Given f(x) = 8 - 5x, find f(2).

Answer:124.38

Step-by-step explanation:

103.65*.20=20.73 103.65+20.73=124.38

The required unit rate for the dollars per class is 16 dollars per class,

Given that,
The "constant of proportionality" between to cost and the number of classes is 16. The unit rate for dollars per class is to be determined.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
Let, y be the dollars is directly proportional to the x classes,
According to the question,
y = kx
k = 16
y = 16x
Now,
y/x = 16 dollars per class

Thus, the required unit rate for the dollars per class is 16 dollars per class,

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The number 490 is 72% of the number 680.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that 490 is some percentage of the number 680.

The percentage of 490 to the number 680 will be calculated as,

680 x (x / 100) = 490

x = (490 x 100)/680

x = 72%

Therefore, the number 490 is 72% of the number 680.

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The absolute maximum is 1.29, which occurs at x= 9

What is absolute extrema?

An absolute extremum  of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.

Main body:

Given =

f(x) = [tex](x^{2} -64)^{1/11[/tex]

f' (x) = derivative of function f(x)

f'(x) = 1/11 . 2x[tex](x^{2} -64)^{-10/11[/tex]

   =  2x/11[tex](x^{2} -64)^{-10/11[/tex]

putting f'(x) = 0

2x/11[tex](x^{2} -64)^{-10/11[/tex]  = 0

       [tex](x^{2} -64)^{-10/11[/tex]  = 0

         [tex]x^{2} -64[/tex]            = 0

x² = 64

x = ±8

We are given interval [-8,9].

Hence, calculating f(x) at -8, 8, 9.

f(-8) =  0

f(8) = 0

f(9) = [tex]17^{1/11[/tex]

     = 1.29

Hence, absolute maximum value is 1.29 at x=9.

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The equally likely events are

The probability that all three children are male

0.875.

the probability that at least one child is female.

0.875.

(a) The equally likely events for the gender of the three children, from oldest to youngest, are:

(b) The probability that all three children are male is (0.5)^3 = 0.125.

The probability that at least one child is female is the complement of the event "all three children are male," which means it is 1 - 0.125 = 0.875.

In conclusion, The probability that at least one child is female is 1 - (0.5)^3 = 0.875.

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In that order. ao(t) is always the function is [tex]$$m_1=A-2 I $$[/tex].

What is function ?

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

given: [tex]$\quad d_1=4 \quad$[/tex] and [tex]$A_2=6$[/tex]

[tex]$$m_0=\Sigma=\left[\begin{array}{cc}1 & 0 \\0 & 1\end{array}\right]$$[/tex]

By putzes method

[tex]$$\text { matrix } m_1=A-N_1 p_0=A-d_1 m_0$$[/tex]

here [tex]$r_1=2, m_0=I$[/tex]

[tex]$$m_1=A-2 I $$[/tex]

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Answer:

it also decreased by 3 times.

hope this work out.

Answer:

D

Step-by-step explanation:

x=9 and y=4 is given in the graph, this makes the answer between B and D

Since y=-⅔x+10 and y=x-5, 4=-⅔(9)+10 and 4=9-5

So the answer is D

Answer:

34 in base 2 = 10011

Step-by-step explanation:

34 written in base 2 or in binary form is 10011 . 34 written in base 10 or decimal form is 19 .

Given, Convert 34 in base 5 to base 2

Firstly convert base 5 to base 10 .

34(base 5) = [tex]3\times 5 ^1 + 4\times 5^0[/tex]

34(base 5) = 19(base 10)

Convert base 10 to base 2 .

To convert 19 to binary, divide it by 2 repeatedly and note the remainders:

19 ÷ 2 = 9, remainder 1

9 ÷ 2 = 4, remainder 1

4 ÷ 2 = 2, remainder 0

2 ÷ 2 = 1, remainder 0

Reading the remainders from bottom to top including the last 1.

10011.

So, 19 in binary is 10011.

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Good now whats the question?

