F(x)=(x-5)^2-20 for all real numbers x what the range of f

Answer:

8 bags of cement

9 bags of sand

3 bags of stone

Step-by-step explanation:

Hope this helps :)

We can deduce here that the chicken is traveling at a speed of 0.245 miles per minute.

Speed is the amount of ground a thing covers in a predetermined period of time. It has magnitude but no direction because it is a scalar quantity. Meters per second (m/s), kilometers per hour (km/h), or miles per hour are used to express speed (mph).

In order to find the speed of the chicken, here is the formula to make use of:

Speed = distance / time

Speed =  7.35 miles / 30 minutes = 0.245 miles per minute.

The chicken might have crossed the first place because it is being chased.

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There are 250,000 different completed answer sheets possible using counting principle.

For part a, there are 2 choices for each of the 5 questions, so there are a total of 2^5 = 32 ways to complete part a.

For part b, there are 5 choices for each of the 4 questions, so there are a total of 5^4 = 625 ways to complete part b.

For part c, there are 6 choices for the first question, 5 choices for the second question (since one of the answers has already been used), 4 choices for the third question, and so on. So there are a total of 6 x 5 x 4 x 3 x 2 x 1 = 720 ways to complete part c.

To find the total number of possible completed answer sheets, we need to multiply the number of choices for each part. However, since part b and part c are mutually exclusive (you can only choose one of them), we need to add their totals together. Therefore, the total number of possible completed answer sheets is:

32 x (625 + 720) = 70,240

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Answer:

City B is significantly higher than in City A.

Step-by-step explanation:

To compare the difference of the means in terms of the mean absolute deviations, we can use the concept of standard deviation units. We divide the difference of the means by the average of the mean absolute deviations of the two cities:

D = (71 - 59) / ((3.2 + 2.9) / 2)

D = 12 / 3.05

D ≈ 3.934

The value of D tells us that the difference of the means between the two cities is almost 4 standard deviation units, which is a large difference. This means that the mean high temperature in City B is significantly higher than in City A.

The product of [tex]\sqrt{30}[/tex] and [tex]\sqrt{10}[/tex] is 10[tex]\sqrt{3}[/tex].

The correct answer would be 10[tex]\sqrt{3}[/tex].

To find the product of [tex]\sqrt{30}[/tex] and [tex]\sqrt{10\\}[/tex], we can simplify it by multiplying the square roots and simplifying the result.

[tex]\sqrt{30 * 10 = (30 * 10) = 300}[/tex]

Now, let's simplify [tex]\sqrt{300}[/tex]. To do this, we can find the prime factorization of 300:

[tex]300 = 2 * 2 * 3 * 5 * 5 = 2^2 * 3 * 5^2[/tex]

Taking the square root of 300:

[tex]\sqrt{300}[/tex] = ([tex]\sqrt{(2^2 * 3 * 5^2)}[/tex]

Using the properties of square roots, we can split the square root into separate square roots:

[tex]\sqrt{300}[/tex] = [tex]\sqrt{2^2}[/tex] * [tex]\sqrt{3}[/tex] * [tex]\sqrt{5^2 }[/tex]

Simplifying each square root separately:

[tex]\sqrt{2^2}[/tex] = 2

[tex]\sqrt{3[/tex] = [tex]\sqrt{3[/tex]

[tex]\sqrt{5^2 }[/tex]= 5

Combining the simplified square roots:

[tex]\sqrt{300}[/tex] = 2[tex]\sqrt{3}[/tex] * 5 = 10[tex]\sqrt{3}[/tex]

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The distributive property allows the formula (-128 x 46) + (128 x -36) to be simplified to -10496.

We may use the distributive property of multiplication over addition/subtraction, which asserts that an x (b + c) = an x b + an x c, to simplify the above calculation (-128 x 46) + (128 x -36).

Let's dissect the expression in detail:

(-128 x 46) + (128 x -36)Let's first assess the goods:

-128 x 46 = -5888

128 x -36 = -4608

Reintroduce these values into the phrase now:

(-5888) + (-4608)

We simply add the absolute values of the two negative numbers while maintaining the sign of the negative:

-5888 + (-4608) = -10496

Consequently, -10496 is the reduced expression.

Last but not least, the phrase (-128 x 46) + (128 x -36) becomes -10496. .By applying the distributive property and carrying out the required multiplication, addition, and subtraction, the result is -10496.

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The solution of the system of equations 5x-4y=34 and -x+8y=22 is x = -6 and y = 4, or (x, y) = (-6, 4).

Given the system of equation in the question;

5x - 4y = 34 _____1

-x + 8y = 22 _____2

To solve the system of equation, first solve for x in equation 2 and plug it  into equation 1.

-x + 8y = 22

x = 8y - 22 _____ 3

Plug equation 3 into equation 1

5x - 4y = 34

Plug in x = 8y - 22

5( 8y - 22 ) - 4y = 34

Solve for y

40y - 110 - 4y = 34

40y - 4y = 34 + 110

36y = 144

y = 144/36

y = 4

Plug y = 4 into equation 3

x = 8( 4 ) - 22

x = 32 - 22

x = 10

Therefore, the solution is x = 10 and y = 4.

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If the standard error is smaller than the standard deviation when conducting a regression, it can be concluded that the model is more precise and reliable in predicting the outcome variable.

When conducting a regression, the standard error is a measure of the precision of the estimated regression coefficient. On the other hand, the standard deviation is a measure of the variability of the data points from the mean. If the standard error is smaller than the standard deviation, it means that the estimated regression coefficient is more precise than the variation of the data points. This indicates that the model is more reliable and accurate in predicting the outcome variable.
In practical terms, a smaller standard error means that the predicted values of the outcome variable will be closer to the actual values, resulting in more accurate predictions. However, it is important to note that a smaller standard error does not necessarily mean that the regression model is better. Other factors such as the goodness of fit, significance of the coefficients, and the overall explanatory power of the model should also be considered when evaluating the performance of a regression model.
In conclusion, if the standard error is smaller than the standard deviation when conducting a regression, it can be concluded that the model is more precise and reliable in predicting the outcome variable. However, other factors should also be taken into account to evaluate the overall performance of the model.

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The calculated value of the exponential decay factor is 1/5

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

The table of values

From the table of values, we can see that

x            f(x)

1             625

2             125

3             25

This show that as x increases by 1, the function f(x) values decreases by a constant factor

This means that

The function is a decay function and the rate of decay is calculated as

Rate = 125/625

Evaluate

Rate = 1/5

Hence, the exponential decay factor is 1/5

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Answer:

Ava lives 8/5 or 1 3/5 miles further from the school compared to Jayna.

Step-by-step explanation:

Answer:

0.714

Step-by-step explanation:

5/7

(5X100) / 7 = 500/7.

50/7 = 7 remainder 1. carry that one over and place it before last zero in 500.

10/7 = 1 remainder 3.

we have 71 remainder 3.

3/7: 300/7 = 42.83

we now have answer of 0.714282

= 0.714 to nearest thousandth

The amount of fluid in container B is 9.5 ounces.

to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.

To determine the amount of fluid in container B, we can divide the amount of fluid in container A by the given ratio of 8. Since container A contains 76 ounces, we divide 76 by 8 to find that each unit of the ratio represents 9.5 ounces. Therefore, container B would contain 9.5 ounces of fluid.

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Answer:

a = 157

b = 23

c = 157

Step-by-step explanation:

Angle b is a vertical angle to the angle measuring 23 so they are equal.

b = 23

Angle c  and the angle measuring 23 forms a straight line so they add to 180.

c+23 =180

c = 180-23

c = 157

Angle c and a are vertical angles so they are equal.

c = a = 157

Answer:

a = 157°

c = 157°

b = 23°

Step-by-step explanation:

We know that vertically opposite angles are equal.

∴ b = 23°

We know that angles in a straight line are added up to 180°.

∴ b + c = 180

23 + c = 180

c = 180 - 23

c = 157°

a = 157° ( vertically opposite angles ⇒ c = a )

The area of the triangle with base 2x and height (x - 7) in simplified form is x² - 7x

Area of a triangle = ½ × base × height

Base = 2x

Height = (x - 7)

Area of a triangle = ½ × base × height

= ½ × 2x × (x - 7)

= (2x² - 14x) / 2

= x² - 7x

Hence, the triangle given the dimensions has an area of x² - 7x

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The height of the telephone pole is approximately 26 feet.

According to the given information, the height of the man is 6 feet 2 inches, which we can represent as 6.17 feet, and his shadow is 9 feet 4 inches, which is 9.33 feet.

Using the concept of similar triangles, we can set up the following proportion:

(man's height) / (man's shadow) = (pole's height) / (pole's shadow)

Simplifying the proportion:

6.17 / 9.33 = h / 39.5

To solve for 'h', we can cross-multiply:

6.17 * 39.5 = 9.33 * h

243.215 = 9.33 * h

Dividing both sides by 9.33:

h ≈ 26.06

Rounding to the nearest whole foot, the height of the telephone pole is approximately 26 feet.

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The correct confidence interval for a population mean at a 98% confidence level is approximately (94.685, 121.569). Therefore, the correct choice is (94.725, 121.529).

To construct a confidence interval for a population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, we need to determine the critical value for a 98% confidence level. Since the sample size is large (n = 28), we can use the z-table to find the critical value. For a 98% confidence level, the critical value is approximately 2.33.

Next, we calculate the standard error using the formula:

Standard Error = sample standard deviation / √(sample size)

In this case, the sample standard deviation is 30.4888 and the sample size is 28. Therefore:

Standard Error = 30.4888 / √(28) ≈ 5.769

Now we can construct the confidence interval:

Confidence Interval = 108.127 ± (2.33 * 5.769) = (108.127 ± 13.442) = (94.685, 121.569)

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The most reasonable conclusion is that the instruction to brake smoothly resulted in a decrease in gas consumption, as evidenced by the lower mean and negative difference in means between the two groups.

Based on the information provided, the most reasonable conclusion would be that the instruction given to the first group of drivers to brake smoothly when approaching a red light or stop sign resulted in a decrease in the mean gallons of gas used compared to the second group.

The justification for this conclusion is supported by the fact that the mean for the first group is 43.16 gallons of gas, which is lower than the mean for the second group, which is 54.63 gallons of gas. This indicates that the first group, who received the specific instruction to brake smoothly, consumed less gas on average.

The histogram displaying the differences in means after the data for both groups were combined and redistributed also supports the conclusion. It likely shows a distribution that is centered around a negative value, indicating that the majority of the redistributed groups had a lower mean gas consumption compared to the initial second group.

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It will take all three pumps, Working together, 1.56 minutes to fill the pool.

The given information, we can write three equations as follows:

1) (1/A + 1/B)*35 = C  ---(Equation 1)

2) (1/B + 1/C)*40 = C  ---(Equation 2)

3) (1/A + 1/C)*56 = C  ---(Equation 3)

We want  how many minutes it will take all three pumps, working together, to fill the pool, so let's represent the time taken by all three pumps working together as "t".

When all three pumps work together, they can fill the pool in one minute, so their combined rate is 1/C.

Using the rate formula, we can write the following equation:

1/A + 1/B + 1/C = 1/t   ---(Equation 4)

We have four unknowns (A, B, C, and t), so we need to solve for one of them to get the answer. Let's solve for "t".

First, we can simplify Equations 1, 2, and 3 as follows:

1) 1/A + 1/B = C/35

2) 1/B + 1/C = C/40

3) 1/A + 1/C = C/56

Next, we can substitute these equations into Equation 4 to get:

(C/35) + (C/40) + (C/56) = 1/t

Now, we can simplify and solve for "t":

LCD = 39200

1120C + 980C + 700C = 39200

2800C = 39200

C = 14

Substituting this value of "C" into any of the simplified equations, we can solve for "A" and "B". Let's use Equation 1:

1/A + 1/B = 14/35

5(A+B) = 98

A+B = 19.6

Now we can use A+B+C = 1/t to solve for "t":

t = 1 / (A+B+C) = 1 / (19.6 + 14) = 0.026 hours = 1.56 minutes

Therefore, it will take all three pumps, working together, 1.56 minutes to fill the pool.

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Answer:

[tex]3n = 57[/tex]

[tex]n = 19[/tex]

D is the correct answer.

False. The formula PV - FV(1 + n) does not determine the present value of $1.

But rather it is a formula used to calculate the present value of a future cash flow or investment. PV stands for present value, FV stands for future value, and n represents the number of periods for which the investment will be held. The formula states that the present value of an investment or cash flow is equal to the future value of that investment or cash flow, discounted at a specified rate of return over a specific period of time.

In other words, the formula is used to determine the value today of a future cash flow or investment based on the time value of money. By discounting the future value of the cash flow or investment at a specified rate, the formula calculates the present value that would be equivalent to receiving that cash flow or investment at a future date.

Therefore, the correct statement would be: The formula PV - FV(1 + n) is used to determine the present value of a future cash flow or investment.

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The total surface area of the pyramid is: 208.88 m²

The surface area of the pyramid is simply the sum of the areas of all the given surfaces.

Formula for the area of a triangle is:

Area = ¹/₂bh

where:

b is base

h is height

Area of four side triangles = 4(¹/₂ * 8 * 12) = 192 m²

Using Pythagoras theorem, the height of the base triangle is:

x = 4.22

Area of base = ¹/₂ * 8 * 4.22 = 16.88 m²

Total surface area = 192 + 16.88

= 208.88 m²

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Answer: 39

Step-by-step explanation: 180-141= 39

The annual interest rate, r, is 0.1 or 10%. A 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.

To find the annual interest rate, r, we can rearrange the compound interest formula A = P(1 + r) and solve for r.

Given that an investment of $5,000 grows to $6,050 in 2 years, we can substitute these values into the formula:

$6,050 = $5,000

[tex] {1 + r}^{2}[/tex]

Dividing both sides by $5,000, we have:

1.21 =

[tex](1 + r)^2[/tex]

Taking the square root of both sides, we get:

√1.21 = 1 + r

Simplifying, we have:

1.1 - 1 = r

0.1 = r

This means that the investment grew by 10% annually over the 2-year period. Compound interest is calculated by adding the interest earned to the initial amount, and as time passes, the interest is earned on both the initial amount and the accumulated interest from previous periods. In this case, a 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.

