Solve the following quadratic function by utilizing the square root method.

The probability that 4  of the 9  computers are defective is given by expression 0.3665.

It may be calculated by dividing the number of positive outcomes by the total number of potential outcomes. It is the attribute or state of being probable, the degree to which something is likely to happen. In other words, it is a way to gauge how likely an event is to occur.

out of 18 phones, 6 are defective. 9 of the phones are selected at random without replacement.

the probability that 4 of the 9  phones are defective

18 phones- 6 defective , 12 non-defective

9 phones- 4 defective , 5 non-defective

Required probability = [tex]\frac{^6 C_4*^1^2C_5 }{^1^8C_9}[/tex]

= 15x1188 / 48620

P = 0.3665

after rounding we get 0.3665.

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Complete question:

in a certain shipment of 18 computers, 6 are defective. 9 of the computers are selected at random without replacement. what is the probability that 4  of the 9  computers are defective? express your answer as a fraction or a decimal number rounded to four decimal places.

A. The equation of the line that passes through the point (4,3) and has a slope of -5/2 is y = (-5/2)x + 13.

B. The x-intercept of the equation is x = 26/5 or 5.2

A. To find the equation of a line that passes through the point (4,3) and has a slope of -5/2, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is the given point.

Substituting the values, we get:

y - 3 = (-5/2)(x - 4)

Expanding the right side:

y - 3 = (-5/2)x + 10

Adding 3 to both sides:

y = (-5/2)x + 13

B. To find the x-intercept of this equation, we need to set y = 0 and solve for x:

0 = (-5/2)x + 13

Multiplying both sides by -2/5:

0 = x - (26/5)

Adding (26/5) to both sides:

x = 26/5

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Answer:

8

Step-by-step explanation:

2=3

3÷2=1.5

1.5×5=7.5

round up to get 8

Answer:

Step-by-step explanation:

The solution (16, 2) means 16 small gloves and 2 large gloves can be made in less than or equal to 16 hours and cost less than or equal to $40 in materials to make.

The probability that among 250 randomly selected subjects treated with the drug, exactly 10 of them experience nausea is 0.1317, or 13.17%

The number of subjects experiencing nausea follows a binomial distribution with parameters n=250 (number of trials) and p=0.1 (probability of success, i.e., experiencing nausea). The probability of exactly k subjects experiencing nausea is given by the probability mass function:

where (n choose k) is the binomial coefficient "n choose k", which represents the number of ways to select k subjects out of n.

Using this formula with n=250, p=0.1, and k=10, we get:

This gives a probability of approximately 0.1317, or 13.17%.

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The perimeter of an isosceles triangle is the sum of the length of the sides. In this case, the perimeter is 56 inches. The ratio of the sides is [tex]5:4.[/tex]

To calculate the lengths of the sides and base, we need to first calculate the lengths of the two equal sides. To do this, divide the perimeter (56 inches) by the sum of the ratio (5 + 4) which is 9. This gives us a result of 6.2 inches for the two equal sides.

To calculate the length of the base, multiply the two equal sides by the ratio of 5:4, which gives us a result of 7.5 inches for the base.

Therefore, the lengths of the sides and the base of the triangle are: two equal sides of 6.2 inches, and a base of 7.5 inches.

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The simple regression equation assumes that while the error is not observable, it has a distribution with a mean equal to 0 and a constant variance.

A simple regression equation describes how a single variable relates to another variable. It is one of the most widely used statistical tools. Simple regression is used when one predictor variable, often referred to as an independent variable, is used to explain the variance in a dependent variable.There are two types of simple regression equations, linear and nonlinear.

A linear regression equation is a straight line with a constant slope that represents the relationship between two variables, while a nonlinear regression equation is a curve that represents the relationship between two variables.According to the simple regression equation, while the error is not observable, it has a distribution with a mean equal to 0 and a constant variance. The error is the difference between the actual and predicted values of the dependent variable, and it measures the accuracy of the regression equation's predictions.

The mean of the error is zero, which indicates that the predicted values are equal to the actual values on average. The variance of the error is constant, which indicates that the error is distributed evenly throughout the dataset.

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Using fraction, the total number of cupcakes is obtained to be 5.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.

