Four girls and six boys are in a Spanish club. Three of the people will be chosen at random to represent the group in a photograph. What is the probability that one girl and two boys will be chosen? 40% 50% 60% 70%

Answer:

-4.75

Step-by-step explanation:

Slope = (y2-y1) / (x2-x1)

So applying the formula

(-29-9)/(15-7)

= -38/8 = -4.75

Answer:

hope this helps:)

Step-by-step explanation:

the thousands place is right before the first comma therefore it is in bold here:

69581.491337

since 5 is \(\geq\) 5 you round 9 up to a 10

once you round, the numbers below it all turn into zeros.

giving the number to be 70,000

hope this helps:)

Answer: Heyaa!~

Your Answer Is... 70,000

Step-by-step explanation:

Hopefully this helps you!~

Answer:

a = - \(\frac{13}{16}\)

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (105, 27 ) , thus

y = a(x - 105)² + 27

To find a substitute (109, 14 ) into the equation

14 = a(109 - 105)² + 27 ( subtract 27 from both sides )

- 13 = 16a ( divide both sides by 16 )

a = - \(\frac{13}{16}\)

In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.

This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.

The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.

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Answer:

1.47 is the answer

Answer:

1.4666667 rounded off to 1.47

Step-by-step explanation:

The population of the rabbit in the year 2002 will be 940 rabbits.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

The exponential model consisted the expression;

\(y = A r^{t}\)

Where, A is initial population and r is increase rate and t is time.

So, The initial population and increase rate for the given condition are;

\(740 = A . r^{0} \\\\A = 740\)

And,

\(870 = 740 * r^{7}\)

\(r^{7} = \frac{870}{740}\)

\(r^{7} = \frac{87}{74}\)

r = 1.89/1.84

r = 1.02

So, The exponential  model consisted the expression;

\(y = A r^{t}\)

\(y = 740 r^{12}\)

\(y = 740 * (1.02)^1^2\)

\(y = 740 * 1.27\)

\(y = 939.8\)

Therefore,

The population of the rabbit in the year 2002 will be 940 rabbits.

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the answer is 9.

ie.. the value of x =9

the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

Given: The cylinder is x² + y² = 9, bounded above by the plane z = x and below by the xy-planeWe know that, the cylinder is x² + y² = 9Which is (x/a)² + (y/b)² = 1Where a = 3 and b = 3The plane is z = xThe region is bounded below by the xy-plane Thus, the volume of the region can be found by integrating z = x with limits of x² + y² ≤ 9.So, V = ∭ dx dy dz where the limits are given by the cylinder and the plane.V = ∫∫∫ (x) dV ... (1)Now, converting the integral into cylindrical coordinates we have,∫∫∫ (x) dV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ ... (2)x = r cos θ, y = r sin θ, and z = z.We know that the limits of x² + y² ≤ 9 in cylindrical coordinates are 0 ≤ θ ≤ 2π, 0 ≤ r ≤ 3, 0 ≤ z ≤ r cos θ.Using (2) in (1), we haveV = ∫θ = 0 to 2π ∫r = 0 to 3 ∫z = 0 to r cos θ (r cos θ) rdzdrdθ= ∫θ = 0 to 2π ∫r = 0 to 3 [r² cos θ / 2] dr dθ= ∫θ = 0 to 2π [ 9 cos θ / 2 ] dθ= 9 [ sin θ ]θ = 0 to 2π= 0Thus, the volume of the region contained in the cylinder x² + y² = 9, bounded above by the plane z = x and below by the xy-plane is 0.

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Answer:

G(18,-9)

Step-by-step explanation:

The coordinates of the midpoint of GH are M (8,0) and the coordinates of one endpoint are H(-2, 9). We need to find the coordinates of G. Let G is (x,y).It can be done using mid point formula i.e. \((\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\)

So,

\(8=\dfrac{x-2}{2}\ \text{and}\ 0=\dfrac{9+y}{2}\\\\16=x-2\ \text{and}\ y=-9\\\\x=18\ \text{and}\ y=-9\)

Hence, the coordinates of the other point is (18,-9).

