a certain medical test is known to detect 84% of the people who are afflicted with the disease y. if 10 people with the disease are administered the test, what is the probability that the test will show that: all 10 have the disease, rounded to four decimal places? 0.1749 at least 8 have the disease, rounded to four decimal places? at most 4 have the disease, rounded to fo

Answer:

To complete the square and rewrite the quadratic function y = x² + 7x + 3 in vertex form, we follow these steps:

Factor out the coefficient of x² from the first two terms:

y = 1(x² + 7x) + 3

Take half of the coefficient of x (which is 7 in this case) and square it. Add this value inside the parentheses, and subtract the same value multiplied by the coefficient of x² (which is 1) outside the parentheses to maintain the same value of the expression:

y = 1(x² + 7x + (7/2)² - (7/2)²) + 3

Simplify inside the parentheses by combining the first three terms using the square of the binomial formula (a + b)² = a² + 2ab + b²:

y = 1(x + 7/2)² - 1/4 + 3

Combine the constant terms to simplify:

y = 1(x + 7/2)² + 11/4

Therefore, the quadratic function y = x² + 7x + 3 can be written in vertex form as y = (x + 7/2)² + 11/4. The vertex is located at the point (-7/2, 11/4).

Hope This Helps!

Answer:

To solve the equation XX/2-6=-18, we need to isolate the variable on one side of the equation. First, we can add 6 to both sides of the equation to eliminate the constant term on the left side: XX/2-6+6=-18+6 Simplifying the left side, we get: XX/2=-12 Next, we can multiply both sides by 2 to eliminate the fraction: 2*(XX/2) = 2*(-12) Simplifying the left side, we get: XX = -24 Therefore, the value of XX that satisfies the equation is -24.

The required probability of  more than five students being born on Christmas Day as per total of 1095 students is approximately 0.0735.

Let X be the number of students in the college who were born on Christmas Day.

Birth rates are constant throughout the year,

Assume that X follows a binomial distribution with

n = 1095

and p = 1/365,

where n is the total number of students in the college

And p is the probability that a student is born on Christmas Day.

The probability of more than five students being born on Christmas Day can be written as,

P(X > 5) = 1 - P(X ≤ 5)

Use the normal approximation to the binomial distribution to estimate P(X ≤ 5)

And then subtract this value from 1 to obtain an estimate of P(X > 5).

Use the normal approximation,

First check if the conditions for using it are met.

For a binomial distribution with n trials and probability of success p, the mean and standard deviation are,

μ = np

σ = √(np(1-p))

here, we have,

μ = 1095 × (1/365)

  = 3

σ = √(1095 ×(1/365) × (1 - 1/365))

  ≈ 1.73

Expected value is greater than 5 .

And the standard deviation is not too small ( σ > 1),

Use the normal approximation to the binomial distribution.

Using the continuity correction, we can rewrite P(X ≤ 5) ,

P(X ≤ 5) ≈ P(Z ≤ (5.5 - μ) / σ)

where Z is a standard normal variable.

Substituting the values for μ and σ, we get,

P(X ≤ 5) ≈ P(Z ≤ (5.5 - 3) / 1.73)

≈ P(Z ≤ 1.45)

≈ 0.9265

Using a standard normal table

P(Z ≤ 4.39) ≈ 0.9265

Probability of fewer than or equal to 5 students being born on Christmas Day is very close to 1.

This implies,

Estimation of the probability of more than five students being born on Christmas Day as,

P(X > 5)

≈ 1 - 0.9265

≈ 0.0735

This means that the probability of more than five students being born on Christmas Day is extremely small.

Conclude that it is unlikely that more than five students were born on Christmas Day.

Therefore, the probability of  more than five students being born on Christmas Day is approximately 0.0735.

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a) The anomalous result in the table is the Durablast battery in the second trial, which recorded a time taken of 768 seconds.

b) The mean averages for each brand of battery are 955.33, 852 and 908 seconds.

c) the amount of charge stored by each brand of battery is 1098.6 coulombs, 1065 coulombs and 1089.6 coulombs.

d) The results of this experiment can be presented in a table format, showing the current flowing, the mean time taken, and the amount of charge stored for each brand of battery.

