7. Which of the following represents the range of the function g(x) = -3(x + 5)² +10
(1) y ≤ 10
(2) y> -15
(3) y > 10
(4) y ≤ 15

The difference between f(8) and f(4) lies between -16 and 12, inclusive. Therefore, we can estimate that f(8) - f(4) is between -16 and 12.

The Mean Value Theorem is a fundamental result in calculus that relates the average rate of change of a function over an interval to its instantaneous rate of change at some point within the interval. It states that if a function f(x) is continuous on a closed interval [a,b] and differentiable on the open interval (a,b), then there exists some c in (a,b) such that:

f'(c) = [f(b) - f(a)] / (b - a)

In this problem, we are given that f(x) is continuous on [4,8] and differentiable on (4,8), and we are asked to estimate f(8) - f(4) using the Mean Value Theorem.

To do this, we first apply the Mean Value Theorem to obtain an expression for f(8) - f(4) in terms of f'(c) for some c in (4,8):

f'(c) = [f(8) - f(4)] / (8 - 4)

Rearranging, we get:

f(8) - f(4) = f'(c) [tex]\times[/tex] 4

So we need to find an estimate for f'(c) to find an estimate for f(8) - f(4).

We are given that −4≤f′(x)≤3 for all x in (4,8), which means that f'(x) lies between -4 and 3 for all x in (4,8). Since c is also in (4,8), it follows that f'(c) is also between -4 and 3. Therefore, we can say that:

-4 ≤ f'(c) ≤ 3

Substituting this inequality into our expression for f(8) - f(4), we get:

-4 * 4 ≤ f(8) - f(4) ≤ 3 [tex]\times[/tex] 4

Simplifying, we get:

-16 ≤ f(8) - f(4) ≤ 12

This means that the difference between f(8) and f(4) lies between -16 and 12, inclusive. Therefore, we can estimate that f(8) - f(4) is between -16 and 12.

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Hong opened a money investment account with $6600, which increased by 7.5% by the end of the year. The final amount in the account was $7095.

Hong opened an money investment account with $6600. At the end of the year, the amount in the account had increased by 7.5%. To solve the problem, we can start by calculating the amount of the increase in Hong's account:

Increase = $6600 x 7.5% = $495

Then, we can add the increase to the initial amount to find the final amount:

Final amount = $6600 + $495 = $7095

Therefore, there was $7095 in Hong's account at the end of the year.

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The circumference of the circle with a radius of 6 feet would be approximately 37.7 feet.

The circumference of a circle is the distance around the outer edge of the circle. It is the perimeter of the circle, which is the total length of the boundary that encloses the area of the circle.

The formula for the circumference of a circle is

C = 2πr

Where C is the circumference, r is the radius, and π is approximately 3.14.

If a circle has a radius of 3 feet, the circumference would be

C = 2πr

C = 2π(3)

C ≈ 18.85 feet

When the radius doubles to 6 feet, the circumference would be

C = 2πr

C = 2π(6)

C ≈ 37.7 feet

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Answer:

double, and 36

Step-by-step explanation:

Mc graw hill

Q...

Therefore, the statement that is true is: "The solution to the equation is x = 0.1."

In mathematics, an equation is a statement that shows the equality between two expressions. It is made up of two sides: the left-hand side (LHS) and the right-hand side (RHS), which are connected by an equal sign (=). An equation indicates that the two expressions on either side of the equal sign have the same value. Equations can take different forms, depending on the types of expressions involved and the operations used.

Here,

However, we can solve the equation ourselves to find the solution and then check the options.

5x − 6 + 7 = 15x (Given equation)

Simplifying the left-hand side of the equation, we get:

5x + 1 = 15x

Subtracting 5x from both sides, we get:

1 = 10x

Dividing both sides by 10, we get:

x = 1/10

Now we can check each option to see which statement is true:

x = 0.1: This is true, as 1/10 is equal to 0.1.

x = -0.1: This is false, as we found that x = 0.1, not x = -0.1.

x = 10: This is false, as we found that x = 0.1, not x = 10.

The equation has no solution: This is false, as we found a solution for x, namely x = 0.1.

The solution to the equation is x = 1: This is false, as we found that x = 0.1, not x = 1.

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Complete question:

The steps to solve equation 5x−6+7=15x are shown. Which statement about the solution is true?

x = 0.1

x = -0.1

x = 10

The equation has no solution

The solution to the equation is x = 1

Answer:

116in2

Step-by-step explanation:

Top Rectangle Shape: 2in x 3in = 6in2

Middle Rectangle Shape: (9in+3in) x (9in-2in) = 84in2

Far Left Rectangle Shape: (9in-2in-5in) x (6in) = 12in2

Bottom Triangle Shape: [6in - (9in-5in-2in] x [(9in+3in-11in)+6in] x 1/2 = 14in2

Total: 6in2 + 84in2 + 12in2 + 14in2 = 116in2

*Recommend dividing shape to avoid trapezoids

The derivative of [tex]fm(x) = Xm * x^n / (2^{(n+1)})[/tex] with respect to x is [tex]fm'(x) = (Xm-1)x^{n(n+1)}/2^{(n+1)}[/tex].

We can start by using the power rule of differentiation. Taking the derivative of Xm with respect to x gives mXm-1.

Next, we need to find the derivative of the series n=1 n x · x n !2, which involves using the product and chain rules.

First, we can rewrite the series as:

[tex]x(1!/2) * x^{2(2!/2)} *x^{3(3!/2)} * ... * x^n(n!/2)[/tex]

Taking the derivative of each term in the series with respect to x, we get:

[tex]1/2x^{(1-1)} * 1/2x^{(2-1)} * 2/2x^{(3-1)} * ... * n/2x^{(n-1)}[/tex]

Simplifying each term, we get:

[tex]1/2x^{(0)} * 1/2x * 1/x * ... * n/2x^{(n-1)}[/tex]

Combining all the terms, we get:

[tex](1/2 + 1/4 + 2/6 + ... + n/2n) * x^{(-1)}[/tex]

To simplify the series 1/2 + 1/4 + 2/6 + ... + n/2n, we can factor out 1/2 and simplify the remaining terms:

1/2(1/1 + 1/2 + 1/3 + ... + 1/n)

This is the harmonic series, which does not have a closed-form solution. However, we can approximate it using the integral test:

∫(1 to n) 1/x dx = ln(n)

So, the harmonic series can be approximated as ln(n), and the derivative of the series can be written as:

[tex](1/2 ln(x) ) * x^{(-1)}[/tex]

Putting it all together, we get the derivative of fm(x) as:

[tex]f0m(x) = mXm-1 *(1/2 ln(x)) * x^{(-1)}[/tex]

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Answer:

it 50°

Step-by-step explanation:

D is the reflection of x

Answer:

a. SSS

Step-by-step explanation:

Answer:

Step-by-step explanation:

qacfascffaafa

The inequality is 76.26 - 72.61x ≥ 0 and the value of x is x ≤ 1.05. Audrey can purchase at most 1 biking outfit while staying within her budget.

A mathematical statement called an inequality compares two values, frequently by employing symbols. When there is an inequality, one value is either bigger than or less than the other, not necessarily equal to it. For instance, the inequality x > 5 asserts that x is bigger than, but not necessarily the same as, 5. Relationships between different numbers, such as the sum of money spent on shopping and the sum of money left in a budget, are sometimes described as having inequalities.

Let us suppose the number of outfits = x.

Given that, the total amount Audrey has is $440.

Now, the inequality can be written as:

40 - 259.52 - 2(3.07) - 29.12 - 72.61x ≥ 0

76.26 - 72.61x ≥ 0

-72.61x ≥ -76.26

x ≤ 1.05

Hence, Audrey can purchase at most 1 biking outfit while staying within her budget.

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Answer:

[tex]69.85in^2[/tex]

Step-by-step explanation:

To work out an area of a sector, the general formula is [tex]\pi r^2\times\frac{\theta}{360}[/tex] where theta [tex](\theta)[/tex] is the angle.

To work out the total angle of the shaded area:

[tex]360 - (143\times 2)\\= 360 - 286\\= 74[/tex]

Now we know the angle, we work out the area (To nearest hundredth, 2d.p.):

[tex]\pi\times(10.4in)^2\times\frac{74}{360}\\ = 69.85 in^2[/tex]

Hope this helps!!!

Answer:

Median is 9

mode is 10

range4:

Answer:

Step-by-step explanation:

pretty hard to explain but if you do a bunch of questions and answer them correctly then you'll get points. Yes the points from challenges count, Nothing else counts for the ranking.

Answer: 4 2/5

Step-by-step explanation:

1 divided by 2 is 1/2, so if 1/2 times 2 equals one cup, then all we have to do is times 2 1/5 by two. 2 x 2 is 4, and 1/5 times 2 is 2/5.  Add them together, and you get 4 2/5. Alex will need 4 2/5 cups of dip.