1(a) The value of f(2) in the fuction f(x) = x³+7x²-36 0, 1 (b) The factors of the function f(x) =  (x-2)(x+3)(x+6) 2 The initial amount that must be invested is $53263.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

(a) To calculate the f(2), we substitute 2 into the function below.

(b) To factor f(x), we need to look for the zeros of f(x). The zeros of f(x) are

Putting them in polynomial form

(2) To calculate the amount he would invest initially to have the neccessary amount in 4 years, we use the formula below.

Formula:

Where:

Make P the subject of the equation

From the question,

Given:

Substitute these values into equation 2

Hence, 1(a) The value of f(2) = 0, 1 (b) The factors of f(x) =  (x-2)(x+3)(x+6) 2 The initial amount that must be invested is $53263.

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Thus, 18 weeks are needed for the population of beetles to reach 183. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will take place.

The number of possible outcomes is divided by the total of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event but by probability that it won't.

For instance, how many heads would appear if you throw a coin 100 times? Assuming a probability of 1/2, we can anticipate 50 heads. However, when we actually attempt it, we might just get 48 heads, 55 heads, or anything else, but most of the time it will be close to 50.

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The curve for the vector equation r(t) = <t, -t, 2t>, is |r(t)| =  (√6)t.

Find the curve in the attachment

A vector is a physical quantity that has both magnitude and direction

A vector equation is a linear combination of vector quantities

A curve is a path which an object follows.

Since we are given the vector equation r(t) = <t, -t, 2t>, to sketch the curve of the vector equation, we need to know the magnitude of the vector.

The magnitude of a vector r = <a, b, c> is |r| = √(a² + b² + c²)

So, to sketch the vector equation, since r(t) = <t, -t, 2t>, comapring bothnequations,

So, the magnitude of r(t) =  √(a² + b² + c²)

=  √(t² + (-t)² + (2t)²)

= √(t² + t² + 4t²)

= √(6t²)

= (√6)t

Since |r(t)| =  (√6)t, we sketch the curve for this equation

Find the curve in the attachment

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The smaller eigenvalue is -4 with multiplicity 2 and larger eigenvalue is 6 has multiplicity 1

If A is a square matrix of order n x n and v is a non-zero column vector of order n x 1 such that Av = λv , then the scalar (real number) λ is called an eigenvalue of the matrix A that corresponds to the eigenvector v.

According to the question,

We have a 3 x 3 matrix that has only two real distinct eigenvalues

Let two distinct eigen values be a and b

Its given that tr(A) = - 2

Det(A) = 96

If we add all the eigen values of a matrix it gives us trace of this and product of eigen values result to the determinant

Therefore , 2a + b = -2 --------(1)

a²b = 96 --------(2)

Using substitution method for solving these equations

=> b = -2 - 2a

Substituting the value of b in equation (2)

=> a²( -2 -2a) = 96

=> -2a² - 2a³ = 96

=> a²(1 + a) + 48 = 0

=> a³ + a² + 48 =0

Solving the cubic equation

a = -4 , 1.5-3i , 1.5+3i (but eigen values are only real)

therefore , a = -4

b = -2 -2(-4)

=> -2+8

=> 6

hence, the eigen values = -4 and 6

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a) The percentage of $680 which is $490 is 72.06%.

b) When a price is reduced from $680 to $490, the percentage decrease is 27.94%.

The percentage is the ratio of a value to another.

Percentages are depicted as fractional values expressed over 100.

To determine percentages, the smaller value is expressed as the numerator, while the more considerable value is described as the denominator.

The result is then multiplied by 100.

For instance:

$490 of $680 is 72.06% ($490/$680 x 100)

Price reduction from $680 to $490, the percentage decrease is computed as the difference between $680 and $490 divided by $680, multiplied by 100.

Thus, the percentage decrease in price from $680 to $490 is 27.94%, showing that the original price of the good or service has been reduced from 100% to 72.06%.

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Answer:

-80x + 28y -56

4(-20x + 7y -14)

Step-by-step explanation:

The first answer is distributing the 8 through the whole expression.  The second answer is when you factor out a 4.

Answer: There is a 54% chance that you will not choose one of those cards.

