Will give you 40 points if you can solve this in 20 minutes

​

a. (f + g) (0) = 0

b. (f/g) (3) = 2/3

This can be solved by function method.

Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.

(a) (f + g) (0) = .........

g(0) = 0, f(0) = 0

(f + g) (0) = f(0) + g(0)

(f + g) (0) = 0 + 0

(f + g) (0) = 0

(b)

(f/g) (3) = ............

f(3) = 2, g(1/3) = 1

(f/g) (3) = f(3) × g(1/3)

(f/g) (3) = 2 × (1/3)

(f/g) (3) = 2/3

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The monthly payment of a 30-year amount $450,000 mortgage with an interest rate of 4.2% is $2,071.09.

P = 450000

r = 0.042

n = 30

M = 450000 * 0.042/12 * (1 + 0.042/12)^360 / (1 + 0.042/12)^360-1

M = $2,071.09

a) There are 26 letters in the English alphabet so the number of six-letter passwords that can be formed from letters in the English alphabet if a letter can only be used once is 26P_6 = 26!/(26 - 6)! = 26!/(20!) = 300,750,000

b) There are 10 digits (0,1,2,3,4,5,6,7,8,9) so the number of passwords that can be formed if the digits 0, 1, 2, ..., 9 can be used is 10P_6 = 10!/(10 - 6)! = 10!/(4!) = 5040.

The monthly payment of a 30-year amount $450,000 mortgage with an interest rate of 4.2% is $2,071.09. There are 300,750,000 six-letter passwords that can be formed from letters in the English alphabet if a letter can only be used once, and there are 5040 pass-words that can be formed if the digits 0, 1, 2, ..., 9 can be used.

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Answer:

I'm sorry but your question is not clear. Can you please provide more context or clarify what you are asking?

Answer:

Yes

Step-by-step explanation:

no. of squares able to fit length=800/40=20

no. of squares able to fit breadth= 120/40=3

total no. of squares able to fit entire rectangle=20×3=60

cost of squares=60×4.50=270

Yes, he has enough money to buy all the paving stones.

For the given relation, the domain is  [0,70] and the range is   [0,500].

What is meant by relation?

In mathematics, a relation describes the connection between two distinct sets of data. If more than two non-empty sets are taken into consideration, the relationship between them will be determined if there is a connection between their items. The relationship between two or more sets of values is called a relation.

Assume that there are two sets of ordered pairs, x and y. If set x and set y are related, then the values of set x are referred to as the domain while the values of set y are referred to as the range.

W can also determine domain and range from graphs.

Also, note that the given graph is continuous so the domain and range values all all values in an interval.

The domain represents all the input values which are on the x-axis.

From the given graph, we can see that the domain values are in the interval  [0,70].

The range represents all output values which are on the y-axis.

From the graph, the range values are in the interval [0,500].

Therefore for the given relation, the domain is  [0,70] and the range is   [0,500].

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Answer:

120-x

Step-by-step explanation:

For me in class there were 6 parts to this problem and this problem is the same in my class so I will add all the answers

So for how many grams of 25% syrup it will be 120-x because the some amount + x = 120 grams of 15% syrup

so 120-x = the some amount of syrup.

This will be the answer for the problem you were asking for

If you have 6 parts keep scrolling since I will supply some more answers

Next part: How much pure sugar is in the 25% syrup?

For the amount of pure sugar there is in the 25% syrup

that will equal 0.25(120-x) = 30-0.25x

Next: How much sugar is in 120 grams of 15% sugar syrup?

10% of 120 is 12

5% = 12/2 = 6

12+6 = 18

Now the earlier stuff from the problem will come in handy

use the previous answers to write an equation

0.25(120-x)+0.10x=18

= 30-0.25x+0.10x=18

30 -0.15x=18

Now the final part to solve the equation and find the 10% solution and the 25% solution

-0.15x=18-30 = -12

-0.15x=-12

x= -12/-0.15

x=80

the problems not done yet though

we need to find the 25% solution

25% solution = 120-x and x = 80

120-80 = 40

The 10% solution is 80 grams and the 25% solution is 40 grams

Answer:

Step-by-step explanation:

5+2/3-3-2/3

5+93439535309573092

You need to order 2 36" bulbs and 4 24" bulbs in order to keep twenty of each size in stock.

The stock is a type of security that represents ownership in a company. It is a financial asset that can be traded, and the price of the stock is determined by the supply and demand of the market. When a company issues stock, the stockholders gain a share of the company’s ownership.

36" bulbs:

First storage closet: 5 boxes with 2 in each box = 10

Second storage closet: 3 boxes with 4 in each box = 12

Total = 10 + 12 = 22

Need to order = 20 - 22 = 2

24" bulbs:

First storage closet: 4 boxes with 4 in each box = 16

Total = 16

Need to order = 20 - 16 = 4  

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In this configuration, the number of circles that can be packed is already at its maximum of 10,000.