Answer:

132 in.

Step-by-step explanation:

C = πd

C = 22/7 × 42 in.

C = 132 in.

A rating of 6 is not a good description of the center of this data set because the data is skewed to the right, with more students rating the importance of reducing pollution as 7, 8, 9, or 10.

A rating of 6 is not a good description of the center of this data set because the dot plot is skewed to the right. There are more dots to the right of 6 than to the left, indicating that there are more students who rated the importance of reducing pollution as 7, 8, 9, or 10 than those who rated it as 2, 3, 4, 5, or 6.

The center of a data set is typically measured by its mean, median, or mode. In this case, the median would be a better measure of the center than the mean or mode because the dot plot is skewed. The median would be the middle value when the data set is ordered from smallest to largest.

If we order the data set from smallest to largest, we get

2, 3, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10

The median of this data set is 9, which is higher than 6. Therefore, a rating of 6 is not a good description of the center of this data set.

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Answer:

A = 47 degrees

Step-by-step explanation:

cosineA = adjacent/hypotenuse

cosineA =  34/50

cosineA = 0.68

reverse cosine

A = 47 (rounded to the nearest whole number)

Answer:

3(y-2)=2(y-1)-3

or, 3y-6 =2y-2-3

or, 3y-6 =2y-5

or 3y-2y =6-5

or y=1

hence, the value of y is 1

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[tex] \texttt{2(x + 2) = - 8} \\ \: \: \: \: \texttt{2x + 2 = - 8} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \texttt{2x = - 8 - 2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \texttt{2x = - 10} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{x = \cancel\frac{ - 10}{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\texttt \purple{ x = - 5} \: }[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps-

The required equation of change is : C= $40 - 10x, where x is the highest price of gas and C is the change.

Let's start by finding the total cost of the 10 gallons of gas. Let's assume that the price of gas is x dollars per gallon at the gas station with the highest price. Then, the total cost of 10 gallons of gas is:

10x dollars

Since Steve paid with two $20 bills, the total amount he paid is:

$40

Therefore, the equation we need to solve to find Steve's change is:

$40 - 10x = C

where C is the amount of change that Steve will receive. We can simplify this equation by subtracting 10x from both sides:

$40 - 10x - 10x = C - 10x

$40 - 20x = C - 10x

Then, we can simplify further by adding 10x to both sides:

$40 - 20x + 10x = C

$40 - 10x = C

Now, we have an equation that relates the price of gas to the amount of change that Steve will receive. To solve for C, we need to know the price of gas at the gas station with the highest price. Once we know that value, we can substitute it into the equation and solve for C.

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The complete question is :

Steve bought 10 gallons of gas at the gas station with the highest price. He paid with two $20 bills. Write and solve an equation to find his change.

Answer:

4.8kg

Step-by-step explanation:

Answer:

Step-by-step explanation:

24 / 5 = 4.8.

20% of 24 kg is 4.8kg

The closest answer choice is A. Domain: All real numbers; Range: All real numbers.

What are the domain and range?

The domain of a function is the set of all possible input values (often represented by x) for which the function is defined. The range of a function is the set of all possible output values (often represented by y) that the function can produce, based on its input values. In other words, the domain is the set of all valid inputs, and the range is the set of all possible outputs.

The domain and range of an exponential growth function depend on the specific equation of the function.

However, in general, an exponential growth function has a domain of all real numbers and a range of y > 0.

This is because an exponential growth function always has a positive output, and it can take any positive input value.

Therefore, the closest answer choice is A. Domain: All real numbers; Range: All real numbers.

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Answer:

80

Step-by-step explanation:

First, let's mark all animals as x. Now we can form an equation:

[tex] \frac{1}{3} x + \frac{1}{4} x + \frac{1}{5} x + \frac{1}{6} x + 4 = x[/tex]

Then, let's multiply this whole equation by 60, since it's a common denominator:

20x + 15x + 12x + 10x +240 = 60x

57x = -240 + 60x

57x - 60x = -240

-3x = -240 / : (-3)

x = 80

Answer:

For the second set of numbers, 23, 16, 4, 10, 16, 65, 8:

Mean: To find the mean, we add up all the numbers and divide by the total number of numbers:

(23 + 16 + 4 + 10 + 16 + 65 + 8) / 7 = 142 / 7 = 20.2857 (rounded to 4 decimal places)

Median: To find the median, we need to first arrange the numbers in order from smallest to largest:

4, 8, 10, 16, 16, 23, 65

There are an odd number of numbers (7), so the median is the middle number, which is 16.

