There are 100 gadgets within which 12 are not functioning properly. What is the probability to find 3 disfunctional gadgets within 10 randomly taken ones. 2. The probability

Answer:

\( \sqrt{128} - \sqrt{72} = 2.82842712474619 \\ \\ 2.82842712474619 \div \sqrt{8 } = 1\)

HOPE IT HELPS! :)

Answer:

80º and 100º

Step-by-step explanation:

The amount of interest in 7 years will be $126.

To calculate the interest earned by Buddy after 7 years, we can use the formula for simple interest, which is given by:

I = Prt

Where I is the interest earned, P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the time period in years.

We are given that Buddy invests $600 in a savings account that pays 3% interest, which means that the annual interest rate r is 0.03. Therefore, we can plug these values into the formula and solve for I:

I = 600 x  0.03 x 7

I = $126

Therefore, Buddy will earn $126 in interest after 7 years.

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Answer:

Let m represent the number of minutes.

Amount of water in Karla's tank:  100 + 5m

Amount of water in Jake's tank:  50 + 10m

Same amount of water:  100 + 5m  =  50 + 10 m

--->                                         100  =  50 + 5m

--->                                            50  =  5m

--->                                            10 = m

In ten minutes, Karla's tank will have 100 + 5(10)  =  100 + 50  =  150 gallons.

In ten minutes, Jake's tank will have 50 + 10(10)  =  50 + 100  =  150 gallons.

Step-by-step explanation:

hope this helped!

Answer: 2/5

Step-by-step explanation: Find a number that both the numerator and denominator can be divided by that is the same for both. In this case, both can be divided by 3. That gives us 4/10. Now we do the same thing again, this time the number is 2. Dividing both by 2 gives us 2/5.

The simplest form of the fraction 12/30 is 2/5.

The given fraction is 12/30.

We have to simplify the fraction to simplest form.

To simplify the fraction 12/30 to its simplest form, we need to find the greatest common divisor (GCD) of the numerator and denominator and then divide both by the GCD.

The GCD of 12 and 30 is 6.

We can divide both the numerator (12) and denominator (30) by 6:

12 ÷ 6 = 2

30 ÷ 6 = 5

Therefore, the simplest form of 12/30 is 2/5.

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Answer: (50,-20)

Step-by-step explanation:

Point B is (100,0).

Point A is (0,-40).

To find C you need the midpoint of both A and B, which means you add both coordinate x and coordinate y together to find the middle of both.

Midpoint of x coordinates:

100+0= 100

100÷2= 50

Midpoint of y coordinates:

0+(-40)= -40

-40÷2= -20

Therefore, point C is (50,-20)

Answer: 5.

Step-by-step explanation: The .57 doesn't matter so we can remove that.

Multiply 32 by 0.15

32 x 0.15 = 4.8

After you get your result, round it to the nearest tenths.

4.8 = 5

hope this helps

By examining the truth table, we can determine the two expressions are equivalent and it is possible for one of them to be true and the other false.

Given two Boolean expressions, it is possible for one of them to be true and the other false if they are not equivalent. For example, consider the two expressions: φ ∧ (ψ ∨ θ) and (φ ∧ ψ) ∨ (φ ∧ θ).

It is possible to construct a truth table for these two expressions, which shows all possible combinations of truth values for φ, ψ, and θ, along with the corresponding truth values for the two expressions.

Boolean logic is a branch of mathematical logic that deals with binary operations (i.e., true or false values) and is often used in computer science. One of the basic operations in Boolean logic is the logical conjunction (denoted by ∧), which represents the and operator. For example, if φ and ψ are two propositions, then φ ∧ ψ is true if and only if both φ and ψ are true.

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Answer:

try mathaway algebra type in the equation and youll get an answer right away

Step-by-step explanation:

B

To find the average you add them all up and divide by how many numbers there are. 2+3+6+13+16=40 There are 5 numbers so 40/5=8

A would be 7 and c would be 9, so the answer is b.

Answer:

A. $ (5 + 2x), B. = $ 305

Step-by-step explanation:

x miles

A. cost for x miles = 5 + 2x ($)

B. cost for 150 miles = 5 + 2*150 =305 ($)

Answer:

A. let the mile driven = x

5 + 2x

B. × = 150 mile

taxi service = $5 + $2(150)

= $305

*in an equation u dont have to write the symbol . for example, $, ml, km, etc.

Answer:

The vertical line test is a way to figure out if a figure on a graph is a function. Imagine a vertical line goes across the graph from left to right. If the line touches two points at the same time, it's not a function.

Answer:

Sample Response: The vertical line test is a way to determine if a relation is a function. This test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function because two different outputs have the same input.

