Suppose that ƒ(−1)=10 and ƒ'(x)≥−3 for all values of x. What is the least possible value of ƒ(3)?

Approx 16 revolutions the wheel go through to travel the distance 25 meters by a diameter of 50 cm.

In the given question, a wheel having a diameter of 50 cm.

If the elf travels a distance of 25 meters then we have to find how many revolutions did the wheel go through.

Since we have the wheel's diameter, we can determine the radius of the wheel. As we already know, the length of a wheel's revolution is equal to its circumference, which is a circle with a diameter of 2πr.

We will now enter the radius value into the algorithm to determine how many revolutions the wheel must make. To reach the desired result, divide the total distance by the distance covered in one revolution to determine the number of revolutions needed to travel 25 m.

r = [tex]\frac{50}{2}[/tex] = 25 cm

The radius of the wheel is 25 cm.

Now we put the value of r in the formula of circumference.

2πr = 2π×25

2πr = 50π cm

Total distance is 25 m. So we convert m in cm by multiplying the 100.

Now the total distance is 2500 cm.

2500 = n × 50π

Now putting the value of π = 3.14

2500 = n×50 × 3.14

2500 = n×157

Divide by 157 on both side, we get

n = 15.924

n = 16(approx)

Hence, approx 16 revolutions the wheel go through to travel the distance 25 meters by a diameter of 50 cm.

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The equation which describes the nth term for the sequence 3/5,1/5,1/15,1/45,\cdots2 is  an = 3/5 (1/3)n-1 , which is option C.

We use the formula an=a1+(n−1)d an = a1 + (n−1)d , to calculate the nth term of a given sequence. The 'n' here  represents a number.

Using the nth term we can any number on the sequence which allows us to locate any term in a series.

By substituting different values for the term number, we can create a series utilizing the nth term (n).

To find the tenth term we use the sequence formula and substitute a random number in place of n.

Example if we need to find the first 50 term then we will substitute n as 50.

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The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A car is traveling at a speed of 61 kilometers per hour.

Convert the speed into a kilometer per minute. Then we have

Speed = 61 / 60

Speed = 1.01667 kilometers per minute

Then the number of kilometers will the car travel in 20 minutes will be given as,

1.01667 = d / 20

d = 1.01667 x 20

d = 20.33 kilometers

The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

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Answer:

√28 and √11

Step-by-step explanation:

Note : -

Irrational number is any real number that cannot be expressed as the quotient of two integers.

Here,

√28 = 5.291.......

5.291.... is an infinite number, it keeps going, it cannot be expressed in terms of a fraction.

Similarly,

√11 = 3.316......

Hence,

√28 and √11 are irrational numbers.

You can identify equivalent expressions if one of the expressions can be written like the other and it is usually written by combining any like terms on each side of the equation such as x-terms with x-terms and constants with constants.

These are the type of expressions that have similar value or worth but do not look the same.

This type of expression can be identified if one of the expressions can be written like the other and example can be seen below:

3(x + 3) and 3x + 9

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Answer:

The tree is 9.1 meters high.

Step-by-step explanation:

We can use the Pythagorean Theorem to solve this problem. Let T be the height of the tree. We can set up the following equation:

4.2^2 + T^2 = 6.5^2

Solving for T, we get:

T = sqrt(6.5^2 - 4.2^2)

T = sqrt(41.25 - 17.64)

T = sqrt(23.61)

T = 4.878

Since the height of the tree is measured to the nearest tenth, we can round this value to 9.1 meters.

The Osborne 1 was the first laptop ever released, and it weighed 11 kg in 1981. Since then, the average rate of weight decrease has been 4.7% per year. This means that in 2019, a laptop would have weighed around 2.3 kg.

1981: 11 kg

1982: 10.5 kg (11 kg - 0.55 kg = 10.5 kg)

1983: 10.02 kg (10.5 kg - 0.48 kg = 10.02 kg)

1984: 9.55 kg (10.02 kg - 0.47 kg = 9.55 kg)

2019: 2.3 kg (3.44 kg - 1.14 kg = 2.3 kg)

The Osborne 1 was the first laptop ever released in 1981, and it weighed 11 kg. Since then, the average rate of weight decrease has been 4.7% per year. This means that the mass of a laptop decreases by 0.47 kg every year on average. So, in 1982 it would have weighed 10.5 kg, in 1983 it would have weighed 10.02 kg, and so on. By 2019, the weight of a laptop would have decreased to 2.3 kg as a result of this 4.7% average rate of weight decrease.

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Answer: The answer is 11 1/4

Step-by-step explanation:

Answer:  -100

Step-by-step explanation:   -7(15)+5

It said x=15 so put 15 in and solve from there and that would be -100

HOPE THIS HELPS ANY I JUST completed FUNCTIONS AND MAN IT WAS FUN

Answer:

7/12

Step-by-step explanation:

y = 12

x = 7

y = Kx

K = y/x

K = 7/12

The length of the actual statue in feet would be = 64.96 ft

A scale model is defined as the the exact type of an object but with a different measurement.