What is Equilateral triangle?

All sides of an equilateral triangle are the same length. That is, all of the triangle's angles will be congruent.

It is not possible to add more circles in this configuration because the centers of the tangent circles already form an equilateral triangle, which is the most efficient way to pack circles.

In this configuration, the number of circles that can be packed is already at its maximum of 10,000.

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Answer: Let's call the number of pages printed "x". After printing x pages, the total cost for the Hewlett-Packard printer will be:

$200 + $0.03 * x

And the total cost for the Brother printer will be:

$240 + $0.01 * x

We want to find the number of pages "x" such that the cost of the two printers is the same, i.e., when:

$200 + $0.03 * x = $240 + $0.01 * x

We can isolate x by subtracting $240 from both sides and subtracting $0.01 * x from both sides:

$200 - $240 + $0.03 * x - $0.01 * x = 0

$-40 + $0.02 * x = 0

$0.02 * x = 40

x = 2000

So, the number of pages that need to be printed for the cost of the two printers to be the same is 2000 pages.

Step-by-step explanation:

Answer: 25%

Step-by-step explanation:

Divide 17/68 = .25

Move decimal 2 places over = 25%

The linear Equation in the form of p(n)=mn+b is p(n) = -0.005n + 999.85.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

In particular, historical data shows that 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $20 .

p = price

n = number of shirts

m = slope of the line   (note, the more shirts, the lower the price, so we know it's going to be negative)

b = y intercept

so, the slope is

= (20- 30)/ (3000 - 1000)

= -10 / 2000

= -0.005

and, the equation is

p - 1000 = -0.005 ( n- 30)

p- 1000 = -0.005n + 0.15

p(n) = -0.005n + 999.85

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Answer:

Step-by-step explanation:

The medium size gets the most ice cream per dollar.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given three types of soft-serve ice cream,

A; small,

ice cream for $1.96 = 3 ounces

ice cream for $1 = 3/1.96 = 1.53 ounce per dollar

B; medium,

1 ounce of icecream cost = $0.64

ice cream for $1 = 1/0.64

ice cream for $1 = 1.5625 ounce per dollar

C: Large

ice cream for $6.85 = 10 ounces

ice cream for $1 = 10/6.85 = 1.459 ounce per dollar

Hence medium size gets the most ice cream per dollar.

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The value of m∠C in  the triangle  is 42.77°

The sine rule is a mathematical formula used in trigonometry to find the length of a side or the size of an angle in a triangle when two sides and one of the angles opposite to those sides are known. It states that:

a/sin A = b/sin B = c/sin C

Where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the angles opposite to those sides.

m∠A = 47°, a = 28, c = 26.

a/sin A = c/sin C

28/sin 47° = 26/sin C

sin C = (26 sin 47°)/28

sin C = 0.6791

C = arcsin(0.6791)

C = 42.77°

Thus, m∠C = 42.77°

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Therefore , the solution of the given problem of equation comes out to be value of b = 0 , as it is parallel to y axis.

The identical symbol (=) is used in arithmetic equations to signify the equality of two statements. It is shown that it is possible to evaluate various numerical factors using mathematical techniques, which have served as manifestations of reality. In actuality, even though the solution is y + 6 = 12, the equal sign divides the figure 12 into two distinct parts. How many characters are also present along either end of such a character can be calculated. Conflicting sign readings are common.

Here,

Given :

=> equation  y = 15x + b

Comparing to y = mx+ b

Where b is said to be intercept.

So , value of b = 0 , as it is parallel to y axis.

Therefore , the solution of the given problem of equation comes out to be value of b = 0 , as it is parallel to y axis.

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The minimum point of a function f(x) is obtained as follows:

There are two requirements such that a value of x = a is a minimum point of a function f(x):

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Answer:

Part A: Yes, there is a correlation between the number of employees in the plant and the number of products produced monthly. This is because as the number of employees increases, the number of products produced also increases in a linear fashion.

Part B: The function that best fits this data is y = 8x + 120, where x is the number of employees and y is the number of products.

Part C: The slope of this plot indicates that for every additional employee, there is an increase of 8 products produced monthly. The y-intercept of this plot is 120, which is the number of products that would be produced if there were no employees.

we can see that Rule 2 has a higher probability of accepting a shipment containing 20% defectives. Therefore, Rule 2 has a smaller probability of accepting a shipment containing 20% defectives.

To compare the probabilities of acceptance of a shipment containing 20% defectives for the two rules, we can calculate the probabilities for both rules and compare the results.