Answer:

True

Step-by-step explanation:

Angle-Angle-Side congruency

Answer:

A. True

Step-by-step explanation:

Answer:

48 and 32

Step-by-step explanation:

both numbers get rounded by 8 going up and down rounding it to 40

63.75km/hr is the car average speed fpr the entire journey.

The formula for calculating average speed is expressed according to the formula below

Average speed = change in distance/water

Substitute the given parameter

Average speed = 90/2 + 75/4

Average speed = 45 + 18.75

Average speed = 63.75km/hr

Hence the car's average speed for the entire journey is 63.75km/hr

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Answer:85.7 miles per hour

Step-by-step explanation:

Answer:

The answer is 28/5

Step-by-step explanation:

5.6 can be written as 56/10 into vulgar fraction.

Thus, The answer is 56/10 = 28/5

-TheUnknownScientist 72

Jalen need to buy a tire of 69.08 m.

Given that, the tire diameter is 24 inches, we need to calculate the size tire does Jalen need to buy,

To find the same, we will calculate the circumference of the tire,

Circumference = π × diameter

= 3.14 × 22

= 69.08

Hence, Jalen need to buy a tire of 69.08 m.

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The Central Limit Theorem is an important tool that provides the information you will need to use sample means to make inferences about a population mean.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that if we take repeated random samples of size n from any population with a finite mean and variance, then the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

This means that if we take a large enough sample size from a population, the distribution of the sample means will be approximately normal, even if the population distribution is not normal. This is important because the normal distribution is well understood and has many useful properties that make it easier to work with in statistical analyses.

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The price of Ravi's lunch, before tax and tip was added to the total cost of the meal is $13.19.

Both the tax and the tip paid would increase the cost of the meal. Thus, their dollar value has to be subtracted from the total amount he pays.

Value of the lunch after the tip has been removed = (1 - 0.2) x 17.92 = $14.34

Value of the lunch after the tax has been removed = (1 - 0.08) x $14.34 = $13.19

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Answer:

(r + 20)t = r

Step-by-step explanation:

Distance is constant in the scenario above, distance from home to wedding and wedding back home is the same.

From wedding back home. :

Recall : Distance = speed * time

Distance = r * 1 hour

From home to wedding :

Speed = 20 mph more ; r + 20

Time = t

Distance = (r + 20)* t = (r +20)t

Since the distance are the same, we can equate both :

(r + 20)t = r * 1

= (r + 20)t = r

Answer:

B

Step-by-step explanation:

I got it right on edge.

Juan wants to buy a video game for $63  He saves  every Friday $12.

An equation to represent Juan’s total savings, , in dollars, after  Fridays y is  

Part A is

y =12x

Fridays will it take for Juan to save up enough money for the video game is .

Part B

y >  63

12 x > \(5\frac{1}{4}\)

x  =  6

so

That means 6 fridays

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Answer: 14 mile/s2

Step-by-step explanation:

The probability that a poker hand consists of two jacks or two fives is approximately 0.009, or 0.9% when rounded to three decimal places.

To calculate the probability that a poker hand consists of two jacks or two fives, we need to determine the total number of possible two-card hands and the number of favorable outcomes (two jacks or two fives).

Step 1: Calculate the total number of possible two-card hands.
There are 52 cards in a standard deck. To form a two-card hand, we have 52 choices for the first card and 51 choices for the second card. Using the combination formula (nCr), the total number of possible hands is C(52, 2) = 52! / (2! * (52-2)!) = 1,326.

Step 2: Calculate the number of favorable outcomes.
There are 4 jacks and 4 fives in a deck, which gives us 8 possible cards to form our desired hands. For two jacks, there are C(4, 2) = 6 combinations. For two fives, there are also C(4, 2) = 6 combinations.

Step 3: Calculate the probability.
The total number of favorable outcomes is the sum of the combinations of two jacks and two fives, which is 6 + 6 = 12. Now, divide the number of favorable outcomes by the total number of possible hands:

Probability = (Number of favorable outcomes) / (Total number of possible hands) = 12 / 1,326 ≈ 0.00905

So, the probability that a poker hand consists of two jacks or two fives is approximately 0.009, or 0.9% when rounded to three decimal places.

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Using the Newton-Raphson method with an initial guess of 0.5, the Bisection method with initial intervals [0.5, 2] and the Secant method with initial guesses of 2 and 1.5, the equation \(\( \sin(x) = |x| \)\) can be solved to an error tolerance of 0.0005.

To solve the equation \(\( \sin(x) = |x| \)\)using different numerical methods with the given parameters, let's go through each method step by step.

