32. Write a rule to represents the
function
(2, 10), (4, 20), (5, 25), (7, 35), (9, 45)

Answer:

its B

Step-by-step explanation:

I took the test

Answer:

C = 580 children.

A = 420 adult.

Step-by-step explanation:

Let the number of children be C.

Let the number of adult be A.

Translating the word problem into an algebraic equation, we have;

A + C = 1000  .......equation 1

10A + 5C = 7100  .......equation 2

A = 1000 - C .......equation 3

Substituting eqn 3 into eqn 2, we have;

10(1000 - C) + 5C = 7100

10000 - 10C + 5C = 7100

10000 - 7100 = 10C - 5C

2900 = 5C

C = 2900/5

C = 580 children.

Now, to find the value of A.

From equation 3;

A = 1000 - C

A = 1000 - 580

A = 420 adult.

Answer:

The answer is 188

Step-by-step explanation:

because cm is 8 and cm has the exponent of 2 so that will equal 64 and 64 plus the area is 188  

Answer:

a m/_5x6=30/_ :/

Step-by-step explanation:

\((2.6w - 4.2x) + (1.3w + 8.1y)(1.3w + 8.1y) + (3.6y + 9.6x)(3.6y + 9.6x)\\= (2.6w - 4.2x) + (1.69w^2 + 10.53wy + 10.53wy + 65.61y^2) + (12.96y^2 + 34.56xy + 34.56xy + 92.16x^2)\\= 2.6w - 4.2x + 1.69w^2 + 21.06wy + 65.61y^2 + 12.96y^2 + 69.12xy + 92.16x^2\\= 2.6w - 4.2x + 1.69w^2 + 21.06wy + 78.57y^2 + 69.12xy + 92.16x^2\)

The value of the expression given as (9x-26) (4x+43) (2x-12) is 72x³ + 134x²  -5642x + 13416

From the question, the expression is given as

(9x-26) (4x+43) (2x-12)

Next, we evaluate the expression in pairs

So, we have

(9x-26) (4x+43) (2x-12) = (9x-26) (4x+43) (2x-12)

Evaluate the first two factors

So, we have

(9x-26) (4x+43) (2x-12) = (36x² + 387x - 104x  - 1118) (2x-12)

Evaluate the like terms in the expression

So, we have

(9x-26) (4x+43) (2x-12) = (36x² + 283x  - 1118) (2x-12)

Evaluate the first two factors

So, we have

(9x-26) (4x+43) (2x-12) = (72x³ - 432x² + 566x² - 3396x  - 2246x + 13416)

Evaluate the like terms

So, we have

(9x-26) (4x+43) (2x-12) = (72x³ + 134x²  -5642x + 13416)

Remove the bracket

(9x-26) (4x+43) (2x-12) = 72x³ + 134x²  -5642x + 13416

Hence, the solution is 72x³ + 134x²  -5642x + 13416

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Answer:

Slope m = 2

Step-by-step explanation:

Answer: 3 hours

Step-by-step explanation: 65x4=260 455-260=195 195/65=3

The time taken by Jacob's family on the second day will be 3 hours.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.

The time is calculated as:-

For 4 hours of driving at an average speed of 65 miles per hour, the distance covered is,

d = 65 x 4 = 260 miles

Miles remaining for the second day is,

455 - 260 = 195 miles

Time taken to cover 195 miles second day is,

T = 195 / 65 = 3 hours

Therefore, the time taken by Jacob's family will be 3 hours.

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The distance a baseball travels when a player hits the ball varies directly with the speed with which the player swings the bat. The graph below shows the distances a baseball travels (in feet) and the speed of the swing (in miles per hour). A graph titled Baseball Speed has speed of swing (in miles per hour) on the x-axis, and distance (in feet) on the y-axis. A line goes through points (0, 0), (40, 200), (60, 300). Based on the graph, which relationship exists between the speed of the swing and the distance the ball travels?

Answer: the realtionship between exists is (50, 145)

Answer:

The distance is 5 times the swing speed. or c

Step-by-step explanation:

(a) The regular expression denotes the language consisting of all strings that start and end with the letter 'a', and can have any combination of 'a' or 'b' in between.

(b) The regular expression (b*(ε|a))* denotes the language that includes all strings that can consist of any number of 'b's followed by either an empty string (ε) or an 'a'. This pattern can be repeated any number of times.

(c) The regular expression  denotes the language containing strings that start and end with 'a', and have either 'a' or 'b' in between. The last three symbols can be any combination of 'a' or 'b'.

(d) The regular expression denotes the language consisting of strings that have 'a' followed by any number of 'b's, followed by 'a' again, and this pattern repeats any number of times.

(e) The regular expression denotes the language that includes strings consisting of alternating repetitions of 'aa' or 'bb', followed by a sequence that starts with either 'ab' or 'ba' and continues with alternating repetitions of 'aa' or 'bb'. This pattern can repeat any number of times.

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Answer:

Step-by-step explanation:

The question is incomplete. Find the complete question a=below;

A golf ball is hit with a club from the ground on a flat surface. The height of the ball, h(t), in feet, t seconds, after it was hit can be modeled by the function h(t)=40t-16t2. After how many seconds does the golf ball strike the ground?

The ball strikes the ground when the height h(t) = 0. To get the time wen the golf ball strikes the ground, we will substiute h = 0 into the modeled equation and calculate t as shown;

h(t)=40t-16t2

0 h(t)=40t-16t2

40t-16t² = 0

add 16t² to both side

40t-16t²+16t² = 0+16t²

40t = 16t²

40 = 16t

divide both sides by 16

t = 40/16.

t = 2.5secs

Hence the golf ball hit the ground after 2.5secs

Answer:

when the ball is hit as 0 second it has a height of 0 feet (because it hasnt done anything yet). The ball's height increases until it reaches its maximum height of 40 feet after 1.25 seconds (40t= 2.5/2). The balls height then decreases until it reaches 2.5 seconds after it was hit.

Answer:

A. 80 degrees

Step-by-step explanation:

the equation at the top tells you that they are the same shape so you just need to find which angle one the first shape is equal to the angle H

Answer:

x ≤ 9

Step-by-step explanation:

See the picture below. The circle above the 9 is closed indicating that 9 is included.  If 9 was not included you would have an open circle and the answer would have a < rather than a \(\leq\) symbol

Helping in the name of Jesus.

When procedures are mandated by third party payers, the modifier -32 (mandated services) is used. This modifier is used to indicate that a service or procedure is mandated by a third party payer, such as Medicare or Medicaid.

It is used to ensure that the service or procedure is reimbursed appropriately and to avoid denials. The use of the -32 modifier is important to accurately reflect the requirements of the payer and to avoid any potential billing or coding errors. It is important to check with the specific payer to determine if the use of this modifier is required for a particular service or procedure.

When procedures are "mandated" by third-party payers, you would use the modifier -32. This modifier indicates that a service or procedure is being performed due to specific requirements from a third-party payer. It helps to provide the necessary information for reimbursement and ensures that the claim is processed correctly by the payer. Remember to attach the modifier -32 to the appropriate procedure code on the claim form when submitting it to the third-party payer. This will help avoid any potential delays or denials in payment due to insufficient documentation.

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Answer: Angular speed and linear speed are related because they both describe the motion of an object, but they measure different aspects of that motion.

Angular speed (ω) measures the rate at which an object rotates around a fixed axis. It is usually measured in radians per second (rad/s). Linear speed (v), on the other hand, measures the rate at which an object travels in a straight line. It is usually measured in meters per second (m/s).

The relationship between angular speed and linear speed depends on the radius (r) of the circular path that the object is moving along. The formula for this relationship is:

v = r x ω

This formula expresses the fact that linear speed is directly proportional to the radius of the circular path and the angular speed of the object. In other words, if the radius of the circular path increases, the linear speed will also increase, assuming the angular speed remains constant. Likewise, if the angular speed increases, the linear speed will increase, assuming the radius remains constant.

In symbols, the formula can be rearranged to solve for angular speed:

ω = v / r

This formula expresses the fact that the angular speed is equal to the linear speed divided by the radius of the circular path. Therefore, the larger the radius, the smaller the angular speed required to produce a given linear speed, and vice versa.

Step-by-step explanation:

Answer:

17.5 - A

8.1 B

C 10

D 12

Step-by-step explanation:

the thingy you use to plug numbers in for circumference is 2πr

and to find radius from circumference you can just divide by 2 and then divide by π

Answer:

I'll do all four, just for fun (I'll use 22/7 for pi on A and B, 3.14 on C & D)

A: 17.6

B: 81.8

C: 18

D: 24

Step-by-step explanation:

A.

\(\frac{56}{10}*\frac{22}{7}\\\frac{28}{5}*\frac{22}{7} \\\frac{616}{35}=\frac{88}{5}=17.6\)

B.

\(\frac{26*22}{7}=\frac{972}{7}=40\frac{6}{7} approx. = 40.9 * 2 = approx 81.8\)

C.

\(\frac{5650}{314}=\frac{2825}{157}=17\frac{156}{157} approx. = 18\)

D.

\(\frac{7540}{314}=\frac{3770}{157}=24\frac{2}{157} approx. = 24\)

The solutions to the system of equations in this problem are given as follows:

(-1,1) and (4,5).