Specifically, if x is the total number of cupcakes, then we can write -

4/x = 80/100

where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.

Solving for x, we get -

x = 4 / (80/100) = 5

So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.

Therefore, in total there are 5 cupcakes.

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I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.

Arrange the functions according to the average rate of change in the interval 1<1. ×< 3 is:   g(x) < f(x) = h(x) 

In other words, g(x) has the smallest average rate of change, while f(x) and h(x) have the same largest average rate of change.

A function is a mathematical rule that takes an input (or inputs) and produces a corresponding output.

It describes a relationship between two quantities, where each input is associated with exactly one output.

Since the interval of interest is not provided, I will assume that the interval is 1 < x < 3, based on the graphs of the functions given.

To determine the ordering of the functions according to their average rates of change on the interval 1 < x < 3, we can use the following formula:

Average rate of change = (f(b) - f(a)) / (b - a)

where a and b are the endpoints of the interval.

Using this formula, we can calculate the average rates of change of the three functions on the interval 1 < x < 3. Here are the results:

f(x): average rate of change = (f(3) - f(1)) / (3 - 1) = (2 - (-2)) / 2 = 2

g(x): average rate of change = (g(3) - g(1)) / (3 - 1) = (-3 - (-1)) / 2 = -1

h(x): average rate of change = (h(3) - h(1)) / (3 - 1) = (0 - (-4)) / 2 = 2

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The complete question is given below:

Arrange the functions in the period 1 according to the average rate of change. 3 is: g(x) f(x) = h(x)

In other words, g(x) has the lowest average rate of change, whereas f(x) and h(x) both have the highest average rate of change.

A function is a mathematical rule that accepts an input (or inputs) and generates an output.

It defines a relationship among two quantities in which each input corresponds to only one output.

Because the interval of interest is not specified, I will assume that it is 1 x 3 based on the graphs of the functions supplied.

We can use the formula that follows to find the ordering of the functions based on their average frequencies of change on the interval 1 x 3:

Change at an Average Rate = (f(b) - f(a)) / (b - a)

where a and b are the interval's ends.

We can compute the average rates of change of all three functions on the interval 1 x 3 using this formula. Here are the outcomes:

f(x): average rate of change = (f(3) - f(1)) / (3 - 1)

                                              = (2 - (-2)) / 2

                                              = 2

g(x): average rate of change = (g(3) - g(1)) / (3 - 1)

                                               = (-3 - (-1)) / 2

                                               = -1

h(x): average rate of change = (h(3) - h(1)) / (3 - 1)

                                               = (0 - (-4)) / 2

                                               = 2

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Answer: 0.9 or 9/10

Step-by-step explanation:

The question asks how many miles did Camila walk in all, so we have to add 1/2 mile and 2/5 of a mile.

1/2 + 2/5 = 9/10

Answer:

9/10 of a mile

Step-by-step explanation:

1/2 + 2/5

= 5/10 + 4/10

=9/10

it takes Sheela to run the second leg of the race: Ascertain the total or contrast: x = 13.83.

In view of the given circumstances, plan:: 14.06+ x = 27.89

Modify variables to the left half of the situation: x = 27.89 - 14.06

Ascertain the total or contrast: x = 13.83

Speed = Distance/Time - This lets us know how slow or quick an article moves. It portrays the distance voyaged partitioned when taken to cover the distance.

Speed is straightforwardly Relative to Distance and Conversely corresponding to Time. Thus,

Distance = Speed X Time, and

Time = Distance/Speed, as the speed builds the time taken will diminish as well as the other way around.

Utilizing these recipes any fundamental issues can be settled. Nonetheless, the right utilization of units is additionally something essential to consider while utilizing equations.

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The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. The periodic rate is 1.1867%

The finance charge is the cost of borrowing money, and it is typically expressed as a percentage of the outstanding balance. In the given scenario, the finance charge is the interest that is charged on the unpaid balance.

10) The unpaid balance is the previous balance minus the payment, which is:

Unpaid balance = Previous balance - Payment

                           = $678.98 - $150

                           = $528.98

Therefore, the unpaid balance is $528.98.