Public health has a crucial influence on the U.S. healthcare system by promoting disease prevention, health promotion, policy development, emergency preparedness, and more. Positive examples demonstrate how public health efforts improve health outcomes, reduce costs, and enhance population well-being. Negative examples highlight instances where shortcomings in public health can lead to health risks, increased healthcare burden, and adverse consequences for the population.

Public health plays a significant role in shaping the U.S. healthcare system. It encompasses a range of efforts and policies aimed at promoting and protecting the health of the population. Here are some influences of public health on the U.S. healthcare system:

Disease prevention and control: Public health initiatives focus on preventing the spread of infectious diseases, such as vaccination programs, disease surveillance, and outbreak investigations. These efforts help reduce the burden on the healthcare system by preventing illnesses and reducing healthcare costs.

Positive example: Successful vaccination campaigns have led to the eradication or significant reduction of diseases like polio and smallpox, protecting public health and reducing the need for costly treatments.

Negative example: Failure to adequately control and contain infectious diseases can lead to outbreaks and public health emergencies, straining healthcare resources and posing a risk to the population's health.

Health promotion and education: Public health agencies work to educate the public about healthy behaviors, lifestyle choices, and disease prevention strategies. They promote initiatives like smoking cessation programs, healthy eating campaigns, and physical activity promotion.

Positive example: Public health campaigns promoting smoking cessation have contributed to a decrease in smoking rates, resulting in improved public health outcomes and reduced healthcare costs associated with smoking-related diseases.

Negative example: Insufficient public health education and awareness campaigns on the dangers of substance abuse may contribute to increased addiction rates, leading to increased healthcare utilization and negative health outcomes.

Health policy and regulation: Public health agencies play a role in shaping health policies and regulations that govern the healthcare system. They develop and implement guidelines, standards, and regulations to ensure quality care, patient safety, and access to essential health services.

Positive example: Implementation of regulations mandating health insurance coverage for preventive services has increased access to preventive care, enabling early detection and treatment of diseases, and reducing healthcare costs in the long run.

Negative example: Inadequate regulation or enforcement of healthcare safety standards can lead to medical errors, hospital-acquired infections, and compromised patient safety.

Emergency preparedness and response: Public health agencies are responsible for preparing for and responding to public health emergencies, such as natural disasters, disease outbreaks, and bioterrorism events. They coordinate emergency response efforts, develop emergency plans, and ensure the availability of essential resources and healthcare infrastructure.

Positive example: Effective public health emergency preparedness and response during the H1N1 influenza pandemic in 2009 helped mitigate the impact of the virus, protecting public health and minimizing strain on the healthcare system.

Negative example: Inadequate preparedness or response to a public health emergency can lead to delayed or insufficient healthcare services, resulting in higher morbidity and mortality rates.

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- Linear equation for the remaining oil reserves R = -25t + 2000.

-  Ten years from now, there will be 1750 billion barrels of oil in the reserves.

-  If the rate of depletion remains constant, the world's oil reserves will be depleted in approximately 80 years from the present.

A. To find a linear equation for the remaining oil reserves:

Slope-intercept form of a linear equation: y = mx + b

Where y represents the remaining oil reserves (R),

x represents the number of years beyond the present (t),

m represents the slope, and

b represents the y-intercept.

The total oil reserves are decreasing by 25 billion barrels each year, we can determine the slope (m) as -25 billion barrels/year. Since, it is started with 2000 billion barrels initially (at t = 0), the y-intercept (b) is 2000 billion barrels.

Therefore, the linear equation for the remaining oil reserves (R) in terms of the number of years beyond the present (t) is:

R = -25t + 2000

B. To find how much oil will be in the reserves ten years from now (t = 10):

R = -25(10) + 2000

R = -250 + 2000

R = 1750 billion barrels

Therefore, ten years from now, there will be 1750 billion barrels of oil in the reserves.

c. To determine when the world's oil reserves will be depleted:

0 = -25t + 2000

25t = 2000

t = 2000/25

t = 80

Therefore, if the rate of depletion remains constant, the world's oil reserves will be depleted in approximately 80 years from the present.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

The answer is given below

Step-by-step explanation:

The distance from the lake to the car is 3 miles and it takes 2 hours. The velocity of the hiker is 3/2 mi/hr. Therefore f(t) which is the distance from the car t hours after 7 A.M is given by:

