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The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].

The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 can be found through the following.

Recognize that the logarithm function is increasing.

Minimize the argument of the logarithm, i.e., (x - 5)² + 3.

Observe that (x - 5)² is always non-negative since it is a square of a real number.

The minimum value of (x - 5)² occurs when x = 5 (in this case, (x - 5)² = 0).

However, x cannot be equal to 5 because the interval is -5 < x < 5.

Since the interval is open, find the minimum value for (x - 5)² in this interval, which occurs when x is as close to 5 as possible within the given interval. This would be x = 4.999.

Substitute this value of x into the function:

h(x) = log[(4.999 - 5)² + 3] = log[0.001² + 3] ≈ log[3.000001].

Hence, the minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].

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The two column proof is completed as follows

Statement                                               Reason

1. AB || CD                                           Given

2 Construct BE perpendicular to      Construction of side BE

CD  such that point E is on CD

3 Construct CF perpendicular to      Construction of side CF

AB such that point F is on AB

4 ∠ CFB = ∠ BEC = 90°                     All perpendicular angles measure 90°

5 CF = BE                                           Any point on one parallel line is the                          

                                                           same distance from the other line on        

                                                           a perpendicular transversal (1, 2, 3)

6. BC = BC                                         They are measures of the same            

                                                           segment.

7. Δ BCF ≅ Δ CBE                             SAS congruence (4, 6,5)

The SAS congruence theorem, also known as the Side-Angle-Side congruence theorem, states that if two triangles have two sides and the included angle of one triangle congruent to the corresponding parts of another triangle, then the triangles are congruent.

The equality of the included angle is by the alternate interior angles theorem.

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1.143 x 10⁷ ft, or approximately 11.43 million feet is the length of the river.

To find the length of the river, we need to use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the diagonal line connecting the two endpoints of a right triangle) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the length of the southward flowing part of the river "a" and the length of the southeastward flowing part of the river "b". Then we have:

a = 1.1 x 10⁷ ft

b = 3.2 x 10⁶ ft

The length of the river is given by the hypotenuse of a right triangle with sides a and b. Therefore, we can calculate the length of the river, c, as follows:

c² = a² + b²

c² = (1.1 x 10⁷ ft)² + (3.2 x 10⁶ ft)²

c² = 1.21 x 10¹⁴ ft² + 1.024 x 10¹³ ft²

c² = 1.3104 x 10¹⁴ ft²

c = √(1.3104 x 10¹⁴ ft²)

c = 1.143 x 10⁷ ft

Therefore, the length of the river is 1.143 x 10⁷ ft, or approximately 11.43 million feet

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The function g(x) in the form a(x - h)² + k is g(x) = (x + 5)² + 0, where a = 1, h = -5, and k = 0.

What is the function?

Starting with the function f(x) = x², a translation 5 units left can be achieved by replacing x with (x + 5), since (x + 5) is 5 units to the left of x. Therefore, we have:

g(x) = f(x + 5)

g(x) = (x + 5)²

g(x) = x² + 10x + 25

This is the equation of the parabola obtained by translating the graph of y = x² five units to the left. We can write this equation in the desired form of a(x - h)² + k by completing the square:

g(x) = x² + 10x + 25

g(x) = 1(x² + 10x) + 25

g(x) = 1(x² + 10x + 25 - 25) + 25

g(x) = 1((x + 5)² - 25) + 25

g(x) = 1(x + 5)² - 1(25) + 25

g(x) = (x + 5)² + 0

Therefore, the function g(x) in the form a(x - h)² + k is g(x) = (x + 5)² + 0, where a = 1, h = -5, and k = 0.

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Answer:

3/8 - 1/16 simplifies to 5/16.

Step-by-step explanation:

To subtract two fractions, we need to find a common denominator. In this case, the least common multiple of 8 and 16 is 16.

So, we need to rewrite 3/8 and 1/16 with a denominator of 16:

3/8 = 6/16

1/16 = 1/16

Now we can subtract:

6/16 - 1/16 = 5/16

AnswerAns

5/6

Step-by-step explanation

3/8 - 1/16 = (3×2 -1)÷16 = 5/16

Answer:

142

Step-by-step explanation:

∠P + ∠Q = 180

38 + ∠Q = 180

Subtract 38 from both sides

∠Q = 142 degrees

The predicted sales for week 10 is 30.143.

Median is a measure οf central tendency that represents the middle value in a dataset when the values are arranged in οrder οf magnitude.

Tο remοve the aberrant values frοm the time series data, we can replace them with dummy values. We can use the mean οr median οf the remaining values in the series tο replace the aberrant values.

Using mean as the replacement value, we get:

Week 1 2 3 4 5 6 7

Sales 26 28 27 30 23 23 38

Now we can use a regression model to predict the sales for week 10. Let's assume a linear regression model:

Sales = a + b*Week

where a is the intercept and b is the slope of the regression line.

To fit the model, we can use the sales data for weeks 1-7:

Week 1 2 3 4 5 6 7

Sales 26 28 27 30 23 23 38

The least squares estimates for the model parameters are:

b = 1.6429

a = 14.7143

Using these parameter estimates, we can predict the sales for week 10:

Sales(10) = a + b10

= 14.7143 + 1.642910

= 30.143

Therefore, the predicted sales for week 10 is 30.143.

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a. The sample mean for sample 1 is 9.2, and the sample mean for sample 2 is 7.17.

b. The sample standard deviation for sample 1 is approximately 3.29, and the sample standard deviation for sample 2 is approximately 3.65.

c. The point estimate of the difference between the two population means is 2.03.

d. The 90% confidence interval estimate of the difference between the two population means is [-0.44, 4.50].

a. The sample mean for sample 1 is

(10 + 13 + 9 + 8 + 6) / 5 = 9.2

The sample mean for sample 2 is

(7 + 7 + 8 + 4 + 9 + 8) / 6 = 7.1667 ≈ 7.17

b. The sample standard deviation for sample 1 is:

√[((10-9.2)² + (13-9.2)² + (9-9.2)² + (8-9.2)² + (6-9.2)²) / (5-1)]

= √[10.8] ≈ 3.29

The sample standard deviation for sample 2 is

√[((7-7.17)² + (7-7.17)² + (8-7.17)² + (4-7.17)² + (9-7.17)² + (8-7.17)²) / (6-1)]

= √[13.33] ≈ 3.65

c. The point estimate of the difference between the two population means is:

9.2 - 7.17 = 2.03

d. To calculate the 90% confidence interval estimate of the difference between the two population means, we need to first calculate the standard error of the difference between the sample means:

s.e.(difference between sample means) = √[(s1²/n1) + (s2²/n2)]

= √[(3.29²/5) + (3.65²/6)]

= √[2.60]

≈ 1.61

Next, we can use the t-distribution with degrees of freedom equal to the smaller of n1-1 and n2-1 (in this case, 4) and a 90% confidence level to find the critical value, t*:

t* = 1.533 (from t-distribution table or calculator)

Finally, we can construct the confidence interval estimate:

9.2 - 7.17 ± (t* * s.e.(difference between sample means))

= 2.03 ± (1.533 * 1.61)

= 2.03 ± 2.47

= [ -0.44 , 4.50 ]

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The statement that is true about rhombus is d. some rhombuses have four right angles.

A rhombus is a parallelogram with equal-length sides, though the angles at the opposing ends need not be equal, nor must the sides be parallel. If a rhombus is also a cube, it can have four right angles. It can be viewed as an equal-sided trapezoid as well.

A parallelogram has two sets of parallel sides, whereas a trapezoid only has one pair of parallel sides. Therefore, it is untrue that a trapezoid has two sets of parallel edges. Not all rectangles are squares, but they are all quadrilaterals with four right angles. A unique variety of parallelogram called a square has equal-length edges. Therefore, it is untrue to say that all circles are squares.

Complete Question:

which statement about a quadrilateral is true?

a. a rhombus has exactly one pair of parallel sides.

b. a trapezoid has two pairs of parallel sides.

c. all rectangles are squares.

d. some rhombuses have four right angles.

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To find the total percentage decrease, we first need to find the new values of the stocks in Company A and Company B after the decrease.

The new value of the stock in Company A is: $5800 - (1% \times $5800) = $5742

The new value of the stock in Company B is: $7470 - (20% \times $7470) = $5976

To find the total value after the decrease, we add these two values: $5742 + $5976 = $11718

To find the percentage decrease from the original total value ($5800 + $7470 = $13270) to the new total value ($11718), we use the formula:

percentage decrease = [(original value - new value) / original value] x 100%

percentage decrease = [($13270 - $11718) / $13270] x 100%

percentage decrease = 11.7%

Therefore, the total percentage decrease in the investor's stock account is 11.7%.

Step-by-step explanation:

if it is between 0 and pi/2 (90°), or between 3pi/2 (270°) and 2pi (360°).

for angle = 0, cos = 1. therefore, positive.

0 <= 5pi/12 <= pi/2. therefore, positive.

pi/2 <= 5pi/6 <= pi. therefore, negative.

pi/2 <= 3pi/4 <= pi. therefore, negative.

3pi/2 <= 5pi/3 <= 2pi. therefore, positive.

you do know how to compare fractions, right ?

you need to bring then to the same denominator by multiplying numerator and denominator by the same factor.

e.g. comparing 5pi/12 with pi/2.

to bring them both to .../12, we have to multiply pi/2 by 6/6.

so, we are comparing 5pi/12 and 6pi/12.

and we see, 5pi/12 is smaller.

the others work the same way.

3pi/6 <= 5pi/6 <= 6pi/6

2pi/4 <= 3pi/4 <= 4pi/4

9pi/6 <= 10pi/6 <= 12pi/6

now you see it clearly.

Answer:

The formula for the volume of a sphere is:

V = (4/3)πr^3

where V is the volume and r is the radius of the sphere.

We are given that the volume of the sphere is 36π cm^3, so we can write:

36π = (4/3)πr^3

Simplifying:

r^3 = (36/4) * 3

r^3 = 27

r = 3

Therefore, the radius of the sphere is 3 cm.

The circumference of a great circle on a sphere is given by the formula:

C = 2πr

where r is the radius of the sphere.

So, the circumference of the great circle is:

C = 2π(3) = 6π

Therefore, the circumference of the great circle of the sphere is 6π cm.

we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.

The sample provides information about the favorite snack of a random sample of people, but we need to use this information to make a prediction about the whole population of 2600 people.

First, we can calculate the proportion of the sample who chose pretzels or cookies as their favorite snack:

proportion = (number of people who chose pretzels + number of people who chose cookies) / total number of people in the sample

proportion = (16 + 54) / (30 + 16 + 54 + 64)

proportion = 70 / 164

proportion ≈ 0.4268

Next, we can use this proportion to estimate the number of people who will choose pretzels or cookies as their favorite snack out of the whole population:

predicted number of people = proportion × total number of people in the population

predicted number of people = 0.4268 × 2600

predicted number of people ≈ 1110.8

Rounding to the nearest whole number, we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.

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The probabilities of rolling each number on the die are 1÷6, which is correctly represented by the branching probabilities from each die-rolling node.

What is an experiment ?

In science and statistics, an experiment is a controlled procedure designed to test a hypothesis or to investigate the effect of one or more factors or variables on an outcome of interest. The experiment involves manipulating one or more variables and observing the effect on one or more outcomes while controlling other factors that might influence the outcome(s).

Based on the image provided, the tree diagram appears to be correct for the described situation. The first event is drawing a card, which has two possible outcomes: "red" and "black." From each outcome of drawing a card, there are six possible outcomes of rolling a die: 1, 2, 3, 4, 5, and 6. The diagram correctly shows all of these possible outcomes and the probabilities of each outcome, assuming that the deck of cards is a standard deck with 26 red cards and 26 black cards, and the die is fair. The branching probabilities from the "drawing a red card" node are 26÷52 or 0.5, and the branching probabilities from the "drawing a black card" node are also 26÷52 or 0.5.

Therefore, The probabilities of rolling each number on the die are 1/6, which is correctly represented by the branching probabilities from each die-rolling node.

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To be 95% confident within a 4% margin of error, the programmer must survey at least 601 computers.

