) for the function\(f(t) = (cos(t)/(1 - 2sin(t)))^5,\)we can apply the chain rule. Let's simplify it step by step:

\(d^2y/dx^2,\)

Using the chain rule, we have:

\(f'(t) = 5(cos(t)/(1 - 2sin(t)))^4 * (-sin(t))/(1 - 2sin(t)) + (cos(t)/(1 - 2sin(t)))^5 * (cos(t))/(1 - 2sin(t))^2\)

Simplifying further:

\(f'(t) = (-5sin(t)(cos(t))^4)/(1 - 2sin(t))^5 + (cos(t)^2)/(1 - 2sin(t))^2\)

This is the simplified expression for f'(t).

To find dy/dx using implicit differentiation, we differentiate both sides of the equation\(x^2 + xy + y^3 = 0\)with respect to x:

\(d/dx(x^2 + xy + y^3) = d/dx(0)\)

Applying the chain rule and simplifying, we get:

\(2x + y + 3y^2 * dy/dx = 0\)

Now, we can solve for dy/dx:

\(dy/dx = -(2x + y)/(3y^2)\)

This is the expression for dy/dx in terms of x and y.

To find \(d^2y/dx^2,\)we differentiate the expression for dy/dx with respect to x:

\(d/dx(-(2x + y)/(3y^2))\)

Simplifying and applying the quotient rule results in:

\(d^2y/dx^2 = (2 - 3y(dy/dx))/(3y^2)\)

Substituting the expression for dy/dx, we have:

\(d^2y/dx^2 = (2 - 3y(-(2x + y)/(3y^2)))/(3y^2)\)

Simplifying further:

\(d^2y/dx^2 = (2 + 2x)/(3y) - (2 - 3x)/(3y^3)\)

This is how d2y/dx2 is expressed in terms of x and y.

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Where the above is given, the required angle m∠BAC = 45°.

In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

According to conditions angle b = 90°

The sum of angles of a triangle= 180°

That is a + b + c = 180

Therefore, c = a

       a = (180 - b)/2

          = (180 - 90) / 2

          = 90 / 2

          = 45°

Hence, the required angle m∠BAC = 45°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?

The number of possibilities to make three-digit numbers from 1,4,5,6,3 that the first digit is even and the third digit is odd is 24.

1) To find the number of possibilities to make three-digit numbers from 1, 4, 5, 6, 3 where the first digit is even and the third digit is odd, follow these steps:

Identify the even numbers (for the first digit) - 4 and 6.
Identify the odd numbers (for the third digit) - 1, 3, and 5.
Calculate the possibilities for the second digit. Since we're using the remaining digits, there are 3 options left for each combination.
Multiply the possibilities together: 2 (even numbers) x 3 (second digit options) x 3 (odd numbers) = 18 possibilities.

2) To find the number of ways 5 students can seat in a circle, use the formula (n-1)!. Where n is the number of students.

For 5 students, there are (5-1)! = 4! = 4 x 3 x 2 x 1 = 24 ways for them to sit in a circle.

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Answer:

x = 2

Step-by-step explanation:

a line with an undefined slope is a vertical line with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (2, 5 ) with x- coordinate 2 , then

x = 2 ← equation of line

Since the triangular prism is regular, the base is an equilateral triangle with side length 24, and the height of the prism is 4, we can find the values needed to calculate the lateral area, surface area, and volume.

To find the lateral area, surface area, and volume of a regular triangular prism, we use the following formulas:

Lateral area = perimeter of base x height

Surface area = (2 x area of base) + (perimeter of base x height)

Volume = area of base x height

First, we need to find the perimeter and area of the base triangle:

Perimeter of base = 3 x side length = 3 x 24 = 72

Area of base = (1/2) x base x height = (1/2) x 24 x 24 x sqrt(3)/2 = 144sqrt(3)

Next, we can use these values to calculate the lateral area, surface area, and volume:

Lateral area = perimeter of base x height = 72 x 4 = 288

Surface area = (2 x area of base) + (perimeter of base x height) = (2 x 144sqrt(3)) + (72 x 4) = 288sqrt(3) + 288

Volume = area of base x height = 144sqrt(3) x 4 = 576sqrt(3)

Therefore, the lateral area of the regular triangular prism is 288 square units, the surface area is 288sqrt(3) + 288 square units, and the volume is 576sqrt(3) cubic units.

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

The area of the quadrilateral ABCD is 26 square units

The quadrilateral ABCD is a trapezoid, and it  has the following parameters:

The lengths of these sides can be calculated using

d = √[(x2 - x1)^2 +(y2 - y1)^2]

So, we have

BC = √[(0 - 4)^2 +(3 + 1)^2] = 4√2

AD = √[(-5 - 4)^2 +(4 + 5)^2] = 9√2

CE = √[(2 - 4)^2 +(-3 + 1)^2] = 2√2

The area of the quadrilateral ABCD is then calculated as

Area = 0.5 * (BC + AD) * CE

This gives

Area = 0.5 * (4√2 + 9√2) * 2√2

Evaluate

Area = 26

Hence, the area of the quadrilateral ABCD is 26 square units

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Answer:

-3

Step-by-step explanation: Because it is just like saying 6-3

Answer:

3

Step-by-step explanation:

6+(-3)

A addition symbol and subtraction symbol both make a negative symbol.

6-3

6-3= 3

Hope this helps!

Answer:

2 7/12

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation: