Write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result.

A company did a study on the physical activity level and weight gain of its employees. Age was not considered, so it might be an example of a confounding variable.

A confounding variable is an unmeasured third variable that influences, or confounds, the relationship between an independent and a dependent variable. For example, in a study looking at the relationship between smoking and lung cancer, age may be a confounding variable because people who smoke tend to be older than those who do not.

This would mean that age is influencing both smoking and the risk of lung cancer, so the true effect of smoking on the risk of lung cancer cannot be determined without taking age into account. The presence of a confounding variable can distort the results of an experiment and lead to inaccurate conclusions.

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To determine the times at which v(t) has a local minimum and maximum, we need to find the critical points of the function. A critical point is a value of t for which either the first derivative, v'(t), or the second derivative, v''(t), is equal to zero or does not exist.

The first derivative of v(t) is given by:

v'(t) = a + 2bt + y

Setting v'(t) equal to zero and solving for t, we get:

0 = a + 2bt + y

t = -a / 2b = -(3 m/s^4) / (2(-24 m/s^2)) = 3/48 s

The second derivative of v(t) is given by:

v''(t) = 2b

Since b is negative, v''(t) is negative, so v(t) has a local maximum at t = 3/48 s.

Similarly, since the second derivative is constant and negative, the function v(t) has a local minimum.

Therefore, the times at which v(t) has a local minimum and maximum are 3/48 s and 3/48 s, respectively, expressed as two numbers separated by a comma: 3/48 s, 3/48 s.

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The value of the z-score corresponding to each position in the distribution is given by = { -2 , -1 , 0 , 1 , 2 }

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the z-scores corresponding to each position in the distribution be z

Now , the equation will be

The mean of the data μ = 50

The standard deviation of the data σ = 10

The value of x for the letters A, B, C, and D is given by { 30 , 50 , 60 , 70 }

Substituting the values in the equation , we get

The Z-score is calculated using the formula:

z = (x - μ)/σ

For letter A ,

z = ( 30 - 50 ) / 10

On simplifying the equation , we get

z = -20/10

z = -2

And , for letter B ,

z = ( 50 - 50 ) / 10

z = 0/10

z = 0

For letter C ,

z = ( 60 - 50 ) / 10

z = 10/10

z = 1

For letter D ,

z = ( 70 - 50 ) / 10

z = 20/10

z = 2

Now , the k-scores of the letters E , F , G and H is calculated by

The mean of the letters = 100

The standard deviation of the letters = 20

So , the k-scores of the letters are = { 60 , 80 , 100 , 140 }

Now , the mean of the data is given by = ( 60 + 80 + 100 + 120 + 140 ) / 5

So , the mean is μ = 500/5 = 100

Hence , the z-scores of the letters are solved

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Answer:

1 + 2/7

Step-by-step explanation:

9/7 =

(7+2) / 7 =

7/7 + 2/7 =  ==> use distribution

1 + 2/7  ==> 7/7 = 1, so simplify the expression

The domain and the range of the functions are:

Function 1

Given that

f(x) = 5x - 2, x < 1

         x - 7, x ≥ 1

The functions in the piecewise function are linear functions

Because there are no hole in the domain value, this means that the range and the domain are the set of real numbers

Function 2

Given that

g(x) = -x , x < -5

         3, x > -5

The functions in the piecewise function are also linear functions

However, there is a hole in the domain value at x = -5

This means that the domain incudes all real values except -5

While the range is 3 and values greater than 5

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The domain and range of the two piecewise functions are:

Please refer to the attached graphs below for each piecewise function's graph.

f(x) = {5x-2, if x < 1}

        {x - 7, if x ≥ 1}

From the given function, we can make the first graph. We know that the domain for each function individually are:

f(x) = 5x - 2, if x < 1

dom f(x) = (-∞,1)

Range = (-∞, 3)

f(x) = x - 7, if x ≥ 1

dom f(x) = (1, ∞)

Range = (-6, ∞)

By combining both function's domains and range, we can find the piecewise function domain and range are:

D =  (-∞,∞) --> include 1

R =  (-∞,∞)

g(x) = {-x, if x < -5}

         {3, if x > -5}

From the given function, we know each domain and range are:

g(x) = -x, if x < -5

dom g(x) = (-∞, -5)

Range = (5, ∞)

g(x) = 3, if x > -5

dom g(x) =  (-5, ∞)

Range = 3

By combining both functions' domain and range, we got:

dom =  (-∞, -5) ∪  (-5,∞) --> not including 5

Range =  (3, ∞)

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For the given triangles ΔABC ≈ ΔBKJ, the value of KJ is, 9

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

The triangle, ΔABC

one segment KJ which is intersecting sides AB & BC

ΔABC has one similar triangle inside, which is ΔBKJ

Triangle ΔABC and ΔBKJ similar,

So, we can say ΔABC ≈ ΔBKJ

And it is known that

for similar triangles, ratio of lengths of sides are equal for similar triangles

so, AB/AC = KB/KJ

AB  = 2KB

⇒  2KB/18 = KB/KJ

⇒   2/18  = 1/KJ

⇒   KJ  = 9

Hence, the length of KJ is 9 unit

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Gina should buy from Stickers4u.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Gina is going to buy 100 stickers.

If she buys from the shop - Stickers4u,

then the cost is,

= 100/25 x 2.15

= 4 x 2.15

= 8.6.

And if she buys from the World stationary,

then the cost is,

= (100 - 50)/10 x 1.65

= 5 x 1.65

= 8.25

Therefore, she should buy from Stickers4u.

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The least squares approximating line y=zo + zix for each of the following sets of data points is (1, 1), (3, 2), (4, 3), (6, 4)

This line is determined by minimizing the distance between the data points and the line. The method of least squares is used in many areas, including regression analysis and trend analysis.

To find the least squares approximating line for a set of data points, you need to use the following formula:

=> y = b0 + b1x,

where b0 is the y-intercept and b1 is the slope of the line.

You can use this formula to find the values of b0 and b1 that minimize the difference between the data points and the line.

For example, let's take a look at the first set of data points (1, 1), (3, 2), (4, 3), (6, 4). To find the least squares approximating line, we need to calculate the values of b0 and b1.

This can be done by using a mathematical formula that involves finding the sum of the squares of the differences between the data points and the line.

Therefore, option (a) is correct.

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From the following numerical expressions given, the numerical expression which results in a positive number is (-67) - (-12).

In mathematics, subtraction is the process of finding the difference between two numbers. If two numbers have the same sign (both positive or both negative), the result of their subtraction will have the same sign as the numbers being subtracted.

However, if the numbers have different signs, the result of their subtraction will have the sign of the number with the larger absolute value. In this case, (-67) and (-12) have different signs, but (-12) has a larger absolute value than (-67). Therefore, the result of the subtraction will be positive.

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the option b is equal to the rational expression when x≠-6?

Answer:

[tex]\dashrightarrow \: \frac{ {x}^{2} - 36}{x + 6} \\ \\ \dashrightarrow \: \frac{( \cancel{x + 6})(x - 6)}{\cancel{x + 6}} \\ \\ \dashrightarrow\boxed{ \: x - 6 \: }[/tex]

therefore , option ( B ) is correct.

• Step 2 was done by keeping in mind the algebraic identity "a² - b² = ( a + b )( a - b)"

hope helpful! :)

The first 6 terms of the given sequences are  for A: 1, 2, 2, 4, 8, 16

for B: 5, 5, 17, 59, 177, 521, and for C: 2, 1, 3, 6, 15, 45

A. The 1st sequence is a geometric sequence, where each term is the product of the two preceding terms. The 1st term is 1, the 2nd term is 2, and the rest of the terms are calculated as below:

a3 = a1 * a2 = 1 * 2 = 2

a4 = a2 * a3 = 2 * 2 = 4

a5 = a3 * a4 = 2 * 4 = 8

a6 = a4 * a5 = 4 * 8 = 16

So, the first six terms of the sequence are 1, 2, 2, 4, 8, and 16.

B. The 2nd sequence can be calculated by using the formula

an = 2 * an - 1 + 3 * an - 2 for n greater than or equal to 2. The 1st term a1 is 5 and the 2nd term a2 is 5, so the rest of the terms are calculated as below:

a3 = 2 * a2 + 3 * a1 = 2 * 5 + 3 * 5 = 17

a4 = 2 * a3 + 3 * a2 = 2 * 17 + 3 * 5 = 59

a5 = 2 * a4 + 3 * a3 = 2 * 59 + 3 * 17 = 177

a6 = 2 * a5 + 3 * a4 = 2 * 177 + 3 * 59 = 521

So, the first six terms of the sequence are 5, 5, 17, 59, 177, and 521.

C. The 3rd sequence follows the formula gn = n * gn - 1 + gn - 2. The 1st term g1 is 2 and the 2nd term g2 is 1, so the rest of the terms are calculated as below:

g3 = 3 * g2 + g1 = 3 * 1 + 2 = 5

g4 = 4 * g3 + g2 = 4 * 5 + 1 = 21

g5 = 5 * g4 + g3 = 5 * 21 + 5 = 110

g6 = 6 * g5 + g4 = 6 * 110 + 21 = 786

So, the first six terms of the sequence are 2, 1, 3, 6, 15, and 45.

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The value of ∠x in the given triangle is 33° i.e. B.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As we know

The sum of all the three angles of a triangle =180°

x+105+42=180

∠x=33°

hence,

          The value of ∠x in the given triangle is 33°.

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The amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage is $55,398.6

Interest is the fee paid for having access to borrowed funds. While the interest rate used to compute interest is often reported as an annual percentage rate, interest expense or revenue is sometimes expressed as a dollar figure (APR). The compensation a lender or financial organization receives for giving out money is called interest.

Given a family wants to purchase a house that cost $135,000,

down payment = $20,000

mortgage = $1,15,000

Case 1: For a 15-year mortgage their monthly payment would be 776.85

there will be 12 payments in a year

total amount to be paid in 15 years = 15*12*776.85

total amount to be paid in 15 years =  $1,38,033

Case 2: For a 30-year mortgage their monthly payment would be 537.31

total amount to be paid in 30 years = 30*12*537.31

total amount to be paid in 30 years = $1,93,431.6

the amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage is

$1,38,033 - $1,93,431.6 = $55,398.6

Hence the amount they would save is $55,398.6.

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The correct question is,

determine the amount they would save on the cost of the house if they selected the 15 year mortgage rather than the 30 year mortgage.

Answer:

208

Step-by-step explanation:

Answer:

x = 18

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 , then

sum = 180° × 3 = 540°

sum the 5 interior angles and equate to 540

3x + 23 + 95 + 7x - 4 + 90 + 9x - 6 = 540

19x + 198 = 540 ( subtract 198 from both sides )

19x = 342 ( divide both sides by 19 )

x = 18

There are 11 1/3 based in the area outside and the total surface area of the outside of the glass is 80.07 square inches

From the question, we have the following parameters that can be used in our computation:

Height, h = 7 inches

Radius, r = 1.5 inches

π = 3.14

The area of the base is calculated as

Base area = πr²

So, we have

Base area = π * 1.5²

Base area = 2.25π

The surface area of the outside of the glass is

Surface area = 2πr(r + h)

So, we have

Surface area = 2π * 1.5 * (1.5 + 7)

Surface area = 25.5π

The number of base is

Number = 25.5π/2.25π

Evaluate

Number = 11 1/3

In (a), we have

Surface area = 25.5π

This gives

Surface area = 25.5 * 3.14

Evaluate

Surface area = 80.07

Hence, the area is 80.07 square inches

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The probability that at least one of them has been vaccinated is 0.9259.

What is binomial distribution?

The binomial distribution gives out either success or failure as two possible results in an experiment, is the discrete probability distribution used in probability theory and statistics.

The proportion of people vaccinated is 58%.

Three people are selected at random, that is, n=3

p=0.58,

the probability mass function,

[tex]^{n}C_{x}p^{x}(1-p)^{n-x}[/tex]

[tex]p(X=0)= ^{3}C_{x}0.58^{0}(0.42)^{3-0 } = 0.07408[/tex]

p( X≥1)= 1 - p(X=0)

          = 1 - 0.07408

          = 0.9259

The probability that at least one of them has been vaccinated is 0.9259.

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Answer: 3 1/3

2/3 x 5 = 10/3 = 3 1/3

2 x 5/3 = 10/3 = 3 1/3

Answer:

[tex]= \dfrac{10}{3}[/tex]

Step-by-step explanation:

We can rewrite any whole number as itself over 1.

For example, [tex]5 = \dfrac{5}{1}[/tex].

We can use this tactic to rewrite one of the given (equivalent) expressions. I'll use the one on the left side of the equation.

[tex]\dfrac{2}{3} \times 5 = \dfrac{2}{3} \times \dfrac{5}{1}[/tex]

Then, we can simplify the multiplication of fractions by multiplying out the both the numerators and denominators.

[tex]= \dfrac{2}{3} \times \dfrac{5}{1}[/tex]

[tex]= \dfrac{2\times 5}{3 \times 1}[/tex]

[tex]= \dfrac{10}{3}[/tex]

The number of ways in which the runners can finish first, second and third as required from the task content is; 166,320 ways.

It follows from the task content that the number of ways in which runners can finish first, second and third is to be determined from a total of 56 runners.

On this note, this situation describes an arrangement and hence is best represented as a permutation as follows;

⁵⁶P₃

= 166,320.

Ultimately, the number of ways in which the runners can finish is; 166,320.

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The volume of the triangular prism is 2,160 ft³.

The volume of a triangular prism can be calculated using the formula V = BH, where B is the area of the base of the triangle and H is the height of the prism.

In this case, the base of the triangle is 1 / 2 bh = 1 / 2 (18 x 12) = 108 square ft. The height of the prism is 20 ft. Therefore, the volume of the triangular prism is V = Bh = ((108 sq ft) (20 ft)) cubic ft = 2,160 ft³.

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The half-distance left is 40/7 or 5.714 miles

Given that:

The total race is 16 miles long.

Kim walked for 2/6 of the race, which is (2/6) * 16 = 16/3 miles.

After walking 16/3 miles, there are 16 - 16/3 = 32/3 miles left in the race.

Kim then sprints for 3/7 of the remaining distance, which is (3/7) * 32/3 = 32/7 miles.

Half of the race is left after she finished sprinting and walking, which is

16 - 32/7 = 80/7 miles

Divide this by 2:

80/7 ÷2

= 40/7 miles are left.

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The value of expression y ' (2) is, 135/16.

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

We have to given that;

The expression is,

⇒ y = (x - 1/x)³

Now, We can differentiate with respect to x as;

⇒ y (x) = (x - 1/x)³

⇒ y' (x) = 3 (x - 1/x)² × (1 - (-1/x²))

⇒ y' (x) = 3 (x - 1/x)² (1 + 1/x²)

Substitute x = 2;

⇒ y' (2) = 3 (2 - 1/2)² (1 + 1/2²)

⇒ y' (2) = 3 (3/2)² (1 + 1/4)

⇒ y' (2) = 3 × 9/4 × 5/4

⇒ y' (2) = 135/16

Thus, We get;

⇒ y' (2) = 135/16

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The system of equations that has a solution with x-coordinate of 3.5 and 6 is C. y = 1/2x + 3 and y = -(x - 5)² + 7.

To determine if a coordinate is a solution to a system of equations, substitute the values for the x and y in both equations and check if both resulting equations are true. If both resulting equations are true, then the coordinate is a solution to the system of equations.