The scale model of a statue = 1 In = 11.2 ft

The length of the model = 5.8 inches

Therefore it length in feet = X ft

That is; 1 in = 11.2 ft

5.8 in = X ft

make X ft the subject of formula;

X ft = 5.8 × 11.2 = 64.96 ft

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The domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.

From the graph, vertex is (h, k)=(0, 4) and (x, y)=(2, 0)

Here, y= a(x - h)² + k

0=a(2-0)+4

-4=2a

a=2

Substitute, a=2 and (h, k)=(0, 4) in y= a(x - h)² + k, we get

y=2(x-0)²+4

y=2x²+4

So, f(x)=2x²+4

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (-∞,∞),{x|x∈R}

Range: [4,∞),{y|y≥4}

Now,

(a) f(-3)= 2(-3)²+4=18

(b) f(2)= 2(2)²+4=12

(c) f(0)= 2(0)²+4=4

(d) f(3)= 2(3)²+4=18

Therefore, the domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.

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Answer:

Step-by-step explanation:

(-2,4)

(0,5)

(2,6)

(4,7)

Answer: 4, 5, 6, 7,

Step-by-step explanation: From the formula   y = x / 2 + 5

substitute x with the value -2

It becomes -2 / 2 + 5

that equals 4

then do the same for the rest

when x = 0

y = 0 / 2 + 5

y = 5

when x = 2

y = 2 / 2 + 5

y = 1 + 5

y = 6

when x = 4

y = 4 / 2 + 5

y = 2 + 5

y = 7

I hope this was helpful

The algebraic solutions are x < -5 and x > 3.

The graph is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x² + 2x > 15

x² + 2x - 15 > 0

x² + (5 - 3)x - 15 > 0

x² + 5x - 3x - 15 > 0

x(x + 5) - 3(x + 5) > 0

(x - 3)(x + 5) > 0

x + 5 > 0 and x - 3 > 0

x < -5 and x > 3

The graph is given below.

Thus,

x < -5 and x > 3 is the solution.

The graph is given below.

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Answer:

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

15 inches of wire costs 90 cents, then 1 inch of wire costs:

The length of wire for 72 cents:

Therefore , the solution of the given problem of equation comes out to be  9x^3 - 8x^2.

A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.

Here,

Polynomial function total

Polynomial functions are those that have a leading degree of three or higher. given the total;

(7x^3-4x^2)+(2x^3-4x^2)

Expand => (7x 3-4 times) + (2x 3-4 times)

= > 7x^3-4x^2 + 2x^3-4x^2

assemble similar terms

=> 7x^3 + 2x^3 - 4x^2 -4x^2

=> 9x^3 - 8x^2

Therefore , the solution of the given problem of equation comes out to be 9x^3 - 8x^2.

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Answer:

37

Hope this helps :)

Answer:

515 x + 285 y = 11080

x + y = 30

Step-by-step explanation:

The student is testing each soil's permeability, and soil X is more permeable than soil Y. The correct option is A.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before. Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.

Porosity can be defined as the quality of the material having pores or holes. The permeability can be defined as the state or quality of a material that allows liquids or gases to pass through it.

The soil which does not hold much water can be considered of high porosity and high permeability. As it is only possible if the soil has a large number of pores and it is not in compact form.  

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As the p-value of the test is of 0.215 > 0.05, there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:

[tex]H_0: \mu = 8.5[/tex]

At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:

[tex]H_1: \mu \neq 8.5[/tex]

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]

Hence the test statistic is calculated as follows:

[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}}[/tex]

z = (8.8 - 8.5)/(1.11/square root of 21)

z = 1.24.

The p-value is obtained using a z-distribution calculator.

We have a two-tailed test, as we are testing if the mean is different of a value, with a test statistic of z = 1.24, hence the p-value is of:

0.215.

(2 multiplied by the subtraction of one and the p-value of z = 1.24).

The p-value is greater than the significance level of 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a difference between the two methods.

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If [tex]\frac{1}{4}[/tex] of fruit punch is pineapple juice. About [tex]\frac{1}{6}[/tex] of the fruit punch is orange juice, then fraction of punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .

The fraction of pineapple juice in fruit punch is = [tex]\frac{1}{4}[/tex] ;

the fraction of orange juice in fruit punch is = [tex]\frac{1}{6}[/tex] ;

the equation that can be used to find the fraction of fruit punch that is pineapple juice or orange juice is

⇒ [tex]Frcation Of (Pinapple Juice +Orange Juice)[/tex]

substituting the values ,

we get the equation as ;

⇒ [tex]\frac{1}{4} +\frac{1}{6}[/tex]

taking LCM as 4 and 6 as 12 and solving further  ,

we get ;

⇒ [tex]\frac{3}{12} +\frac{2}{12}[/tex] ; = [tex]\frac{5}{12}[/tex] .