To estimate the percentage of computers that use a new operating system with a 95% confidence level and a 4% margin of error, you must first determine the required sample size. Here's a step-by-step explanation:
Identify the confidence level and margin of error: In this case, the confidence level is 95% and the margin of error is 4%.
Determine the standard value (Z-score) for the desired confidence level: For a 95% confidence level, the Z-score is 1.96. This value can be found using a Z-score table or an online calculator.
Use the formula for sample size calculation:
  n = (Z^2 * p * (1-p)) / E^2
  Where n is the required sample size, Z is the Z-score, p is the estimated proportion of computers using the new operating system, and E is the margin of error.
Since we do not have an estimate for the proportion (p), we will assume the worst-case scenario (p=0.5) to ensure the largest possible sample size:
  n = (1.96^2 * 0.5 * 0.5) / 0.04^2
Calculate the sample size:
  n ≈ (3.8416 * 0.25) / 0.0016
  n ≈ 0.9604 / 0.0016
  n ≈ 600.25
Round up to the nearest whole number: Since we cannot survey a fraction of a computer, we will round up to the next whole number, which is 601.

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Answer:

13 meters.

Step-by-step explanation:

We can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height

We are given that the base area (length x width) of the prism is 54 m², so we can write:

length x width = 54 m²

We are also given that the volume of the prism is 702 m³, so we can write:

Volume = length x width x height = 702 m³

We want to find the height of the prism, so we can rearrange the formula for the volume to solve for height:

height = Volume / (length x width)

Substituting the given values, we get:

height = 702 m³ / 54 m²

Simplifying this expression, we can divide both the numerator and the denominator by the greatest common factor of 54 and 702, which is 18:

height = (702/18) m / (54/18) m = 39 m / 3 m

height = 13 meters

Therefore, the height of the rectangular prism is 13 meters.

Hence, the value of y is 23 when x = 7.

Describe equation?

A mathematical equation is a formula that uses the equals symbol (=) to denote the equality of two expressions.

A formula would be 3x - 5 = 16,

for instance. We may determine the value of the variable x by solving this equation: x = 73.

The slope-intercept representation of the equation can be used to determine the equation of a line running through the points (x1, y1) and (x2, y2):

y - y1 = m(x - x1) (x - x1)

where m is the line's slope. The following formula can be used to determine the line's slope:

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

Now put the x and y value in this:

slope of the line using the points (1, 5) and (3, 11):

m = (11 - 5) / (3 - 1) = 6 / 2 = 3

We can use the slope of the line to determine the equation of the line now that we know it:

y - y1 = m(x - x1) (x - x1)

y - 5 = 3(x - 1) (x - 1)

y - 5 = 3x - 3 = 3x + 2

In light of this, the equation for the line connecting points (1, 5) and (3, 11) is y=3x+2

To determine the value of y for x = 7, we can utilize the equation of the line we discovered earlier:

y = 3x + 2

y = 3(7) + 2

y = 21 + 2

y = **23**

Graph calculation given below:

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Answer: f(4) = 11

Step-by-step explanation: See image below.

Answer: 11

Step-by-step explanation:

you need to put 4 where the X is: f(4)=(2*4)+3 = 11

Answer:

Sure, I can help you with that. (a) His total wage for a basic week can be calculated as follows: Total wage for a basic week = Basic rate per hour x Number of hours worked in a basic week Total wage for a basic week = $16 x 40 Total wage for a basic week = $640 Therefore, his total wage for a basic week is $640. (b) His wage for a week in which he worked 47 hours can be calculated as follows: Wage for a week with overtime = (Basic rate per hour + Overtime rate per hour) x Number of overtime hours worked + Total wage for a basic week Overtime rate per hour = Basic rate per hour + $4 Overtime rate per hour = $16 + $4 Overtime rate per hour = $20 Wage for a week with overtime =$16

Answer:

To find A+3B, we need to first find A and B. A = 1 + r + 7r^2 B = 1 - r^2 Now we can substitute these expressions into A+3B: A+3B = (1 + r + 7r^2) + 3(1 - r^2) Simplifying this expression, we get: A+3B = 1 + r + 7r^2 + 3 - 3r^2 A+3B = 4 + r + 4r^2 So the expression that equals A+3B in standard form is 4 + r + 4r^2.