A. y = x + 3.5

y = 3.5 + 3.5 = 7

y = x² + 6

7 = 3.5² + 6

7 ≠ 18.25

B. y = x - 7

y = 3.5 - 7 = -3.5

y = -(x - 6)²

-3.5 = -(3.5 - 6)²

-3.5 ≠ -6.25

C. y = 1/2x + 3

y = 1/2(3.5) + 3 = 4.75

y = -(x - 5)² + 7

4.75 = -(3.5 - 5)² + 7

4.75 = 4.75

y = 1/2x + 3

y = 1/2(6) + 3 = 6

y = -(x - 5)² + 7

6 = -(6 - 5)² + 7

6 = 6

D. y = 1/2x + 7

y = 1/2(3.5) + 7 = 8.75

y = -(x - 6)² + 3.5

8.75 = -(3.5 - 6)² + 3.5

8.75 ≠ -2.75

Only the system of equation in option C holds the equations true, hence, C. y = 1/2x + 3 and y = -(x - 5)² + 7 are the system of equations that has the given solution stated in the problem.

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Answer:

-------------------------------

The perimeter of given semicircle is the sum of the diameter and half of the circumference:

John's average speed for the entire trip is 50 km/h. So the minimum average speed for the entire trip would be 60 km/h.

To calculate John's average speed, we need to determine the total distance he covered and the total time he spent driving. Given that John drove 60 km/h for 2 hours in the morning, and 40 km/h for a different amount of time in the evening, we can calculate the total distance as follows:

[tex]d = 60 × 2 + 40 × T[/tex]

where T is the total time spent driving in the evening.

To find John's average speed, we need to divide the total distance by the total time:

Average speed = [tex]d / (2 + T)[/tex]

Since we do not know the value of T, we cannot determine the exact average speed. However, we can determine an upper bound on the average speed by assuming that T is 0 (i.e., John drove back to town immediately after arriving at his mother's house). In this case, John's average speed would be equal to the speed he drove in the morning, which was 60 km/h.

Hence the minimum average speed for the entire trip would be 60 km/h, and the maximum average speed would be equal to the speed he drove in the evening, which was 40 km/h. The average of these two speeds is 50 km/h.

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Answer:

Step-by-step explanation:

customers: 6

minutes: 40

Answer:

132

Step-by-step explanation:

180 - 48 = 132   These angles are supplemental.  They add to 180

Answer:

<GAE = 48

Step-by-step explanation:

<BAC = 48

<BAC = <GAE

To have a balanced budget, you must B. have your gross pay equal your spending and savings.

A balanced budget is a financial plan in which expenses are equal to or less than the amount of revenue generated. This means that the government or organization is not spending more money than it takes in and is not running a deficit. The result is a balanced financial position, where there is no debt and assets are equal to liabilities.

This indicates that there is no shortfall and that the person is spending just what they get as their gross income.

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Null hypothesis [tex]H_0[/tex] : p = 0.5 and alternative hypothesis [tex]H_1: $p \neq 0.5$[/tex]

The standardized statistic from the data is 3.1623

The observed standardized statistic is 3.1623

Based on the standardized statistic, we conclude that there is enough evidence to suggest that these monkeys can interpret human gestures better than random chance.

As per the given data: a choice between two boxes, 30 out of 40 monkeys approached the box that the human had gestured toward, and 10 approached the other box.

Here, p =  proportion of rhesus monkeys who tan interpret human gestures better.

a) Null hypothesis [tex]H_0[/tex] : p = 0.5

Alternative hypothesis [tex]H_1: $p \neq 0.5$[/tex]

b) Given, [tex]$\hat{p}=\frac{x}{n}=\frac{30}{40}=0.75, p_0=0.5$[/tex]

Standardized test statistic,

[tex]$Z=\frac{\hat{p}-p_0}{\frac{p_0\left(1-p_0\right)}{n}} \stackrel{H_0}{\sim} N(0,1)$[/tex]

Therefore the standardized statistic from the data = 3.1623

c) Assuming [tex]$H_0$[/tex] is true, the value of the observed standardized statistic is 3.1623 standard deviations above the mean(=0).

d) Now, p-value [tex]$=2 \times \min [p(z > 3.1623), p(z \leq 3.1623)]$[/tex]

= 0.00157

Since p-value <0.05, we reject [tex]$H_0$[/tex].

We conclude that there is enough evidence to suggest that these monkeys can interpret human gestures better than random chance.

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