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The value of x in the parallel lines is 15.

Option C is the correct answer.

We have,

The concept being used here is the concept of alternate exterior angles and the parallel lines property.

Alternate exterior angles are pairs of angles that lie on opposite sides of a transversal and are located outside the two parallel lines.

According to the property of alternate exterior angles, when two parallel lines are intersected by a transversal, the alternate exterior angles are congruent or equal in measure.

Since lines s and t are parallel lines,

8x + 7 and 127 are alternate exterior angles.

So,

8x + 7 = 127

Now,

Solve for x.

8x + 7 = 127

8x = 127 - 7

8x = 120

x = 120/8

x = 15

Thus,

The value of x in the parallel lines is 15.

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The value of (f•g)(5) is 21.

Given are two functions f(x) = 3x+2 and g(x)= √x-1, we need to determine (f•g)(5),

So, firstly determine (f•g)(x),

Therefore,

(f•g)(x) = (3x+2)(√x-1)

Now for, (f•g)(5) put x = 5,

We get,

(f•g)(5) = (3·5+2)(√5-1)

(f•g)(5) = 17 × 1.23

(f•g)(5) = 21

Hence the value of (f•g)(5) is 21.

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The p-value of the test is approximately 0.299.

To find the p-value of the test, we need to conduct a hypothesis test. Let's set up the hypotheses first:

Null Hypothesis (H0): The modification of the process did not reduce the number of flaws per pair of shoes.

Alternate Hypothesis (Ha): The modification of the process did reduce the number of flaws per pair of shoes.

We can use a one-sample t-test to analyze the data. The test statistic can be calculated using the formula:

t = ( - μ) / (s / √n),

where  is the sample mean, μ is the population mean (2.5 flaws), s is the sample standard deviation (0.66), and n is the sample size (30).

Substituting the values into the formula, we get:

t = (2.2 - 2.5) / (0.66 / √30) ≈ -1.054

To find the p-value associated with this test statistic, we need to consult the t-distribution table or use statistical software. The p-value represents the probability of observing a test statistic as extreme as the one calculated under the null hypothesis.

Assuming a two-tailed test, the p-value is the probability of observing a t-value more extreme than -1.054 or more extreme than 1.054. Looking up the p-value in the t-distribution table or using software, we find that the p-value is approximately 0.299.

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The calculated area of the middle shape is 18 square units

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

The figures

From the figure, we have the middle shape to be a rectangle

The width of the rectangle is

Width = 6

The length of the rectangle is calculated as follows

15 = 3 * 5

27 = 3 * 3 * 3

The common factor is 3

So, we have

Length = 3

The area of the rectangle is calculated as

Area = Length * Width

So, we have

Area = 3 * 6

Evaluate

Area = 18

Hence, the area of the middle shape is 18 square units

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Answer:

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

There are 6 sides on each cube, so there are a total of 6 x 6 = 36 possible outcomes.

The combinations that result in a sum greater than 9 are:

There are 6 favorable outcomes.

Therefore, the probability of two numbers whose sum is greater than 9 is:

Answer:

Step-by-step explanation:

Sure, here is the input table for f(x) and g(x) using inputs from 0 to 5:

| Input (x) | f(x) = 25x^(2) | g(x) = 3*3^(x) |

|-----------|----------------|----------------|

| 0         | 0              | 3              |

| 1         | 25            | 9              |

| 2         | 100           | 27             |

| 3         | 225           | 81             |

| 4         | 400           | 243            |

| 5         | 625           | 729            |

As x gets very large, g(x) will have greater output values than f(x). This is because the function g(x) has an exponential growth while f(x) only has quadratic growth. As x gets larger, the base of the exponent in g(x) becomes more significant and results in a much larger output value compared to f(x).

The probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.

The answer to this question involves using the formula for combinations and multiplying the probabilities of each selected car.

Calculate the number of ways to select two mid-sized cars and four compact cars.
- Choose 2 mid-sized cars from 10: C(10, 2) = 10! / (2! * (10 - 2)!) = 45 ways
- Choose 4 compact cars from 15: C(15, 4) = 15! / (4! * (15 - 4)!) = 1365 ways

There are a total of 25 cars to choose from and we need to select 2 mid-sized cars from the 10 available and 4 compact cars from the 15 available. Using the formula for combinations, we get:

C(10,2) * C(15,4) = 45 * 1365 = 61,425

This represents the number of ways we can select exactly 2 mid-sized cars and 4 compact cars. To find the probability, we divide this number by the total number of possible selections:

C(25,6) = 53,130

So the probability of selecting exactly 2 mid-sized cars and 4 compact cars is:

61,425 / 53,130 ≈ 0.1156 or 11.56%

In conclusion, the probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.

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