It is an unexpected or unusual outcome that does not agree with the expected or accepted outcome. It may be a result of a mistake, an anomaly in the data, or a misinterpretation of the data.

a) The anomalous result in the table is the Durablast battery in the second trial, which recorded a time taken of 768 seconds.

b) The mean averages for each brand of battery are:

Longalast: 955.33 seconds

Durablast: 852 seconds

Morelife: 908 seconds

c) The amount of charge stored by each brand of battery can be calculated by multiplying the current flowing into the toothbrush (amps) by the mean time taken (seconds) for each battery:

Longalast: 1.15 amps x 955.33 seconds = 1098.6 coulombs

Durablast: 1.25 amps x 852 seconds = 1065 coulombs

Morelife: 1.20 amps x 908 seconds = 1089.6 coulombs

d) The results of this experiment can be presented in a table format, showing the current flowing, the mean time taken, and the amount of charge stored for each brand of battery. This would allow the reader to easily compare the performance of each battery, as well as to identify any anomalous results.

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The volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.

We are given that the radius of the cylinder is 1.2 cm and the height is 4 cm.

So,

⇒ Volume = π[tex]r^{2}[/tex]h

⇒ Volume = π * [tex](1.2)^{2}[/tex] * 4

⇒ Volume = 3.14 * 5.76

⇒ Volume = 18.0864 cubic cm

Similarly,

⇒ Total surface area = 2πrh + 2π[tex]r^{2}[/tex]

⇒ Total surface area = 2π * 1.2 * 4 + 2π[tex](1.2)^{2}[/tex]

⇒ Total surface area = 2π * 4.8 + 2π * 1.44

⇒ Total surface area = 2π * (4.8 + 1.44)

⇒ Total surface area = 2 * 3.14 * 6.24

⇒ Total surface area = 39.1872 square cm

Hence, the  volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.

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The solution to the inequality 32 ≤ −5z − 32 is z ≥ -12.8.

To solve for z in the inequality 32 ≤ -5z - 32, we first add 32 to both sides:

32 + 32 ≤ -5z

64 ≤ -5z

Then, we can divide both sides by -5, but we need to reverse the inequality since we are dividing by a negative number:

-5z ≤ 64

z ≥ -64/5

z ≥ -12.8

Therefore, the solution to the inequality is z ≥ -12.8.

Option (d) is correct: z ≥ -12.8.

The complete question is:

Solve 32 ≤ −5z − 32.

Answer choices:

a) z ≤ 0

b) z ≥ 0

c) z ≤ −12.8

d) z ≥ −12.8

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Answer:

0.986

Step-by-step explanation:

4.93 ×100÷5×100 = 493÷500=0.986

The area of the shape as shown in the picture is 68.76 m².

Area is the region bounded by a plane shape.

To calculate the area of the picture above, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 68.76 m².

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By answering the presented question, we may conclude that The resulting true inequality is: 25 ≤ 27.

In mathematics, an inequality is a non-equal connection between two of a expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.

inequality: -125 ≥ -135

-125 ÷ -5 ≤ -135 ÷ -5

25 ≤ 27

The resulting true inequality is: 25 ≤ 27.

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Answer:

32.83= 15(x) +1.93

32.83- 1.93= 30.90

30.9= 15x

30.9/ 15 =2.06

X= 2.06

Which means each bottled juice cost 2.06 each

Step-by-step explanation:

Answer:

how many fluid ounsous you need

Step-by-step explanation:

Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).

When two quantities, including such time and distance or hours and compensation, change directly, they do so at a predictable rate.

The constant of variation is another name for the constant rate of increase or decline. We will examine three different methods of showing direct variation in this lesson: an equation, a table, and just a graph.

For the given question:

y varies directly as the square root of x.

y ∝ √x

y = k√x  

Here, k is the constant of proportionality

Now,

y=43 when x=289 .

43 = k√289

k = 43/√289

k = 2.53

Now, y when  x=191.

y = k√x  

y = 2.53√191

y = 34.96

Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).

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If we multiply 21 by 4, we get 84 .the value of k is 84, as it is 4 times as many as 21.

Multiplication is a mathematical operation that combines two or more numbers to find their product. It is an operation of repeated addition or scaling up of a number. In multiplication, the numbers being multiplied are called factors, and the result is called the product. Multiplication is denoted by the "×" symbol or by placing the numbers adjacent to each other.

The value of k is 4 times as many as 21," we can break it down as follows:

"4 times" means multiplication, where we are multiplying a number by 4.

"As many as" implies equality, meaning the value on one side of the comparison is equal to the value on the other side.

"21" is a specific number mentioned in the statement.

Therefore,  if we multiply 21 by 4, we get 84 .the value of k is 84, as it is 4 times as many as 21.