11) The periodic rate is the annual percentage rate (APR) divided by the number of periods per year. Since the period is monthly, we divide the APR by 12. The periodic rate is:

Periodic rate = APR / 12

                     = 14.24% / 12

                     = 1.1867%

Therefore, the periodic rate is 1.1867%.

12) The finance charge is the unpaid balance multiplied by the periodic rate. The finance charge is:

Financial charge = Unpaid balance times the periodic rate

                            = $528.98 × 1.1867%

                            = $6.28 (rounded to the nearest cent)

Therefore, the finance charge is $6.28.

13) The new balance is the sum of the unpaid balance, the finance charge, and the purchases. The new balance is:

New balance = Unpaid balance + Finance charge + Purchases

                      = $528.98 + $6.28 + $147.20

                      = $682.46

Therefore, the new balance is $682.46.

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Answer:

Step-by-step explanation:

The radical form for each expression is given as follows:

How to obtain the radical form of each expression?

The general format of the exponential expression is given as follows:

To obtain the radical form, we have that:

a is the radicand.

n is the exponent.

m is the root.

Hence the radical form of the exponential expression is given as follows:

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The statement "The graph cοntains the pοint (0, 0)" is true.

Quadratic functiοns are used in different fields οf engineering and science tο οbtain values οf different parameters. Graphically, they are represented by a parabοla.

The statements that are true abοut the functiοn and its graph are:

1.The graph οf the functiοn is a parabοla.

2.The graph οf the functiοn οpens dοwn.

3.The graph cοntains the pοint (0, 0).

The functiοn [tex]f(x) = x^2 - 5x + 12[/tex] is a quadratic functiοn, which means its graph is a parabοla. The leading cοefficient οf the functiοn is pοsitive, which means the parabοla οpens dοwn.

Tο find the value οf f(-10), we can substitute -10 fοr x in the functiοn and evaluate:

[tex]f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162[/tex]

Therefοre, the statement "The value οf f(–10) = 82" is false.

The pοint (20, -8) is nοt οn the graph οf the functiοn, because if we substitute x = 20 in the functiοn, we get:

[tex]f(20) = 20^2 - 5(20) + 12 = 200 - 100 + 12 = 112[/tex]

Therefοre, the statement "The graph cοntains the pοint (20, –8)" is false.

On the οther hand, the pοint (0, 0) is οn the graph οf the functiοn, because if we substitute x = 0 in the functiοn, we get:

[tex]f(0) = 0^2 - 5(0) + 12 = 12[/tex]

Therefοre, the statement "The graph cοntains the pοint (0, 0)" is true.

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The probability that a woman chosen at random from this population is more than 67 inches tall is approximately 0.1492 or 14.92%.

To find the probability that a woman chosen at random from this population is more than 67 inches tall, we need to calculate the z-score for this height and then find the corresponding probability from the standard normal distribution.

The z-score is calculated as:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean of the distribution, and σ is the standard deviation.

In this case, x = 67, μ = 64.3, and σ = 2.6. Substituting these values into the formula, we get:

z = (67 - 64.3) / 2.6

= 1.04

Next, we look up the probability corresponding to a z-score of 1.04 in a standard normal distribution table or using a calculator. The probability of a z-score being less than 1.04 is 0.8508.

Since we are interested in the probability of a woman being more than 67 inches tall, we need to subtract this probability from 1:

P(x > 67) = 1 - P(z < 1.04)

= 1 - 0.8508

≈ 0.1492

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The water level is rising at a rate of 32 ft/min when the water is 6 inches deep.

How to solve rise of water level?

Let's first draw a diagram to better understand the problem:

            /|\

           / | \

          /  |  \

         /   |h \

        /    |   \

       /     |    \

      /      |     \

     /       |      \

    /        |       \

   /         |        \

  /_________|

       b

where h is the height of the water, b is the width of the trough at water level, and 10 is the length of the trough.

Since the trough is being filled at a rate of 12 ft³/min, the volume of water in the trough is increasing at a rate of 12 ft³/min. Let's use this to find the rate at which the water level is rising.