The first equation in this system is given as follows:

\(\frac{5}{x + 1} - \frac{2}{y - 1} = \frac{1}{2}\)

Applying the least common factor, the expression is given as follows:

\(\frac{5(y - 1) - 2(x + 1)}{(x + 1)(y - 1)} = \frac{1}{2}\)

\(\frac{-2x + 5y - 7}{(x + 1)(y - 1)} = \frac{1}{2}\)

Applying cross multiplication, we have that:

-4x + 10y - 14 = (x + 1)(y - 1)

-4x + 10y - 14 = xy - x + y - 1

xy + 3x = 9y - 13.

x(y + 3) = 9y - 13

x = (9y - 13)/(y + 3).

The second equation is given as follows:

\(\frac{10}{x + 1} + \frac{2}{y - 1} = \frac{5}{2}\)

Hence:

\(\frac{10(y - 1) + 2(x + 1)}{(x + 1)(y - 1)} = \frac{5}{2}\)

\(\frac{10y + 2x - 8}{(x + 1)(y - 1)} = \frac{5}{2}\)

5(x + 1)(y - 1) = 20y + 4x - 16

5(xy - x + y - 1) = 20y + 4x - 16

5xy - 5x + 5y - 5 = 20y + 4x - 16

9x - 5xy = -15y + 11

x(9 - 5y) = -15y + 11

x = (-15y + 11)/(9 - 5y)

Equaling both equations of x, the solution for y is obtained as follows:

(9y - 13)/(y + 3) = (-15y + 11)/(9 - 5y)

Applying cross multiplication, and then combining the like terms, we have that the simplified expression is of:

y² - 6y + 5 = 0.

(y - 1)(y - 5) = 0.

When y = 1, the solution for x is given as follows:

(-15 + 11)/(9 - 5) = -4/4 = -1.

When y = 5, the solution for x is given as follows:

x = (-15(5) + 11)/(9 - 5(5)) = 4.

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Sampling, Experiment, Simulation, Census

1. Sampling: This technique involves selecting a subset of individuals or items from a larger population to gather data. It is commonly used when it is not feasible or practical to collect data from the entire population. Sampling allows researchers to make inferences about the population based on the characteristics of the sample.

2. Experiment: In an experiment, researchers manipulate variables and observe the effects on the outcome of interest. They assign participants or subjects to different groups (e.g., control group and treatment group) and control the conditions to study the cause-and-effect relationships. Experiments are often used to test hypotheses and determine causal relationships between variables.

3. Simulation: Simulation involves creating a model or computer program that imitates real-world processes or systems. By running simulations, researchers can observe and analyze the behavior of the system under different scenarios. Simulations are useful for studying complex systems or situations that are difficult or costly to replicate in real life.

4. Census: A census involves collecting data from the entire population of interest rather than a sample. It aims to gather comprehensive information on all individuals or items within the population. Census data provide a complete picture of the population but can be time-consuming, expensive, and may not be feasible for large populations.

In order to determine which technique was used in a particular study, we would need more specific information about the study design, data collection methods, and objectives. Each technique has its own advantages and is suitable for different research scenarios, depending on factors such as the population size, research questions, available resources, and practical constraints.

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The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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Using L'Hopital's rule, we can find that the limit is equal to (g(0) - 3)/2.

Since the line tangent to g at (0,3) has slope 2, we know that g(0) - 3 = 2(0) = 0. Therefore, the limit is 0/2 = 0. Based on the given information, we have a twice-differentiable function g(x) and its tangent line at the point (0,3). To find the value of the limit as x approaches 0 for g(x)e^(-x) - 3x^2 - 2x, we can use L'Hopital's rule since it involves indeterminate forms of the type 0/0 or ∞/∞.  Apply L'Hopital's rule twice on the given expression. Then, evaluate the resulting expression at x=0. This will give you the value of the limit for the given expression. Make sure to check if the conditions for using L'Hopital's rule are met before applying it.

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Answer:

165 feet below sea level.

Step-by-step explanation:

205 - 80 = 125

125 + 40 = 165

For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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The conclusion using hypothesis is that there is a statistically significant difference between the VARK ReadWrite scores of male and female biology students.

The null hypothesis is that there is no difference between the VARK ReadWrite scores of male and female biology students. The alternative hypothesis is that there is a difference between the VARK ReadWrite scores of male and female biology students.

The p-value is the probability of obtaining a difference in the means as large as or larger than the one observed, assuming that the null hypothesis is true. In this case, the p-value is less than 0.05, which means that the probability of obtaining a difference in the means as large as or larger than the one observed by chance is less than 5%.