Step-by-step explanation: There are 4 of ever card in a deck.

3, 4, 5, 6, 7, and 8 are 6 different types of cards

6 x 4 = 24

24 divided by 52 ( the total cards ) = .46

So there is a 54% chance that you will not choose one of those cards.

We are told that 6 is two-fifths of the brownies. So we can figure it out as such:

[tex]\frac{6}{x} = \frac{2}{5}[/tex]

Cross multiply

6 * 5 = x * 2

30 = 2x

Divide both sides of the equal sign by 2 to get x by itself

[tex]\frac{30}{2} =\frac{2x}{2}[/tex]

15 = x

15/5 = 3. Every third piece is 1/5 of the pan.

The statements which best summarizes the pattern of causality captured by the graph attached are: A change in E causes a shift of the budget constraint; and, the relationship between S and P is not a causal relationship.

Causality means that there is a clear cause-effect relationship between two variables. By using a controlled study is the most effective way of establishing causality among variables. In a controlled study, the sample or population is split in two, with both groups being comparable in almost every way. Then, the two groups receive different treatments, and the outcomes of each group are assessed.

Although part of your question is missing, you might be referring to this full question: Which of the following statements best summarizes the pattern of causality captured by the graph above? Check all that apply. (Graph is attached.)

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Answer:

-25

Step-by-step explanation:

Therefore, the probability that a woman will give birth to two boys is only one in three, whereas the probability that a man will do so is one in two.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

The woman may have at least one boy in the three following ways: 1) older boy, younger girl; 2) older girl younger boy; 3) older boy, younger boy.

But the man's children may be distributed in only two ways: 1) older boy, younger girl; or 2) older boy, younger boy.

So the chances are only 1 out of 3 that the woman has two boys, but the chances are 1 out of 2 that the man has two boys.

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Therefore, the probability of the first case : 94.5% and second case:9.7%

the likelihood that an event will take place. The proportion of feasible outcomes to outcomes in an exhaustive set of equally likely outcomes that result in a particular event. a field of mathematics that focuses on the investigation of probability.

Here,

Thus, the probabilities of following cases comes out to be:

1) The odds that either the pedestrian or the driver weren't are

=>(246+603+83)*100/986

=>(932/986)*100 =94.5%

2) The likelihood that both incidents involved inebriated pedestrians is equal to

=>(305/978)*(304/977)*100 = 9.7%

Therefore, the probability of the first case : 94.5% and second case:9.7%

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Step-by-step explanation:

since AD is an altitude (height) of ABC, the angle at D must be 90° (that is the definition of an altitude or height).

so,

90 = x² + 6x + 18

72 = x² + 6x

0 = x² + 6x - 72

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (-6 ± sqrt(6² - 4×1×-72))/(2×1) =

= (-6 ± sqrt(36 + 288))/2 = (-6 ± sqrt(324))/2 =

= (-6 ± 18)/2 = -3 ± 9

x1 = -3 + 9 = 6

x2 = -3 - 9 = -12

so, the 2 solutions are

x = 6

x = -12

Answer:

18 jumps

Step-by-step explanation:

5*10 = 50cm

50/100 = 0.5m (metre conversion)

9/0.5 = 18

Answer: The variable

Hope this helps :)

Step-by-step explanation:

The length of the diagonal of the right triangle is 21.2 units.

The game is played on a square court divided into four smaller squares that meet at the centre.

A right triangle QTS is formed, where QTS is 45°. Using trigonometric function, the length of the diagonal can be found as follows:

Therefore,

sin 45 = opposite / hypotenuse

opposite side = 15 feet

hypotenuse side = 15 feet

The hypotenuse side is the diagonal.

Hence,

sin 45° = 15 / h

cross multiply

h = 15 / sin 45

h = 15 / 0.70710678118

h = 21.2132034356

h = 21.2 units

Therefore,

length of diagonal = 21.2 units

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Total amount payable including sales tax and tip =  $68.12

A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.

Given:

Bill at dinner was before tax and tip = $58.24

Sales tax = 6%

Tip = 18%

As per the question:

first, we will calculate the amount payable after adding tax.

