If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
A. 1 minute
B. 5 minutes
C. 10 minutes
D. 15 minutes
E. 100 minutes

Slope 1 is the blue line.

Slope 2 is the yellow line.

Slope 1/5 is the black line.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Take two coordinates from each line.

Yellow line.

(0, 3) and (1, 5)

m = (5 - 3) / (1 - 0) = 2/1 = 2

Slope = 2

Blue line.

(0, 8) and (1, 9)

m = (9 - 8) / (1 - 0) = 1/1 = 1

Slope = 1

Black line.

(0, 5) and (5, 6)

m = (6 - 5)/(5 - 0) = 1/5

Slope = 1/5

Thus,

The blue line has slope 1.

The yellow line has slope 2.

The black line has slope 1/5.

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Answer:

47/8 or 5 7/8

Step-by-step explanation:

(11 3/4) /2 = 47/8 or 5 7/8

The division of  [tex]11\frac{3}{4}[/tex]  by 2 is equal to fraction 47/8.

To divide the mixed number [tex]11\frac{3}{4}[/tex] by 2:

we can convert the mixed number to an improper fraction and then perform the division.

[tex]11\frac{3}{4}[/tex] can be expressed as the improper fraction:

[tex]11\frac{3}{4}[/tex]  = (11 × 4 + 3) / 4 = 47/4

Now, we can divide 47/4 by 2:

(47/4) ÷ 2

= (47/4) × (1/2)

= (47 × 1) / (4 × 2)

= 47/8

Therefore, the division of  [tex]11\frac{3}{4}[/tex]  by 2 is equal to  47/8.

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Answer: 4.5

Step-by-step explanation: 18b=4

18/4=4.5

4/4=1

4.5/1=4.5

Answer:

the answer is C

Step-by-step explanation:

this is because it passes the vertical and horizontal line test

Answer:

C

Step-by-step explanation:

Claira must make fifteen payments of 334.44 each in equal amounts toward her new car, which she purchased for 5700.

For $5,700, Claire gets a brand-new vehicle. She made a 12% down payment. We must ascertain the fifteen equal monthly payments.

to find out the 15 equal monthly payment we shall use the formula,

for monthly installments =   [tex]\frac{P(1-D)}{m}[/tex]    

Where P stands for principal amount, D for down payment and m use for month.

we have P=5700

D=12%=0.12

m=15

Therefore, monthly payment = [tex]\frac{5700(1-0.12)}{15}[/tex]

=[tex]\frac{5700(0.88)}{15}[/tex][tex]= \frac{5016}{15} =334.44[/tex]

Thus, she has to make 15 payments of ∈ 344.44. for her new purchased car.

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The height of the given tree to the nearest foot is; 21 ft

If Carlos, mirror, and bottom of tree are points on the ground all on one line, then it means that the two right triangle are these:

LEFT Triangle: y and 31 as the legs and unknown hypotenuse.

RIGHT Triangle: 6 and 8.7 as legs and unknown hypotenuse.

The two angles at the mirror are of same measure; that is, the 31 and the hypotenuse of LEFT triangle makes same angle measure as the 8.7 and the hypotenuse of the RIGHT triangle.

Thus, using concept of similar triangles, we can say that;

y/31 = 6/8.7

y = (31 * 6)/8.7

y = 21 ft

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The inverse of FX =- 3x is  FX = (1/3)x.

The inverse of FX = -3x is a mathematical equation that finds the inverse of a given function.

In this case, the inverse of the given equation is FX = (1/3)x.

The inverse of an equation is the equation that, when solved, produces the same result as the original equation. In this case, when using the inverse equation, the x-value is multiplied by 1/3 to find the corresponding y-value.

The inverse of the equation FX = -3x is the equation x = 1/3Fx.

In mathematics, inverse meaning is the concept of reversing a given equation or operation.

This can be done by switching the terms and operations in the equation, so that the result of the equation is the opposite of what it was before.