The volume of water in the trough is given by the formula:

V = (1/2)bh²

where b is the width of the trough at water level, h is the height of the water, and 1/2 is the area of the triangular cross-section of the trough. We want to find the rate at which h is changing when h = 6 inches = 0.5 ft.

Differentiating both sides of the formula with respect to time t, we get:

dV/dt = (1/2)(db/dt)(h^2) + (1/2)(b)(2h)(dh/dt)

where db/dt is the rate at which the width of the trough at water level is changing, and dh/dt is the rate at which the water level is changing (i.e., the rate we want to find).

We know that dV/dt = 12 ft³/min and h = 0.5 ft. We also know that the width of the trough at the water level is 3 ft. To find db/dt, we need to use similar triangles. The triangle formed by the water and the sides of the trough is similar to the isosceles triangle at the end of the trough. Therefore, the ratio of the width of the trough at the water level to the height of the water is constant:

b/h = 3/1

Solving for b, we get:

b = 3h

on diffrentiating

db/dt = 3(dh/dt)

Substituting the values we know into the formula for dV/dt, we get:

12 = (1/2)(3h)(h²) + (1/2)(3h)(2h)(dh/dt)

12 = (3/2)h³+ 3h²(dh/dt)

4 = h²(dh/dt)

Solving for dh/dt, we get:

Therefore, the water level is rising at a rate of 32 ft/min when the water is 6 inches deep.

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Answer:

1.45 pounds

Step-by-step explanation:

6.6 divided by 4

The x-intercept and y-intercept of the graph of -7x + 3y = 21 are -3 and 7 respectively.

The x-intercept of a graph is the point where a line crosses the x-axis, while the y-intercept of a graph is the point where a line crosses the y-axis.

Therefore, the x-intercept is the value of x when y = 0 while the y-intercept is the value of y when x = 0.

Hence, let's find the x and y-intercept of -7x + 3y = 21

x-intercept

-7x + 3(0) = 21

-7x = 21

x = 21 / -7

x = -3

Y-intercept

-7x + 3y = 21

-7(0) + 3y = 21

3y = 21

y = 21 / 3

y = 7

Therefore,

x-intercept = (-3, 0)

y -intercept = (0, 7)

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Slope intercept form of the given equation is y=16/5x-16/5

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. where, m and c are real integers in the slope-intercept form of the linear equation.

The slope, m, refers measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, the y-coordinate of the location where the line's graph crosses the y-axis.

16x-5y=16

Writing equation in slope intercept form

16-5y=16

-5y=16-16x

y=16/-5 +16/5x

y=16/5x-16/5.

hence, Slope intercept form of the given equation is y=16/5x-16/5

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Answer:

let W =with of field (M)

L=length of field=(7/5)×W

P=perimeter of field =2×(L+W) =240m

substiting L as fungtion of w in last equation:

2×(7/5)×W+W=240m

(12/5×w=120m

W=(5×+20m)/12=50m

L=(7/5×50m)=70m

The period of the Markov chain is 2.

The period of this Markov chain is determined by the number of times you have to go through the probability transition matrix before you return to the same state. The period for this Markov chain is 2, as you can see from the probability transition matrix below:

 P(i,j)   State 0   State 1    State 0   0.5   0.5    State 1   0.3   0.7  


Starting from State 0, the probability of transitioning to State 0 is 0.5, and the probability of transitioning to State 1 is 0.5. If we start from State 1, the probability of transitioning back to State 0 is 0.3, and the probability of transitioning back to State 1 is 0.7.

Therefore, it takes two steps for the chain to return to its original state and the period of this Markov chain is 2.

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The best interpretation of the interval is: We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Option D is correct

A confidence interval is a measure of how accurately an estimate (such as the sample average) corresponds to the actual population parameter. It is a range of values that the researcher believes is very likely to include the actual value of the population parameter.

Here, a 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Thus, we can say that we are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Therefore, option D is correct.

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Answer:

A

Step-by-step explanation:

Since both the x and y coordinates changed signs, this is a reflection over the origin. A reflection over the origin is a reflection across both axes.

Answer: A

In the expression D) -1 and -10 are both extraneous solutions.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

The given logarithmic expression is

=> log(-x)+log(x+11) = 1 .

Here the given expression solution is -1 and -10.