The amount payable after adding sales tax = bill + 6% sales tax of the bill

The amount payable after adding sales tax = 58.24 + [tex]\frac{6}{100} 58.24[/tex]

Amount payable after adding sales tax = A = $57.73

Now we will calculate the total amount payable after adding the tip.

Total amount payable = A + 18% of A

Total amount payable = $57.73 + 18% of $57.73

Total amount payable =  57.73 + 10.40

Total amount payable including sales tax and tip =  $68.12

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Total amount payable including sales tax and tip =  $68.12

A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.

Given:

Bill at dinner was before tax and tip = $58.24

Sales tax = 6%

Tip = 18%

As per the question:

first, we will calculate the amount payable after adding tax.

The amount payable after adding sales tax = bill + 6% sales tax of the bill

The amount payable after adding sales tax = 58.24 +

Amount payable after adding sales tax = A = $57.73

Now we will calculate the total amount payable after adding the tip.

Total amount payable = A + 18% of A

Total amount payable = $57.73 + 18% of $57.73

Total amount payable =  57.73 + 10.40

Total amount payable including sales tax and tip =  $68.12

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Part 1:- The answers are 12, 30, 56, 90

30, 35, 40, 45

2, 3, 4, 5

Part 2:-The correct answer is (D) -23

Part 3:-The surface area for the rectangular prism is 128 square feet.

What is a mathematical expression?

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

part 1:-

Solving expression 1:-

for x=2

[tex]4 {x}^{2} - 2x = 4 \times {2}^{2} - 2 \times 2[/tex]

=4×4 - 4

=16 - 4

=12

for x=3

[tex]4 {x}^{2} - 2x = 4 \times {3}^{2} - 2 \times 3[/tex]

= 4 × 9 - 6

= 36 - 6

= 30

for x=4

[tex]4 {x}^{2} - 2x = 4 \times {4}^{2} - 2 \times 4[/tex]

= 4 × 16 - 8

= 64 - 8

= 56

for x=5

[tex]4 {x}^{2} - 2x = 4 \times {5}^{2} - 2 \times 5[/tex]

= 4×25 - 10

= 100 - 10

= 90

solving expression 2:-

for x = 2

[tex]5x + 20 = 5 \times 2 + 20[/tex]

= 10 + 20

= 30

for x = 3

[tex]5x + 20 = 5 \times 3+ 20[/tex]

= 15 + 20

= 35

for x = 4

[tex]5x + 20 = 5 \times 4 + 20[/tex]

= 20 + 20

= 40

for x = 5

[tex]5x + 20 = 5 \times 5 + 20[/tex]

= 25 + 20

= 45

solving expression 3:-

for x=2

[tex] \frac{8x}{2} - 3x = \frac{8 \times 2}{2} - 3 \times 2[/tex]

= 8 - 6

= 2

for x=3

[tex] \frac{8x}{2} - 3x = \frac{8 \times 3}{2} - 3 \times 3[/tex]

= 12 - 9

= 3

for x=4

[tex] \frac{8x}{2} - 3x = \frac{8 \times 4}{2} - 3 \times 4[/tex]

= 16 - 12

= 4

for x= 5

[tex] \frac{8x}{2} - 3x = \frac{8 \times 5}{2} - 3 \times 5[/tex]

= 30 - 15

= 15

Hence the answers are, 12, 30, 56, 90

30 35, 40, 45

2, 3, 4, 5

part 2:-

Given,

4n - 5r;

for n=-2 and r=3

4n - 5r = 4 × (-2) - 5 × 3

= -8 - 15

= -23

Hence the answer is (D) -23

Part 3:-

Given,

The surface area for a rectangular prism with a square base is given the expression 2 s²+4 s h

s = 4 feet

h = 6 feet

then,

2 s²+4 s h = 2×4²+4×4×6

= 2×16+96

= 32+96

= 128

Hence the answer is 128 square feet.

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20 is the system's transfer function. A differential equation is a mathematical formula that includes one or more terms

Explanation:

4 +2 + 6 + 8 = 20.

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