Therefore , the fraction of fruit  punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .

The given question is incomplete , the complete question is

About 1/4 of fruit punch is pineapple juice. About 1/6 of the fruit punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice .

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Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.

Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<

Here,

Let the quantity of sold laptops, x

y —- the quantity of sold smartphones

The fact that to solve this problem we use inequality help

The problem's underlying inequity is equal to

=> 80x + 60y ≥6800

Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.

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Equation of ellipse is x²/400 + (y-52) ²/256 =1

An ellipse is an oval shaped close geometrical figure. Ellipse has two radius, one is horizontal, and the other is vertical. An ellipse can be stretched either horizontal direction or vertical direction.

given, width of elliptical mirror = 16 inches

height of elliptical mirror = 20 inches

the center of ellipse = (0, 52)

as the width of elliptical mirror is less than height so the ellipse has vertical major axis.

vertical radius is denoted by b.

and horizontal radius is denoted by a.

as per the question, a = 16 inches and b = 20 inches.

we know the equation of ellipse whose major axis is vertical and center at the origin is shown by

x² / b² + y²/ a² = 1

we are given information about an ellipse having center (0, 52) and vertical radius 20 and horizontal radius 16.

the equation of this ellipse is.

x² / (20) ² + (y -52) ²/ (16)² = 1

x²/400 + (y - 52) ² /256 = 1

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Answer: Marissa divided the marked section of the wall into 3 equal parts. If she painted one of these parts blue, then the part that she painted blue is 1 out of the 3 equal parts. So, the fraction of the wall that is blue is 1/3.

Another way of understanding this is that if the wall is divided into 3 equal parts and Marissa painted 1 part, then the fraction of the wall that is painted is 1/3.

So the fraction of the whole wall that is blue is 1/3.

Step-by-step explanation:

The park should be expanded based on the information as the majority want the expansion.

From the information, on the small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded.

Also, the results showed that 150 of the adults who were parents and 40 of the adults who were not parents thought the park should be expanded.

Based on the above the number of people that wants the expansion will be:

= (150 + 40) / 250 × 100

= 190 / 250 × 100

= 76%

It should be expanded.

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Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.

Food items manufactured from (or containing) milk are referred to as dairy products or milk products (also known as lacticinia).

The cow, water buffalo, nanny goat, and ewe are the most popular dairy animals.

Dairy products include staples from Western grocery stores including yogurt, cheese, and butter.

A dairy is a place where dairy products are made .Various amounts of dairy products are consumed worldwide (see consumption patterns worldwide) .

After standardizing the fat content and optional homogenization or pasteurization, milk is produced in a variety of grades with the potential addition of the microorganisms Streptococcus lactis and Leuconostoc citrovorum.

Based on the type of product generated, milk can be divided into a number of distinct categories, including cream, butter, cheese, newborn formula, and yogurt.

Hence, Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.

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Answer:

She needs 18,731.6 Litres of paint to paint her bedroom.

Step-by-step explanation:

So,

V = l × w × h

V = 10.5 × 7 × 9 feet

V = 661.5 cubic feet

We know that,

So,

661.5 × 28.317 = 18,731.6 Litres

Thus, She needs 18,731.6 Litres of paint to paint her bedroom.

There are 12 weeks will Sonja's balance remain above $377.

What is account balance?

The balance is the sum owed on an account in banking and accounting. The term "balance" in bookkeeping refers to the difference between the total of debit entries and the total of credit entries made into an account over the course of a given financial period. The account shows a debit balance when total debits exceed total credits.

Given:

Sonja has a bank account balance of $1400. Each week, her balance changes by -$85.25. She wants to keep the balance above $377.

We have to find the number of  weeks will Sonja's balance remain above $377.

Let, $1400 - $377 = $1023.

⇒  $1023 / $85.25 = 12

Hence, there are 12 weeks will Sonja's balance remain above $377.

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Answer:

70⁰

Step-by-step explanation:

We need to use the knowledge of trigonometry to find the indicated angle. Given the information in relation to the angle we have the opposite and the hypotenuse.

we therefore use Sine in this calculations

Sin ? = opposite/ hypotenuse

= 16/17

= 0.9412

to get the angle we get the sine inverse

Sine inverse of 0.9412 = 70.25⁰

= 70⁰

Answer:

? ≈ 70°

Step-by-step explanation:

using the sine ratio in the right triangle

sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 70° ( to the nearest degree )

The average rate of change is the ratio of the difference between the y coordinates of two points to the x coordinate of the same point.

It can be found by using two points on the graph and substitute into the formula: (y₀ - y₁) / (x₀ - x₁)

The square brackets [] is used to mean the end points as shown is inclusive

A quadratic equation is a polynomial of degree two

The average rate of change here is not constant and is usually  specified by the two points to which it is measured

For instance using points (-3, 0) and (0, -1) we have

=  (y₀ - y₁) / (x₀ - x₁)

=  (-1 - 0) / (0 - (-3))

= -1/3

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