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Answer:

  see attached

Step-by-step explanation:

You want to use q=4 to show q×q³ = q⁴.

The attachment shows your calculator can help with this. It will compute and display the powers of values without requiring the intermediate calculations.

  4 × 4³ = 4 × 64 = 256

 4⁴ = 256 . . . . . . equivalent to 4 × 4³

An exponent signifies repeated multiplication in the same way a coefficient signifies repeated addition.

  4 × 4³ = 4 × (4·4·4) = 4·4·4·4 . . . . . using the associative property of multiplication

  4⁴ = 4·4·4·4 . . . . . . . equivalent to 4 × 4³

__

Additional comment

In literal terms, ...

  q×q³ = q·q·q·q = q⁴

In the given question, we have to find the solution to this system of linear equations 2x+3y=3 and 7x-3y=24.

The given equations are:

2x+3y=3...…….(1)

7x-3y=24...…….(2)

To solve these equations we add equation 1 and 2,

2x+3y+7x-3y = 3+24

9x = 27

Divide by 9 on both side, we get

x = 3

Now putting the value of x in equation 1, we get

2(3) + 3y = 3

6 + 3y = 3

Subtract 6 on both side, we get

3y = -3

Divide by 3 on both side, we get

y = -1

The solution to this system of linear equations 2x+3y=3 and 7x-3y=24 is (3, -1).

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The complete question is:

What is the solution to this system of linear equations 2x+3y=3 and 7x-3y=24?

Answer:

108

Step-by-step explanation:

When multiplying fractions, you first start with the two fractions you want to multiply. You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together.

bye im tyler

For linear inequalities when multiplying by (0,0) , it does not exist.

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.

Given statement,

For linear inequalities when multiplying by (0,0) , It is always greater than sign.

Let the inequality be

ax > by

ax - by > 0

Multiplying with (0,0)

(ax - by)(0x + 0y) > 0

(ax - by).0 > 0

0 = 0

LHS = RHS

there is no inequality remained.

Hence, when multiplying by (0,0) there is no existence of inequality.

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After using inverse function the answers are

a)  f(2) = [tex]\frac{5}{2}[/tex]

b)   [tex]f^{-1}(x)[/tex] = 2x-3.

c) [tex]f^{-1}(12)[/tex] = 21.

What is inverse function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

The output of a function is returned by the inverse function, which also returns the initial value.

Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.

Here the given function f(x) = [tex]\frac{x+3}{2}[/tex]

a) Put x= 2 into f(x) then

=> f(2) = [tex]\frac{2+3}{2}[/tex]

=> f(2) = [tex]\frac{5}{2}[/tex]

b) Now to find inverse function , take y=f(x) then

=> y = f(x)

=> y = [tex]\frac{x+3}{2}[/tex]

Now interchange x and y and solve for y then,

=> x = [tex]\frac{y+3}{2}[/tex]

=> 2x= y+3

=> y = 2x-3

Then y = [tex]f^{-1}(x)[/tex]  

=>  [tex]f^{-1}(x)[/tex] = 2x-3.

c) Now put x=12 into  [tex]f^{-1}(x)[/tex]  = 2x-3 then

=>[tex]f^{-1}(12)[/tex] = 2(12)-3 = 24-3 = 21.

=>[tex]f^{-1}(12)[/tex] = 21.

Hence the answers are ,

a)  f(2) = [tex]\frac{5}{2}[/tex]

b)   [tex]f^{-1}(x)[/tex] = 2x-3.

c) [tex]f^{-1}(12)[/tex] = 21.

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The likelihood of precisely x successes on n further trials in an experiment with two possible outcomes is known as a binomial probability.

The possibility that a variable would take one of two independent values under a particular set of parameters or assumptions is expressed by the statistical distribution known as the binomial distribution.

The utilization of this distribution pattern in statistics has ramifications for finance and other areas as well. It can help banks decide how much money to lend and how much cash they should hold in reserve as well as the risk that a specific borrower will default. In the insurance sector, it's also employed to calculate policy premiums and evaluate risk.