\(f(t)=\frac{3}{2}t\)

When coming back on Sunday morning, the distance g(t) from the car at any point in time is given by:

\(g(t)=3-\frac{3}{2}t\)

a)

\(f(t)=\frac{3}{2}t\\f(0)=\frac{3}{2}(0)=0\ mile\\f(2)=\frac{3}{2}(2)=3\ miles\)

\(g(t)=3-\frac{3}{2}t\\g(0)=3-\frac{3}{2}(0)=3\ miles\\g(2)=3-\frac{3}{2}(2)=2-2=0\ mile\\\)

b)

\(h(t)=f(t)-g(t)=\frac{3}{2}t -(3-\frac{3}{2}t)=\frac{3}{2}t -3+\frac{3}{2}t=3t-3\\h(t)=3t-3\\h(0)=3(0)-3=0-3=-3\\h(2)=3(2)-3=6-3=3\)

c)

According to Intermediate Value Theorem, there exist a point b where f(b) = g(b). i.e. f(b) - g(b) = 0

\(h(b)=f(b)-g(b)=0\\h(0)=-3,h(2)=3\)

This means there exist a point b within the interval [-3, 3] where f(b) - g(b) = 0

Riley needs 18 rooms for 72 puppies.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

Riley works for puppy shelter moving to a new building.

The rooms in the new building are built to hold 4 puppies each.

Now, There are 1 room for 4 puppies.

Number of room for 4 puppies = 1

Hence, Number of room's for 72 puppies = 1/4 × 72

                                                                 = 72/4

                                                                 = 18

So, Riley needs 18 rooms for 72 puppies.

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To solve this problem, we need to use the Central Limit Theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases.

First, we need to find the mean and standard deviation of the sample mean hardness. The mean is simply the population mean, which is given as 50.5. The standard deviation of the sample mean is given by the formula:

standard deviation of sample mean = population standard deviation / sqrt(sample size)

The population standard deviation is given as 0.5, and the sample size is 35, so:

standard deviation of sample mean = 0.5 / sqrt(35) = 0.084

Next, we need to standardize the sample mean hardness using the z-score formula:

z = (sample mean hardness - population mean) / (standard deviation of sample mean)

z = (51 - 50.5) / 0.084 = 5.95

Finally, we need to find the probability that a standard normal distribution is greater than or equal to 5.95. This can be done using a z-table or a calculator. Using a calculator, we get:

P(Z ≥ 5.95) ≈ 0

Therefore, the approximate probability that the sample mean hardness for a random sample of 35 pins is at least 51 is very close to 0.

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0.015 the radius of the balloon changing at the instant the radius is 50cm  

given that

a spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute

radius = 50 centimeters

now we need to find the volume of the balloon

Let V  = volume of the balloon at time t

    r = radius of the balloon at time t

   V = (4/3)πr3

  Given:  dV/dt = 500  

   Find:  dr/dt when r = 50

   dV/dt = (4/3)(3πr^2)(dr/dt)

   500 = 4π(50)^2(dr/dt)  

   dr/dt = 1/(20π)

   dr/dt = 0.015 cm/min

  0.015 the radius of the balloon changing at the instant the radius is   50cm  

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The quotient of the division between 2.09 × 10^9 and 4.053 × 10^(-4) should have three significant digits.

When performing division, the general rule for determining the number of significant digits in the result is to consider the least number of significant digits in the original values being divided. In this case, the value 4.053 × 10^(-4) has three significant digits, while 2.09 × 10^9 has only two significant digits. Therefore, we should limit the quotient to the same number of significant digits as the divisor, which is three.

It's important to note that significant digits represent the reliable and meaningful digits in a measurement or calculation. By adhering to the rules of significant digits, we can maintain accuracy and convey the appropriate level of precision in our calculated results.