Answer:

180 fr

Step-by-step explanation:

its too hard

Step-by-step explanation:

For: x=-1

f(x)= -3*-1 -4 =-1

For: x=0

f(x)= -3*0-4 =-4

For: x=1

f(x)= -3*1 -4 =-7

Therefore, the range of f(x)= [-1, -4, -7]

Answer:

[tex]x {}^{2} - 5[/tex]

To write f(x) = 5(x - 2)2 - 7 in standard form, we need to expand the squared term first:

f(x) = 5(x - 2)(x - 2) - 7

f(x) = 5(x2 - 4x + 4) - 7

f(x) = 5x2 - 20x + 13

Therefore, the standard form of f(x) = 5(x - 2)2 - 7 is f(x) = 5x2 - 20x + 13.

Answer: f(x)=5x2−20x+13

Step-by-step explanation:

This is reflected in the data as the number of bacteria doubles every two hours, which is a characteristic of exponential growth.

Data that changes or grows at an exponential rate over time is referred to as exponential data. This indicates that the data changes quickly, either increasing or decreasing, and that the pace of change quickens over time. Exponential data frequently consists of numbers that rise steadily over time, with the rate of rise accelerating over time.

a.) exponential function would be the ideal option to model this data. An exponential curve is produced as the quantity of bacteria multiplies at an ever-increasingly rapid rate.

b. One way to determine which function is the best choice is to examine the rate of change of the data. In this case, we may calculate the average rate of change for each time period and see if it is constant. If the rate of change is constant, the data can be represented by a linear function. However, if the rate of change increases or decreases, an exponential or quadratic function might be a better fit.

From 0 to 2 hours: (25-10)/(2-0) = 7.5

From 2 to 4 hours: (50-25)/(4-2) = 12.5

From 4 to 6 hours: (100-50)/(6-4) = 25

c. The distance travelled by an automobile at a constant pace is an illustration of data that would be best characterised by a linear function. Imagine a car driving for four hours at a speed of 60 mph. Below is a list of the distance covered each hour:

After 1 hour: 60 miles

After 2 hours: 120 miles

After 3 hours: 180 miles

After 4 hours: 240 miles

In this case, the distance traveled is directly proportional to the time, so a linear function would be the best fit.

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Answer:

Option D.

Step-by-step explanation:

According to this survey results:

Students: 80 like viking and 20 like patriot.

Teachers: 5 like viking and 15 like patriot.

In Option A it is given that patriot is more popular in students while viking is more popular in teachers which is not correct.

In option C patriot is equally popular in students and teachers, which is also not correct. because patriot is popular in 20% of students but 80% in teachers, which is not correct.

In option B there is no difference between students and teachers, this statement is also not correct because there is lots of differences in their choices.

In Option D it is said that viking is more popular in students but patriot is more popular in teachers. this is correct.

Answer: it's 1

Step-by-step explanation:

The x in the numerator determines that the x is in absolute value, meaning only positive integers.

That wouldn't matter anyway, because since any value of x would have to be greater than 0 (meaning only positive values), and both x's are the same x, the equation would have to equal one.

For example, you could plug in 2 to both x's. 2/2 is 1.

Or you could plug in 289 to both x's, in which 289/289 is 1.

No matter what number, as long as it's positive, will be 1.

The area of shaded part in the figures are

1. 7.07cm²

2. 19.54cm²

The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.

The area of a sector is expressed as:

A= tetha/360 × πr²

Area of the shaded part = area of big sector - area of small sector.

1. area of big sector = 90/360 × 3.14 × 5²

= 7065/360

= 19.63cm²

area of small sector = 90/360 × 3.14 × 4²

= 12.56cm²

area of shaded part = 19.63 - 12.56

= 7.07cm²

2. Area of big sector = 40/360 × 3.14 × 9²

= 28.26cm²

area of small sector = 40/360 × 3.14 × 5²

= 8.72

area of shaded part = 28.26-8.72

= 19.54cm²

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