Calculus Math Minimum and maximum

Answer:

14

Step-by-step explanation:

[tex]\frac{4 \text{ miles}}{1 \text{ hour}} \times 3.5 \text{ hours}=14 \text{ miles}[/tex]

Turning of head is rooting reflex.

Reflex is defined as the action which is performed without thought. In other words, it is an unconscious behaviour or involuntary movement. Newborns have different reflexes such as rooting reflex, moro reflex, stepping reflex, tonic neck reflex and grasp reflex.

Rooting reflex acts on touch. Based on this, babies feed themself. They start sucking when the roof of their mouth is touched. Moro reflex occurs on sudden sound or movement of high intensity. Tonic neck reflex results in fencing position of baby. Grasp reflex is seen when baby closes their fingers and stepping reflex concerns legs.

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The newly translated function of  f(x) = 7x + 1 is; g(x) = 7(x - 1) + 1

In transformation of functions, there are different operations such as translation, reflection, dilation, rotation.

Now, we are told that the function is given as;

f ( x ) = 7x + 1

We are told that it is translated by 5 units to the right.

It is pertinent to note that when talking about translation, it is as good as saying moving from one point to the other without changing the dimensions or shape.

Now, when we shift a function f(x) = x - 1 by a units to the left, it means the translated function is; f'(x) = (x + 1) - 1

However, when we shift a function f(x) = x - 1 by a units to the right, it means the translated function is; f'(x) = (x - 1) - 1

Now, applying that translation rule to our given function gives;

g(x) = 7(x - 1) + 1

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For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years.

As given in the question,

The formula given to us is A = P[tex]e^{rt}[/tex] where

A = accumulation value

P = principal money

t = time period

r = interest rate compounded

P = 9500

A = 2*9500

r = 0.12

By applying it in the given formula we get

19000 = 9500 * [tex]e^{0.12t}[/tex]

2 =    [tex]e^{0.12t}[/tex]

Take natural log on both sides

㏑(2) = 0.12t

0.6931 = 0.12t

t = 5.775

Therefore , For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years after rounding it off to one place after decimal.

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If a line's angle with the x-axis is then, that line's slope will be tanα, and the new road's slope will be tan(0) = 0.

D Street is depicted as a vertical line with a 90° angle of inclination in the accompanying figure. In other words, D Street has an infinite slope.

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

A horizontal line now has zero slopes.

The new road has a zero slope as a result.

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You started with a total of 28 muffins

From the question, the given parameters are:

Proportion carried away = 16 of the total muffins

Proportion carried away = 4/7 of the total muffins

The above parameters implies that

4/7 of the total muffins = 16

Represent the amount you started with x

So, we have the following representation

4/7 of x = 16

Express as products

4/7x = 16

Make x the subject

x = 7 * 16/4

Evaluate

x = 28

Hence, the total number of muffins is 28

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Answer:

  Barlow School has 178 more boys

Step-by-step explanation:

At Barlow School, 4/9 of 873 students are boys. At Willow School, 2/3 of 630 students are girls. You want to know which school has more boys, and by how many.

The number of boys is ...

  4/9 × 873 = 388

The 1/3 of students that are not girls are presumed to be boys. That number is ...

  1/3 × 630 = 210

The difference in the number of boys is ...

  388 -210 = 178

Barlow School has 178 more boys.

The statement ""what goes up must come down. the ball went up. it will come down." can be reached through a deductive reasoning.

The mental process of forming deductive deductions is known as deductive reasoning. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if the premises cannot be true while the conclusion is false.

The primary distinction between inductive and deductive thinking is that inductive reasoning seeks to develop a hypothesis, whereas deductive reasoning seeks to test an existing theory. Inductive thinking proceeds from individual observations to broad generalizations, whereas deductive reasoning proceeds in the other direction.

In conclusion, the correct option based on the information is a deductive reasoning.

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the best question is that if they can examine a sample of tires used for 60,000 miles and determine the proportion that is worn out, then how likely is that proportion to be 3.6% or less?

we are given the information that an A tire manufacturer has a 60,000-mile warranty and the manufacturer considers the overall tire quality to be accepted if less than 5% are worn out at 60,000 miles, also the manufacturer tested 250 tires that have been used for 60,000 miles. they find that 3.6% of them are worn out. So here the Hypotheses can be that:

1) The proportion of tires that are worn out after 60,000 miles is equal to 0.05 and

2) The proportion of tires that are worn out after 60,000 miles is less than 0.05.