Now put x=-1 into given expression then,

=> log(-(-1))+log(-1+11) =1

=> log(1)+log(10) =1

=> 0+1=1

=> 1=1

Then -1 is extraneous solution.

Now put x=-10 then,

=> log(-1(-10))+log(-10+11)=1

=> log(10)+log(1)=1

=> 1+0=1

=> 1=1

Then x=-10 is also extraneous solution.

Hence the correct option is D) -1 and -10 are both extraneous solutions.

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The function f(x) = 5/(x+3), vertical asymptote at x = -3,  domain of the function is all real numbers except x = -3,  range is all real numbers except 0.

A function is a mathematical object that takes one or more inputs (usually represented as variables) and produces a single output. In other words, a function is a relation between sets of inputs and outputs that associates each input value with exactly one output value.

A function can be represented by an equation or a graph. The most common way to write a function is in the form f(x) = y, where x is the input variable and y is the output variable. The function f maps each value of x to a corresponding value of y.

Functions can be classified based on their properties, such as their domain (set of allowable input values), range (set of output values), and behavior (e.g., increasing, decreasing, constant, etc.). Some common types of functions include linear, quadratic, exponential, trigonometric, and logarithmic functions.

The function f(x) = 5/(x+3) has a vertical asymptote at x = -3, since the denominator becomes zero at that point.

The domain of the function is all real numbers except x = -3, since division by zero is undefined.

To find the range, we can consider what happens to the function as x approaches -3 from both sides. As x approaches -3 from the left (i.e., as x gets closer and closer to -3 from values less than -3), the function becomes increasingly negative. As x approaches -3 from the right (i.e., as x gets closer and closer to -3 from values greater than -3), the function becomes increasingly positive. This means that the range of the function is all real numbers except 0.

Therefore, the asymptote is x = -3, the domain is all real numbers except x = -3, and the range is all real numbers except 0.

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The new coordinates would be

W' (12 , 6)

X'( 24 , 18 )

Z'(24 ,6 )

What exactly does coordinate geometry mean?

The term "coordinate geometry" refers to the study of geometry using coordinate points (or analytic geometry). Calculating distances between points, segmenting lines into m:n pieces, finding a line's midpoint, figuring out a triangle's area in the Cartesian plane, and other operations are all achievable with coordinate geometry.

Remember that the rule for a dilation by a factor of k about the origin is

 (x,y) = (kx, ky)

Identify the coordinates of the points W, X and Z. Then, apply a dilation by a factor of 3 about the origin to find W', X' and Z', the new coordinates after the dilation.

  w = (4,2)

   x = ( 8, 6 )

   z = ( 8,2)

Apply a dilation by a factor of 3:

  W(4,2) ⇒ W'(3 * 4, 3 * 2) = W' (12 , 6)

 X(8 ,6 ) ⇒ X'(3 * 8 , 3 * 6 ) = X' ( 24 , 18 )

 Z(8 , 2 ) ⇒ Z'(3*8 , 3 * 2) = Z'(24 ,6 )

Therefore, the new coordinates would be

W' (12 , 6)

X'( 24 , 18 )

Z'(24 ,6 )

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An exponential equation, y = (20) 3ᵗ, shows the number of infected people from an outbreak of whooping cough. The number of Infected people reach 1000 after 3.56 weeks.

We have an equation that shows the number of people infected from a whooping cough outbreak. This equation is y is equal to 20 times 3 to the power of t, i.e. y = (20) 3ᵗ -- (1)

where y--> number of infected people

t--> time in weeks

An exponential equation is an equation with exponents where either the exponent or part of the exponent is a variable. As we see 't' is variable so, eqution (1) is an exponential equation. We have to determine time in weeks when the number of infected people count reach 1,000. Substitute, y = 1000 in (1)

=> 1000 = (20)3ᵗ

Dividing by 20 both sides

=> 1000/20 = 3ᵗ

=> 50 = 3ᵗ

Taking natural logarithm both sides,

=> ln(50) = ln( 3ᵗ)

=> ln(50) = t ln(3)

=> t = ln(50)/ln(3)

=> t = 3.56

Hence, required value of t is 3.56 weeks.

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