(b) Newton-Raphson Method:

The Newton-Raphson method uses the iterative formula \(\( x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} \)\) to find the root of a function. In our case, the function is \(\( f(x) = \sin(x) - |x| \).\)

Let's start with an initial guess, \(\( x_0 = 0.5 \)\). Then we can compute the subsequent iterations until we reach the desired error tolerance:

Iteration 1:

\(\( x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} \)\)

To find \(\( f(x_0) \)\), we substitute \(\( x_0 = 0.5 \)\) into the equation:

\(\( f(x_0) = \sin(0.5) - |0.5| \)\)

To find \(\( f'(x_0) \)\), we differentiate the equation with respect to \(\( x \):\( f'(x) = \cos(x) - \text{sgn}(x) \)\)

Now we can substitute the values and compute \(\( x_1 \):\( x_1 = 0.5 - \frac{\sin(0.5) - |0.5|}{\cos(0.5) - \text{sgn}(0.5)} \)\)

We continue this process until the error is less than or equal to 0.0005.

(c) Bisection Method:

The bisection method works by repeatedly dividing the interval between two initial guesses until a root is found.

Let's start with two initial guesses, a = 0.5 and  b = 2 . We will divide the interval in half until we find a root or until the interval becomes smaller than the desired error tolerance.

We start with the initial interval:

\(\( [a_0, b_0] = [0.5, 2] \)\)

Then we compute the midpoint of the interval:

\(\( c_0 = \frac{a_0 + b_0}{2} \)\)

Next, we evaluate \(\( f(a_0) \)\) and \( f(c_0) \) to determine which subinterval contains the root:

- If \(\( f(a_0) \cdot f(c_0) < 0 \),\) the root lies in the interval \(\( [a_0, c_0] \)\).

- If \(\( f(a_0) \cdot f(c_0) > 0 \)\), the root lies in the interval \(\( [c_0, b_0] \).\)

- If \(\( f(a_0) \cdot f(c_0) = 0 \), \( c_0 \)\) is the root.

We continue this process by updating the interval based on the above conditions until the error is less than or equal to 0.0005.

(d) Secant Method:

The secant method is similar to the Newton-Raphson method but uses a numerical approximation for the derivative instead of the analytical derivative. The iterative formula is\(\( x_{n+1} = x_n - \frac{f(x_n) \cdot (x_n - x_{n-1})}{f(x_n) - f(x_{n-1})} \).\)

Let's start with two initial guesses, \(\( x_0 = 2 \)\) and\(\( x_1 = 1.5 \).\) We can compute the subsequent iterations until the error is less than\(\( f(c_0) \)\) or equal

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Three factors that have led the government to provide social assistance to a large part of the South African population are historical inequality, high levels of poverty and unemployment, and the need for social cohesion and stability.

Firstly, historical inequality in South Africa, particularly during the apartheid era, has left a legacy of economic and social disparities. The government recognizes the need to address these inequalities by providing social assistance to uplift marginalized and disadvantaged communities.

Secondly, high levels of poverty and unemployment in South Africa contribute to the necessity of social assistance programs. Many individuals and households struggle to meet their basic needs, and social assistance helps alleviate poverty and provide a safety net for vulnerable populations.

Lastly, social assistance programs are also implemented to promote social cohesion and stability. By ensuring that basic needs are met and reducing extreme poverty, the government aims to create a more equitable society and prevent social unrest.

Overall, these factors have driven the government to prioritize social assistance programs as a means to address historical inequalities, alleviate poverty, and promote social cohesion in South Africa.

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Answer:

The answer is A,

Step-by-step explanation:

Because the constant in a problem does not change, therefore if 115x is changing 350 is the constant so it eliminates B, and they make 115 per hour but not the question so that eliminates D.   but if the factory started with 115 pairs 115 would not be the variable....it would be the constant, so that leaves A, they started with 350 pairs of shoes

Hope this helps!

Answer:

The shortest side of the fence can have a maximum length of 80 feet

Step-by-step explanation:

Inequalities

To solve the problem, we use the following variables:

x=length of the longer side

y=length of the sorter side

The perimeter of a rectangle is calculated as:

P = 2x + 2y

The perimeter of the fence must be no larger than 500 feet. This condition can be written as:

\(2x + 2y \le 500\)

The second condition states the longer side of the fence must be 10 feet more than twice the length of the shorter side.

This can be expressed as:

x = 10 + 2y

Substituting into the inequality:

\(2(10 + 2y) + 2y \le 500\)

This is the inequality needed to determine the maximum length of the shorter side of the fence.

Operating:

\(20 + 4y + 2y \le 500\)

Simplifying:

\(20 + 6y \le 500\)

Subtracting 20:

\(6y \le 500 - 20\)

\(6y \le 480\)

Solving:

\(y \le 480 / 6\)

\(y \le 80\)

The shortest side of the fence can have a maximum length of 80 feet