We need to deny the first hypothesis with an alternative one. You cannot demonstrate that the average is 3.6%, but if you by one means or another decide that the probability the average is greater than 3.6% is lower than 100% minus your confidence level, at that point you'll be able to deny the first hypothesis and acknowledge the second one as new average.

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The dimensions that maximize the area are 150ft × 300ft.

So, let y be the length of the side parallel to the river and x be the length of each of the two sides perpendicular to it.

The following provides the total fencing length:

The rectangular pen's surface area is:

We may determine the value of x required to maximize the area by determining the value of x for which the derivative of the area function is zero:

The value of y is: for x=150

Therefore, the dimensions that maximize the area are 150ft × 300ft.

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The sample size that should be used is 43.

Given that;

The weight of a cereal box is measured as part of a statistical quality control process for the manufacture of cereal. It is understood that the population standard deviation is 0.06 ounces. To attain a margin of error of and a confidence level of 97% 0.02 ounces.

By considering the confidence level scenario, we get to solve how large a sample should be utilized.

The significance level is (α) = 0.03 ( 97% confidence level )

The critical value is (z*) = 2.17 ( From z-table )

The population standard deviation (σ) = 0.06

The margin of error (E) = 0.02

Therefore, the required sample size is;

n = [(z* × σ)/E ]²

n = 42.383

n ≅ 43

Finally, the sample size that should be used is 43.

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Answer:

It would be the last graph (c). It would look like the image below.

Explanation:

Since 3 is negative the answer would have a graph with a line going like this \.

0.3814 is the probability that the sample contains two white balls and two red ones .

What is probability in math?

Total number of balls = 8 + 12 = 20

Total number of elementary cases

           = ( 20 4 )

Total number of favourable cases

           = ( 8 2 ) * ( 12 2 )

Required probability

   = ( 8 2 )  *  ( 12 2 )/( 20  4 )

 = 0.3814

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The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.

It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.

Let's check all the options. Then we have

a) √6, 2.5, 8/3, convert the numbers into a decimal form. Then we have

⇒ 2.449, 2.5, 2.667, order is in ascending form.

b) √8, 11/4, 2.9, convert the numbers into a decimal form. Then we have

⇒ 2.828, 2.75, 2.667, order is not in ascending form.

c) 9/5, 1.9, √5, convert the numbers into a decimal form. Then we have

⇒ 1.8, 1.9, 2.236, order is in ascending form.

d) 13/5, 2.8, √7, convert the numbers into a decimal form. Then we have

⇒ 2.6, 2.8, 2.645, order is not in ascending form.

e) 1.8, 7/4, √3, convert the numbers into a decimal form. Then we have

⇒ 1.8, 1.75, 1.732, order is not in ascending form.

The terms ordered from least to greatest are √6, 2.5, 8/3, and 9/5, 1.9, √5. Then the correct options are A and C.

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Assuming it is a standard deck of 52 cards and a standard dice of 6 faces.

There are 13 heart cards in a standard deck, therefore the odd of getting a heart is 13 : 52 = 1/4.

There is only 1 six in a standard dice, therefore the odd of getting a six is 1/6.

For these events to happen simultaneously, we multiply the chances.

Therefore, the chance of getting a heart in a deck of cards and a six on a dice is 1/4 x 1/6 = 1/24.

Answer:

heart from a deck of cards= 13/52 = 1/4

getting a six on a dice= 1/6 = 1/6

Step-by-step explanation:

heart from a deck of cards :

In the context of ordinary maths questions the answer is so obvious as to almost not be worth mentioning. There are 52 cards in an ordinary deck and 13 of them have heart pips, so 13/52 = 1/4.

six from a dice :

There is a 1/6 chance of rolling a 6. There are only 6 sides on a die, and only 1 of them is 6, so there is a 1/6 chance of rolling a 6.

at the same time is:

13/15 + 1/6 = 31/30 = 1/30

Answer:

The answer should be -5/2

Step-by-step explanation:

To find the slope take two plots from the table:

(-2,6) and (0,1)

M= y2-y1 / x2-x1

M= 1-6 / 0--2=-5/2

The equation that has x = -11 as the solution is given by -

y = x + 11

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following equation that has a variable on both sides and x = -11 as a solution.