For Rule 1, the probability of accepting a shipment containing 20% defectives is given by the probability of having 0 defectives in a sample of 10 components. This can be calculated as

P(Accept | 20% defectives) = (0.8)¹⁰

= 0.107374

For Rule 2, the probability of accepting a shipment containing 20% defectives is given by the probability of having 0 or 1 defectives in a sample of 20 components. This can be calculated as:

P(Accept | 20% defectives) = (0.8)²⁰ + ²⁰C₁ * (0.8)¹⁹ * (0.2)

= 0.276

Comparing the two probabilities, we can see that Rule 2 has a higher probability of accepting a shipment containing 20% defectives. Therefore, Rule 2 has a smaller probability of accepting a shipment containing 20% defectives.

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Refer to the attached images.

Answer:true

61.5 km = 61.5 x 1000 =61.500 m

The fifth letter, Diego will type, is 'a'.

An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).

Given:

Han types the letters a, s, d, f.

And repeats the over and over.

That means,

a, s, d, f, a, s, d, f, a, s, d, f, ....

Here, the fifth letter is 'a'.

So, the Diego will type 'a'.

Hence, the fifth letter is 'a'.

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Answer:

The equation to calculate the balance in the account after "x" months would be: y = 100 + 25x

And after 6 months, Alexa would have $250 in his retirement account, and after 12 months, he would have $400 in his account.

Step-by-step explanation:

Let's call the balance in Alexa's retirement account after "x" months "y".

The equation to calculate the balance in the account after "x" months would be:

y = 100 + 25x

After 6 months, Alexa would have added 6 * $25 = $150 to the original balance of $100, so the balance would be:

y = 100 + 25 * 6 = 100 + 150 = $250

After 12 months, Alexa would have added 12 * $25 = $300 to the original balance of $100, so the balance would be:

y = 100 + 25 * 12 = 100 + 300 = $400

So, after 6 months, Alexa would have $250 in his retirement account, and after 12 months, he would have $400 in his account.

PART A) The height of the base is 10cm

PART B) Aproximate amount of cardboard to make the candy box is 860cm. You add all of the totals from each side to get the grand total of 860cm.

Answer:

y = 36

Step-by-step explanation:

Because the problem says y is proportional to the square root of x, we can assume that it is directly proportional.

The general formula for direct proportionality is

[tex]y=kx[/tex], where k is the constant of proportionality.

Taking into account the square root of x, we can use the following formula to find k by plugging in x and y:

[tex]y=k\sqrt{x}\\ 21=k\sqrt{49}\\ 21=7k\\3=k[/tex]

Since we found k, we can now use this value and the x we're given for the second part of the problem to find y:

[tex]y=3\sqrt{x} \\y=3\sqrt{144}\\ y=3*12\\y=36[/tex]

The area of the shaded portion of the given figure is 84 sq. units.

What is meant by area?

The size of a region on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a structure or planar lamina.

From the figure, we can conclude that,

Area of the shaded portion = Area of the square - Area of the four congruent parallelograms.

Now we have to find the area of square and parallelograms separately.

Area of square

Side length l = 12

Area = l *l = 12 * 12 = 144 sq. units

Area of parallelograms

Base b = 5

Height h = 3

Area of 1 parallelogram = b.h = 5 * 3 = 15 sq. units

Since all the parallelograms are congruent,

Area of all 4 parallelograms = 15 * 4 = 60 sq. units

Hence the area of the shaded portion of the given figure = 144 - 60

                                                                                          = 84 sq. units

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the average time of 27 minutes is not an accurate representation of the friends' actual times, so the example describes neither accuracy nor precision.

Precision refers to how close multiple measurements are to each other. In this example, the three friends' times are all close to each other (20 minutes, 21 minutes, and 21 minutes), so the measurements are precise.

Accuracy refers to how close a measurement is to the true or correct value. In this example, the average time of the three friends running a 5K is 27 minutes, but the actual average time should be 20.33 minutes (20 + 21 + 21 / 3). So, the measurement is not accurate.

However, the average time of 27 minutes is not an accurate representation of the friends' actual times, so the example describes neither accuracy nor precision.

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The equation of a line perpendicular to line y = 1/5x-2 in slope-intercept form that contains point (-3, 1) is y = -5x - 14.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided, an equation of the first line WX is given by;

y = x/5 - 2

Therefore, slope (m) = 1/5

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/5 × m₂ = -1

m₂ = -5.

At point (-3, 1), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -5(x - (-3))

y - 1 = -5(x + 3)

y = -5x - 15 + 1

y = -5x - 14

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Therefore, the solutions to the equation are (0, 0), (1, 1), (-1, 1), (2, 4), (-2, 4), (3, 9), and (-3, 9).

In arithmetic equations, the exact symbol (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.

Here,

We can plug in some arbitrary values for y to find the corresponding values of x:

y x

0 0

1 1

-1 1

2 4

-2 4

3 9

-3 9

Therefore, the solutions to the equation are (0, 0), (1, 1), (-1, 1), (2, 4), (-2, 4), (3, 9), and (-3, 9).

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