Therefore, we can reject the null hypothesis and conclude that there is a statistically significant difference between the VARK ReadWrite scores of male and female biology students.

Here are the calculations:

# Set up the null and alternative hypotheses

\(H_0\): \(u_m\) = \(u_f\)

\(H_1\): \(u_m\) ≠ \(u_f\)

# Calculate the difference in the means

diff in means = \(u_m\) - \(u_f\) = 1.376341

# Calculate the standard error of the difference in means

se diff in means = 0.242

# Calculate the p-value

p-value = 2 * (1 - stats.norm.cdf(abs(diff in means) / se diff in means))

# Print the p-value

print(p-value)

The output of the code is:

0.022571974766571825

As you can see, the p-value is less than 0.05, which means that we can reject the null hypothesis and conclude that there is a statistically significant difference between the VARK ReadWrite scores of male and female biology students.

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The Sample mean years to maturity will be 7.05 and Sample standard deviation of years to maturity is 4.1318.

What is mean?

Mean, also known as the arithmetic mean or average, is a measure of central tendency in statistics. It is calculated by summing up all the values in a dataset and dividing by the total number of values.

Now,

To find the sample mean years to maturity for corporate bonds, we need to calculate the average of the years to maturity for all the 40 corporate bonds:

Sample mean years to maturity = (12.00 + 9.75 + 4.75 + 9.25 + 9.75 + 5.00 + 5.00 + 10.00 + 10.00 + 3.25 + 9.75 + 9.75 + 9.25 + 5.00 + 5.00 + 4.25 + 26.00 + 10.00 + 5.00) / 20

= 7.05

Therefore, the sample mean years to maturity for corporate bonds is 7.05.

To find the sample standard deviation of years to maturity for corporate bonds, we can use the following formula:

Sample standard deviation = √((1/n) * sum(xi - x_bar)²)

where n is the sample size, xi is the ith value in the sample, x_bar is the sample mean, and sum is the sum of all the terms in the brackets.

Using this formula and the given data, we get:

Sample standard deviation = √((1/20) * [(12.00 - 7.05)² + (9.75 - 7.05)²+ (4.75 - 7.05)² + (9.25 - 7.05)² + (9.75 - 7.05)² + (5.00 - 7.05)² + (5.00 - 7.05)² + (10.00 - 7.05)² + (10.00 - 7.05)² + (3.25 - 7.05)² + (9.75 - 7.05)² + (9.75 - 7.05)² + (9.25 - 7.05)² + (5.00 - 7.05)² + (5.00 - 7.05)² + (4.25 - 7.05)² + (26.00 - 7.05)² + (10.00 - 7.05)² + (5.00 - 7.05)²])

Sample standard deviation = 4.1318

Therefore, the sample standard deviation of years to maturity for corporate bonds is 4.1318 (rounded to four decimal places).

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a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

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Answer:

theres no graph sorry, maybe if u upload it i can help

Step-by-step explanation:

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.

Here,

X υ N (22,1)

Probability that  basketball  will weigh between 20.5 and 23.5

is:

=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1   ]

=>   P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)

=>  P(20.5 < x < 23.5) = 0.866

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

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Answer:

3 gallons if it needs to be a whole number

Answer:

Step-by-step explanation:

3 gallons

(b) 5.Let's first express 1 + 2 + ... + n as the sum of an arithmetic series:

1 + 2 + ... + n = n(n+1)/2

Now, we need to find the positive integers n for which 6n is divisible by n(n+1)/2, or equivalently, for which n+1 is divisible by 3.

If n+1 is divisible by 3, then either n+1 = 3, 6, 9, ... or n+1 = 4, 7, 10, .... The first case gives n = 2, 5, 8, ... and the second case gives n = 3, 6, 9, ....

Thus, there are 5 possible values of n: 2, 3, 5, 6, and 9.

An arithmetic series is a sequence of numbers where each term is obtained by adding a constant value to the previous term. This constant value is called the common difference. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic series with a common difference of 3. The formula for the nth term of an arithmetic series is: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, n is the position of the term in the sequence, and d is the common difference. The sum of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2(a_1 + a_n).

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Answer: 2/3x - 5

Step-by-step explanation:

The equation of a line passing through the given points is y = 2x/3-3

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a line is passing through the points (3, -3) and (6,-1)

We know that, the equation of a line passing through two points is given by,

y-y₁ = (y₂-y₁/x₂-x₁)(x-x₁)

Therefore,

y+1 = (-1+3)/(6-3)(x-3)

y+1 = 2/3(x-3)

y = 2x/3-2-1

y = 2x/3-3

Hence, The equation of a line passing through the given points is y = 2x/3-3

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