The likelihood of precisely x successes on n further trials in an experiment with two possible outcomes is known as a binomial probability (commonly called a binomial experiment).

Yes, this is an example of a binomial situation. The probability of a specific number of success outcomes from repeated or numerous incidents can be determined using this method.

Success {Event P} small fish, with prob = 30% = 0.3 .

Failure {Event Q} large fish, with prob = 70% = 0.7

Number of trials = 20.  Let r be number of small fishes out of 20 fishes.

Binomial probability = [tex]$$N c r . (P)^r . (Q)^ {(n-r)[/tex]

P( 5 small fish out of 20) = 20c5  [tex](0.30)^5 (0.70)^{15[/tex]

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92 inches² paper would be needed to wrap the prism completely.

The total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.

Given here: The dimensions of the rectangular prism are 8,3,2 in inches.

Total surface area of a rectangular prism = 2(lb + bh + lh)

Thus TSA= 2(24+16+6)

               =92 inches²

Hence, 92 inches² paper would be needed to wrap the prism completely.

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Finding the roots of a quadratic equation involves the process of factorization. When factoring quadratic equations, the original quadratic expression is changed into the product of two linear factors.

We obtain the quadratic equation when a quadratic polynomial equates to 0. Ax2 + bx + c = 0 is the quadratic equation if ax2 + bx + c is the quadratic polynomial, and a, b, and c are real values such that a 0.

It has two roots, which is the degree of the second quadratic equation. Learn how to factor quadratic equations in this article, which also includes examples and solutions.

Quadratic equations can be factored using a variety of techniques. They are as follows:

1. Dividing a middle word

2. Utilizing a formula

3. Using the quadratic equation

4. Making use of algebraic identities

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The exponential function that grows the least quickly is given as follows:

f(x).

The general format of an exponential function is defined as follows:

y = ab^x.

In which:

To grow the least quickly, we want a function with the lowest rate of change, which is equivalent to the lowest value of b.

The value of b for each function in this problem is given as follows:

Hence function f(x) grows the least quickly, and this means that the correct option is given by the first option.

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h(t) and h-1(t) are inverses of each other.

Inverse is a function that is severs to undo another to the function.thag is produces y,then putting y and into the inverse of f of the produces the output x.

To find the inverse of h(t), we need to first solve for t in the equation h(t) = 16t^2 + 144. This can be done by finding the roots of the equation, which can be done by setting the equation equal to zero and using the quadratic formula,

t = ±√(h(t) - 144)/16

Since h(t) is a quadratic function, the inverse of h(t), h-1(t) will also be a quadratic function. Therefore, h-1(t) can be written as:

h-1(t) = ±√(t - 144)/16

To show that h(t) and h-1(t) are inverses, we can plug in a known value, such as t = 10, and check that the results of both equations are equal.

h(10) = 16(10)^2 + 144 = 272

h-1(272) = ±√(272 - 144)/16 = ±√(128)/16 = 10

Since the results of both equations are equal, it is clear that h(t) and h-1(t) are inverses of each other.

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If R is an odd integer, the next two consecutive odd integers are R+2 and R+4. Option D

You should understand that an odd number is a number that is not divisible by two without remember.  Examples of odd numbers are 1,3,5,7,9 etc.  The difference between two consecutive odd numbers is two.

Two numbers are consecutive if the are counted without jumping any number.  from the list of odd numbers, the difference between them starting from one is two.

So if R is odd, the numbers are in the order

R

R+2

R+2+2

Where R is the first term, R+2 is the second term and R+4 is the third term.

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The only value of x that is in the domain of F(x)=√x5 is x≥0. This means that the answer to the question is option D: x=1.

The domain of the function F(x)=√x5 is all values of x greater than or equal to zero (x≥0). This is because when a number is raised to the fifth power, it can never be negative; so the square root of a negative number is undefined. The calculation to prove this is as follows:

Let x=−5.