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Given the points ( 8 , 5 ) and ( 4 , 4 )

The general slop-intercept form of the equation of the line is:

y = mx + c

where m is the slope and c is y-intercept

The slope will be calculated as following:

So, the equation of the line will be:

Using the one of the given points to find the value of c

Let , we will use the point ( 4 , 4 )

so, when x = 4 , y = 4

So, the slope - intercept equation of the line is:

Therefore, the values of \(a_0\) and \(a_9\) in the Taylor series expansion are: \(a_0 = 1; a_9 = 0.\)

To find the values in the Taylor series expansion of \((1 - x)/e^x\) about 0, we can use the formula for the coefficients of the Taylor series:

\(a_0 = f(0)/0!\\a_9 = f(9)/9!\)

Let's first find f(0):

\(f(0) = (1 - x)/e^x\)

Substituting x = 0:

\(f(0) = (1 - 0)/e^0\)

= 1/1

= 1

Next, let's find f(9):

f(9) = (9th derivative of (1 - x))/9!

To find the 9th derivative, we can repeatedly differentiate (1 - x) with respect to x:

f(x)=0--------------n time

Since all the higher-order derivatives are 0, the 9th derivative is also 0:

f(9) = 0

\(a_0 = f(0)/0!\)

= 1/1

= 1

\(a_9 = f(9)/9!\)

= 0/9!

= 0

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Answer:

k=a+7

Step-by-step explanation:

Take 1 k away from both sides. I hope you found this useful!

Answer:

k = \(\frac{7}{2-a}\)

Step-by-step explanation:

2k = ak + 7 ( subtract ak from both sides )

2k - ak = 7 ← factor out k from each term on the left side

k(2 - a) = 7 ( isolate k by dividing both sides by (2 - a) )

k = \(\frac{7}{2-a}\)

The year it will take Mussman to reach a population of 27,000 resident is 10.7 years

Population growth is the increase in the number of people in a population or dispersed group.

We use exponential function when calculating increase in population per time

p(t) =p(o) e^kt

27000 = 13500 e^0.065t

e^0.065t = 27000/13500

0.065t = ln 2

0.065t = 0.693

t = 0.693/0.065

t = 10.7 years

therefore it will take 10.7years for the resident of Mussman to reach a population of 27000

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Solution 1: Count, which is crazy long so I am going to solution 2.

Solution 2: Calculate.

I am going to split the right part to the left part result two shapes: 8x5 and 6x15

8x5 + 6x15 = 40 + 90 = 130.

Area = 130 units^2

Perimeter: 8x2 + (6x2-5)+ (15x2-5)        (Subtract 5 because the overlap area)

16 + 7 + 25 = 48

Perimeter = 48 units

The function with the asymptotes as x = 2 , x = 4 and y = 2 is given by the relation f(x) = 2 / [(x - 2)(x - 4)]

Given data,

To find a function that has vertical asymptotes at x = 2 and x = 4, and a horizontal asymptote at y = 2, we can start by considering the basic form of a rational function:

f(x) = (ax + b) / (cx + d)

To satisfy the given conditions, we need the denominator of the rational function to have factors of (x - 2) and (x - 4) since these will create the vertical asymptotes at x = 2 and x = 4.

So, f(x) = (ax + b) / [(x - 2)(x - 4)]

Now, let's consider the horizontal asymptote at y = 2. For a rational function, the horizontal asymptote occurs when the degree of the numerator is less than or equal to the degree of the denominator. Since we want a horizontal asymptote at y = 2, which is a horizontal line, the numerator needs to be a constant, and the denominator needs to be linear.

Let's choose a = 0 and b = 2 so that the numerator is a constant equal to 2.

f(x) = 2 / [(x - 2)(x - 4)]

Hence , a formula for the function that satisfies the given conditions is given by f(x) = 2 / [(x - 2)(x - 4)].

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Answer:

143/5

or

28 3/5

Step-by-step explanation:

ywwwwhshshd

Answer:

143/5, 28.6, or 28 3/5

Considering that the two lines intersect at only one point, the system of equations described by them is consistent.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

According to the number of solutions, the system is classified as follows:

In this graph, each equation is described by a line, and they intersect once, meaning that there is one solution and the system is consistent.

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The 10th score should be 9.5 for the mean to be 5.

The mean value is the average value of the given data.

According to the given question  the mean of 9 score is 4.5 what must the 10th score be for the mean of all score to be 5.

The total average score for 9 games is

= ( 9 × 4.5 )

= 40.5.

The total average score for the mean to be 5 in 10 games is

= ( 10 × 5 )

= 50.

∴ The 10th score must be ( 50 - 40.5 ) which is

= 9.5.

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