An equation of a straight line can be used to depict the problem given. We can write the equation as -

y = x + 11

Therefore, the equation that has x = -11 as the solution is given by -

y = x + 11

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The function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function

The function is  

f(x) =[tex]2(\frac{1}{2})^x[/tex]

The function is defined as the expression that represents the relationship between one variable and another variable.

The function is in the form of

f(x) = a × [tex]b^x[/tex]

Such functions are called exponential function

Here  

The value of a = 2

The value of b = 1/2

If the value of b > 1, the function is called exponential growth function.

If the value of b < 1, the function is called exponential decay function.

Here b < 1

Therefore it is exponential decay function

Hence, the function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function

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Answer: 25 cents i am sorry if this is wrong

Step-by-step explanation: 3 dimes are 30 cents plus 50 is 80 plus 35 is $1.15 so then when she removers 3 nickles she is getting rid of 15 cents which would leave $1.00 finally when you remove 75 cents you have 25 cents

The fraction of 1/6 is equivalent to this following decimal number:

0.166.

A fraction is represented by the division of a term x by a term y, as follows:

Fraction = x/y.

The terms that represent x and y are given as follows:

In this problem, the fraction is given as follows:

1/6.

1 is less than 6, hence the equivalent decimal can be obtained as follows:

0.10/6.

10 divided by 6 is one with a remainder by 4, hence 1.4/6 = 1.6667.

Thus the equivalent decimal representing the fraction 1/6 is given as follows:

1/6 = 0.1666.

The problem asks for which decimal number the fraction 1/6 is equivalent.

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Answer:

Her piggy bank can hold 720 pennies.

Step-by-step explanation:

1/2= 3/6, and 2/3=4/6, meaning the difference of 1/6=120 pennies. 120x6=720.

Answer:

67.5 (rounded down to 67, usually)

45/2 is 22.5 so that is for one hour

22.5 x 3 = 67.5

Answer:

add me on brainliest please

Step-by-step explanation:

65 is the answer

The width is 5 units.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

length = width + 1

let the width be x

length= x+ 1

So, area of rectangle= l x w

30 = x( x+ 1)

x² + x - 30=0

x² + 6x - 5x - 30=0

x( x+ 6) - 5(x +6)= 0

(x+ 6)( x- 5)= 0

x= -6 or 5

Hence, the width is 5 units.

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The probability that it has a hairline crack is 19/27.

Given that;

In a shipment of 54 vials, only 16 do not have hairline cracks.

Let shipment of 54 Vials;

x(s) = 54

Let,' A ' be the event that selects 16

x(A) = 16

P(A) = x(A) / x(s)

       = 16/54

But only 16 don't have hairline Crakes;

To solve a given case;

The probability that it has a hairline crack is:

P(A') = 1 - P(A)

       = 1- 16/54

P(A') = 19/27

Hence, the probability that it has a hairline crack is 19/27.

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The age of Marcus now is 20 years as 8 years ago Marcus was 12 years old.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical sentence with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example. x is a variable in the preceding example.

Let his age now be x.

x-8=12

x=20

Marcus is currently 20 years old, although he was 12 years old eight years ago.

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The altitude of the original pyramid is about 75.11 units

Given that,

Let h stand in for the original pyramid's height. The cut-off top then stands at a height of (h -22). The square of the scale factor for height is the scale factor for area, therefore we get :

Altitude of Pyramid means The slant height of a regular pyramid is its lateral face's height. Slant height in a non-rectangular pyramid is not specified. When determining the height (or altitude) of a regular, right pyramid, the vertex (the top) is used as the point perpendicular to the base. The base will intersect at this position.

(Height ratio)^2 = 1/2

((h -22)/h) ^ 2 = 1/2

(h-22) / h = 1/[tex]\sqrt{2}[/tex]

h-22 = h /[tex]\sqrt{2}[/tex]

h = 75.11 units

Consequently, the original pyramid's altitude is around 75.11 units.

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A system of linear inequalities that represents this scenario is given by:

p + s ≥ 10

5.50p + 3.50s ≤ 117

An inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

In order to write a system of linear inequalities to represent the scenario, we would assign variables to the cost of the beginner class and advanced class, and then translate the word problem into algebraic equation as follows:

Since Latisha cannot buy more than (≥) 10 vegetables, the inequality to represent this is as follows:

p + s ≥ 10

Since Latisha's budget cannot exceed (≤) $117, the inequality to represent this is as follows:

5.50p + 3.50s ≤ 117

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