Mode: The mode is the number that appears most frequently in the set. In this case, 16 appears twice, which is more than any other number, so the mode is 16.

Range: To find the range, we subtract the smallest number from the largest number:

65 - 4 = 61

So the mean is 20.2857, the median is 16, the mode is 16, and the range is 61.

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1. Option 1 multiply 18 m by 0.09361 yd is the correct answer.

2. The cost of the wallpaper will be $1013.

A conversion factor is a ratio used to convert a measurement in one unit to the equivalent measurement in another unit.

In order to convert 18 meters to yards, we must multiply 18 m by 0.09361 yd.

This is because when converting from one unit to another, we must use the conversion factor to multiply, rather than divide.

In this case, the conversion factor is 0.09361 yd/m.

Therefore, we must multiply 18 m by 0.09361 yd to get the answer.

Therefore, the correct answer is option 1, which is to multiply 18 m by 0.09361 yd.

2. To answer the second question, Ken is buying wallpaper. It costs $6.49 per meter.

He needs 512 feet.

To calculate how much the wallpaper will cost, first convert 512 feet to meters.

1m = 3.28ft,

therefore 512ft ÷ 3.28ft = 156.1m.

Then multiply the cost of wallpaper per meter, $6.49, by the number of meters needed, 156.1m.

156.1*$6.49=$1013.07.

To round the nearest half dollar, the cost of the wallpaper will be $1013.

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In triangle, value of x and y are 10,10 .

What does a triangle in math mean?

Three edges and three vertices make up the three sides of a triangle, which is a three-sided polygon in geometry. The fact that the internal angles of a triangle add up to 180 degrees is the most crucial aspect of triangles.

                               Triangle's angle sum property is what this characteristic is known as. Three edges and three vertices make up a triangle, which is a polygon. It is one of the fundamental geometric shapes. The symbol represents a triangle with the vertices A, B, and C. triangle with equal sides.

In triangle  ,

sin45° = y/10√2

 1/√2 = y/10√2

  10√2 = √2y

    y = 10

tan45° = x/y

   1 = x /10

   x = 10

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In other words, if a vector v exists such that an is parallel to v, b is parallel expression to v, c is parallel to v, and d is parallel to v, we may conclude that both a||b and c||d exist.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity

We need a condition that assures that an is parallel to b and c is parallel to d to verify both a||b and c||d.

If a and b are both parallel to the same vector, and c and d are both parallel to the same vector, this is one such condition.

In other words, if a vector v exists such that an is parallel to v, b is parallel to v, c is parallel to v, and d is parallel to v, we may conclude that both a||b and c||d exist.

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Answer:

We can use ratios to set up a system of equations and solve for a, b, and c. Since a:b = 3:8, we can write:

a = 3x

b = 8x

Similarly, since b:c = 6:11, we can write:

b = 6y

c = 11y

Now we have two expressions for b, so we can set them equal to each other and solve for y:

8x = 6y

y = 4x/3

Substituting y back into the expression for c, we get:

c = 11y = 44x/3

To find the smallest possible values of a, b, and c, we want to choose values of x that are as small as possible while still being positive integers. Since x must be a multiple of 3 (because a = 3x is a multiple of 3), let's try x = 3. Then we get:

a = 3x = 9

b = 8x = 24

c = 44x/3 = 44

So the smallest possible values of a, b, and c are 9, 24, and 44, respectively.

Step-by-step explanation:

After answering the provided question, we can conclude that the graph of function f(x + 3) is identical to the graph of f(x), but 3 units to the left.

In mathematics, a function seems to be a link between two sets of numbers in which each individual of the first set (known as the realm) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form wherein every value of x generates a unique value of y.

The transformation that altered the parent function f(x) = log2x to its new look displayed in the graph is a three-unit horizontal shift to the left, represented by the function f(x + 3).

In other words, the graph of f(x + 3) is identical to the graph of f(x), but 3 units to the left.

In the graph, we can see that the entire curve has been moved three units to the left. The point (1, 0) on the original graph, for example, would now be situated at (-2, 0) on the modified graph. Thus, the original graph's point (8, 3) would now be situated at (5, 3) on the converted graph.

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