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The percentile value to construct a 90% bootstrap confidence interval for the true mean amount of ammonium in the rainwater is equals to 5%.

If the bootstrap distribution is approximately symmetric, we can construct a confidence interval by finding the percentiles in the bootstrap distribution so that the proportion of bootstrap statistics between the percentiles matches the desired confidence level. We have a forest ranger which select a random rainwater sample from a watershed area in tennessee with

Sample size, n = 10

Ranger measures the amount of ammonium in each sample. Measurements to construct a 90% bootstrap confidence interval for true mean amount of ammonium in the rainwater. We have to determine the p-value for her ordered. Now,

The percentile bootstrap interval is just the interval between the 100×(α/2)100 and 100×(1−α/2) percentiles of the distribution of θ estimates obtained from resampling, where θ represents a parameter of interest and α is the level of significance. but we have to determine percentile value for 90% confidence interval. Here, level of significance for 90% is α = 1 - 0.90 = 0.10, α/2 = 0.05

So, percentile value = α/2 = 0.05

= 5%

The number of the bootstrap sample that must be chopped off to produce a 90% confidence interval is N = 10 ×α/2

=> N = 10× 0.05 = 0.5

Hence, required percentile value is 5%.

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The domain of the function is option B ("The domain is all real numbers.") is generally the default assumption unless there are any specific restrictions on the function's definition.

What is domain of the function?

The domain of a function is the set of all possible input values for which the function is defined.

In option A, the domain is restricted to all real numbers greater than 0, which means that the function is undefined for any input less than or equal to 0.

Option B indicates that the domain includes all real numbers, which could be the case for some functions but not all.

Option C suggests that the domain excludes a single value of 0, which could be true for some functions as well.

Option D indicates that the domain includes all real numbers less than 0, which may not be the case for most functions.

Without knowing the specific function in question, it is difficult to determine the correct answer. However, option B ("The domain is all real numbers.") is generally the default assumption unless there are any specific restrictions on the function's definition.

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Complete question is: The domain of the function is option B ("The domain is all real numbers.") is generally the default assumption unless there are any specific restrictions on the function's definition.

Answer:

A banana costs $0.05

Step-by-step explanation:

Let a = the cost of an apple

Let b = the cost of a banana.

a + b = 1.10

a = b + 1  Substitute b + 1 for a in the bold equation.

b + 1 + b = 1.10  Combine like terms

2b + 1 = 1.10  Subtract 1 from both sides

2b = .10  Divide both sides by 2

b = .05

An apple would cost

a = .05 + 1

a = 1.05

An apple and a banana together would cost 1.10

a + b = 1.10

1.05 + .05 = 1.10

1.10 = 1.10 checks.

Helping in the name of Jesus.

Hello and regards taylahflynn2965

Answer: The cost of the banana is $0.05.

This is an exercise in elementary algebra, which is a branch of mathematics that focuses on the study of the fundamental operations and properties of numbers and algebraic expressions. In particular, in elementary algebra you learn to solve problems by manipulating algebraic expressions and applying basic algebraic rules and procedures.

One of the fundamental skills of elementary algebra is solving systems of linear equations with two variables. Such a system is a set of two or more equations involving two or more variables. In the case of a system of two linear equations with two variables, the solution of the system consists in finding the numerical values of the two variables that satisfy both equations.

The substitution technique is one of the main tools used to solve systems of linear equations with two variables in elementary algebra. This technique consists of isolating one of the variables in one of the equations and substituting that expression in the other equation. The resulting equation is then solved to find the value of the other variable. Finally, this value is substituted into one of the original equations to find the value of the other variable.

Let x be the cost of the banana.

From the statement, we know that:

Solving the equation:

2x + $1 = $1.10

2x = $1.10 - $1

2x = $0.10

x = $0.10 / 2

x = $0.05

Therefore, the cost of the banana is $0.05.

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To find the expected value of the largest of the three claims, we will first need to understand the probability density function (pdf) of the maximum of the three independent random variables.   The formula is = ∫x * 3 * F(x)^2 * f(x) dx

Let's denote the common density function as f(x), and the cumulative distribution function (CDF) as F(x), where x is the amount of a claim in thousands.
Step 1: Find the CDF of the maximum of three claims
Since the claims are independent random variables, the CDF of the maximum of three claims (denoted as M) is given by the product of the individual CDFs: F_M(x) = F(x)^3.
Step 2: Find the pdf of the maximum of three claims
To obtain the pdf of M, we need to differentiate the CDF with respect to x. Let's denote the pdf of M as f_M(x):
f_M(x) = d(F_M(x))/dx = d(F(x)^3)/dx = 3 * F(x)^2 * f(x).
Step 3: Compute the expected value of the largest claim
The expected value of the largest claim (denoted as E[M]) is given by the integral of the product of the pdf and the variable x over the support of the distribution:
E[M] = ∫x * f_M(x) dx
= ∫x * 3 * F(x)^2 * f(x) dx
To evaluate this integral, you would need the specific form of the common density function f(x) and the cumulative distribution function F(x). However, the general formula for the expected value of the largest claim is provided above.

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The measures of central tendency of the dot plot is:

Range = 6

Mode: 5.5 and 6

Median is 6

A measure of central tendency is defined as a single value that explains the way by which a group of data cluster near the center value. In other words it is the center of data set.

The range is the difference between the highest and lowest values of the dataset. Thus:

Range = 11 - 5

Range = 6

Mode is defined as the term that has the most frequency of occurrence. Thus, the mode of the dot plot is:

5.5 and 6

The median is defined as the middle term when arranged in ascending or descending order:

5, 5, 5.5, 5.5, 5.5, 5.5, 6, 6, 6, 6, 6.5. 6.5, 7, 7, 7.5, 8, 8, 9, 11

Thus, the median is 6

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Step-by-step explanation:

We can use the kinematic equations of motion to solve this problem. Let's assume the initial velocity of the snowball is 18 feet per second and its initial height is 25 feet. Also, we know that the acceleration due to gravity is -32.2 feet per second squared (assuming downward direction as negative).

To find out when the snowball hits the ground, we can use the equation:

h = 25 + 18t - 16t^2

where h is the height of the snowball at time t. We want to find the value of t when h = 0 (since the snowball hits the ground at that point). Therefore, we can rewrite the equation as:

16t^2 - 18t - 25 = 0

Solving for t using the quadratic formula, we get:

t = (18 ± √(18^2 + 41625))/(2*16)

t = 2.25 seconds or -0.875 seconds

Since time cannot be negative, the snowball hits the ground after 2.25 seconds.

To find the maximum height the snowball reaches, we can use the fact that the maximum height occurs at the vertex of the parabolic trajectory. The x-coordinate of the vertex is given by:

t = -b/2a

where a and b are the coefficients of the quadratic equation. In this case, a = -16 and b = 18, so:

t = -18/(2*(-16)) = 0.5625 seconds

To find the corresponding height, we can substitute t = 0.5625 seconds into the equation for h:

h = 25 + 18(0.5625) - 16(0.5625)^2

h = 28.2656 feet

Therefore, the maximum height the snowball reaches is 28.2656 feet.

Answer:

d=91

Step-by-step explanation:

Answer:   d=91

Step-by-step explanation:

First thing first, you have to use the distributive property. Distribute the 8 to the d-87.

(8*d) - (8*87) = 32  =    8d - 696= 32  

Next, you have to add 696 to both sides of the equation:

8d-696 +696= 32+696  =  8d= 728

Last step is to divide both sides by 8:

8d/8 = 728/8 =  

d= 91

We can check this by plugging the number 91 to the variable d in the equation:

(8*91) - (8 *87) = 32    =  728 - 696= 32

Answer:

The average monthly revenue last year would be 99,020.

Step-by-step explanation:

69,314 = 70%

69,314 ÷ 70 = 990.2 (this equals one percent of the revenue)

990.2 × 100 = 99,020

99,020 = 100%

There were approximately 304,657,600 Americans in July 2009.

To find out how many Americans were there in July 2009, we'll use the given data in the student question:
Initial population (July 2008): 302,000,000 people
Growth rate (2008): 0.88%
Step 1: Convert the growth rate percentage to a decimal.
0.88% = 0.0088
Step 2: Calculate the population increase for 2009.
Increase = Initial population × Growth rate
Increase = 302,000,000 × 0.0088
Increase ≈ 2,657,600 people
Step 3: Add the population increase to the initial population to get the population in July 2009.
Population (July 2009) = Initial population + Increase
Population (July 2009) ≈ 302,000,000 + 2,657,600
Population (July 2009) ≈ 304,657,600 people.

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Answer:

24 ft

Step-by-step explanation:

The perimeter is the sum of a shape's side lengths.

We can add the given side lengths of this polygon to solve for its perimeter.

2 + 4 + 3 + 7 + 4 + 4 = 24 ft

Answer:

It would be true

Step-by-step explanation:

A linear pair is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then it would be supplementary.

The following descriptions of the function passing through (0,7) and (4,4) are true:

The slope of the function is -3/4 and the y-intercept is 7.

The function is linear and continuous.

y=-3/4x + 7 represents this function.

y = -4/3x + 9 represents this function.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output. A function is often represented by a mathematical expression, formula or graph. Functions can be described using different notations, such as f(x), y = f(x), or y = g(u,v), and they can take various forms, such as linear, quadratic, polynomial, exponential, logarithmic, trigonometric, and many others.

Here,

To determine which descriptions of the function are true, we need to use the information given about the two points (0,7) and (4,4) to find the slope and y-intercept of the linear function that passes through them. Using the formula for the slope of a line:

slope = (4 - 7) / (4 - 0) = -3/4

So the slope of the function is -3/4.

To find the y-intercept, we can use the point-slope form of the equation of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. We can use either of the two points given:

y - 7 = (-3/4)(x - 0)

y - 7 = (-3/4)x

y = (-3/4)x + 7

So the y-intercept of the function is 7.

Using this information, we can now evaluate the given descriptions of the function:

y = 7x - 3/4: This represents the function, but the slope is incorrect (should be -3/4).

The function is decreasing: This is not true, since the slope is negative but less than -1.

y=-3/4x + 7: This represents the function, and the slope and y-intercept are both correct.

The slope of the function is -4/3 and the y-intercept is 9: This is not true, since the slope is -3/4 and the y-intercept is 7.

The function is increasing: This is not true, since the slope is negative.

The slope of the function is -3/4 and the y-intercept is 7: This is true, as shown by the calculations above.

y = -4/3x + 9: This represents a different function with a different slope and y-intercept.

The function is linear and continuous: This is true, since the function is a linear equation and is continuous over its domain.

The function is linear and discrete: This is not true, since the function is continuous over its domain.

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The interval over which the function f(x) increase is {∞, 1}.

The interval over which the function f(x) decrease is {1, ∞}.

The interval over which the function g(x) increase is {3, ∞}.

The interval over which the function g(x) decrease is {∞, 3}.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of f(x), we can logically deduce that the function f(x) increases over the interval {∞, 1}. On the other hand, the function f(x) decreases over the interval {1, ∞}.

By critically observing the graph of g(x), we can logically deduce that the function f(x) increases over the interval {3, ∞}. On the other hand, the function f(x) decreases over the interval {∞, 3}.

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The sums of vectors are:

u + v =   <4, 1>  this is true.

v + w = <1, -3> this is false.

w + u = <-6, 1> this is true.

Remember that the sum between two vectors <a, b> and <c, d> is:

<a, b> +  <c, d> = <a + c, b + d>

The vectors in the graph are:

w = <-4, -3>

v = <6, -3>

u = <-2, 4>

Then the sums are:

u + v = <6, -3> + <-2, 4>

        = <6 - 2, -3 + 4> = <4, 1>  this is true.

v + w = <6, -3> + <-4, -3> = <6 - 4, -3 - 3> = <2, -6>  the second sum is false.

w + u = <-4, -3> + <-2, 4> = < -4 - 2, -3 + 4> = <-6, 1> so the last sum is true.,

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The relationship of those who attend religious services regularly are less likely to consume alcohol regularly.

Yes, there can be a relationship between attendance at religious services and alcohol consumption. In the given random sample of 1000 adults, both their attendance at religious services and daily alcohol consumption were recorded.

To analyze the relationship, you can follow these steps:

1. Organize the data: Create a contingency table that displays the frequency of each combination of attendance at religious services and alcohol consumption.

2. Calculate percentages: Determine the percentage of adults who attend religious services and drink alcohol daily, as well as the percentages for the other categories (e.g., attend services and don't drink daily, don't attend services and drink daily, etc.).

3. Identify trends or patterns: Compare the percentages to see if there is a relationship between attendance at religious services and daily alcohol consumption.

For example,

If the percentage of adults who attend religious services and drink daily is significantly lower than the percentage of those who don't attend services and drink daily, this suggests a relationship.

4. Statistical testing: Perform a chi-square test to determine if the observed relationship is statistically significant.

This test compares the observed frequencies in the contingency table to the frequencies that would be expected if there was no relationship between attendance at religious services and alcohol consumption.

5. Interpret the results: If the chi-square test shows that the relationship is statistically significant, this supports the hypothesis that there is a relationship between attendance at religious services and alcohol consumption in the sample of 1000 adults.

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