F(x)=√(−5)5=√(−25)=undefined

Therefore, the only value of x that is in the domain of F(x)=√x5 is x≥0. This means that the answer to the question is option D: x=1.

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The missing reason in Step 8 is substitution of  x = c cos (A)

Given data :

The given steps are used to prove the formula for law of cosines.

From step 5 it is noticed that our equation is

a² = b² - 2ab + c² ...... (1)

From step 7 it is noticed that the value of x is c cos (A)

So by substituting c cos (A)  for x in equation (1) we get the equation of step 8, i.e.,

a² = b² - 2bc cos(A) + c²

Hence, the missing reason in Step 8 is substitution of  x = c cos (A)

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The system of equations that has no solutions is

y>2 and y<−3

Option B is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

y > 2 and y > -3

This will have a solution because there are common values greater than 2 and greater than -3.

y > 2 and y < −3

This will have no solution because there are no common values greater than 2 and less than -3.

y < 2 and y > −3y

This will have a solution because there are common values less than 2 and greater than -3.

y < 2 and y < −3

This will have a solution because there are common values less than 2 and less than -3.

Thus,

y>2 and y<−3 have no solutions.

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The value of r in equation R+7 = -6+5r+8-3r is -5/3.

A formula declares that two things are equal. The equals sign "=" will be present. According to that formula, the left (x + 2) is equal to the right (6)

The statement "this equals that" is analogous to an equation.

A variable is a symbol used to represent an unknown number. Typically, a letter like x or y is used.

A Constant is a number that exists by itself.

When multiplying a variable, a coefficient is used (4x means 4 times x, so 4 is a coefficient)

In reality, variables have a coefficient of 1 when there isn't a number next to them (x is really 1x)

Given the problem R+7=-6+5r+8-3r

R+7=-6+5r+8-3r

R+5r-3r = -6+8-7

R + 2R = −5

3r =  −5

r = -5/3

Thus, The value of r in equation R+7 = -6+5r+8-3r is -5/3.

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To begin solving a polynomial problem, express it in standard form. When it reaches zero, factor it and then set each variable factor to zero. The answers to the resultant equations are the original solutions. Factoring cannot solve all polynomial problems.

Polynomials are sums of terms of the form where k can be any number and n can be any positive integer. 3x+2x-5, for example, is a polynomial. A primer on polynomials. This video defines words such as degree, standard form, monomial, binomial, and trinomial.

A polynomial may be categorized into four categories based on its degree. There are four types of polynomials: zero polynomial, linear polynomial, quadratic polynomial, and cubic polynomial.

A polynomial function is one that uses only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 2x+5 is a polynomial with an exponent of one.

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The total electrostatic force on the third particle will be 56 N in -x direction.

q1 = +40 μC, x1 = -20 cm = - 0.2 m

q2 = -50 μC, x2 = 30 cm = 0.3 m

q = -4 μC, x = 0

We know that, the electrostatic force between two charges

F = kQ1Q2/d²

k = 9 × 10⁹ Nm²/C²

here, d: distance between two charges

F1 = k(40×10⁻⁶)(-4× 10⁻⁶)/(0.2)²

F1 = - 36 N {(-) sign shows the force is attraction force}

so, the direction of F1 on q is -x-direction

F2 = k(-50×10⁻⁶)(-4× 10⁻⁶)/(0.3)²

F2 = 20 N {Repulsive force because both particles are having negative charge}

so, the direction of F2 on q is in the -x-direction

So Total force F = F1+F2 = 20+36 = 56 N

Therefore, the total electrostatic force on the third particle will be 56 N in the -x direction.

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The distribution of density along one axis will be equal to that on all the axis as the density is uniform and center of the sphere is at the origin.

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point.

The particle P is attracted to a solid sphere of uniform density and radius R by a gravitational force of attraction F1. The particle is located 2R from the sphere's center. The sphere now develops a spherical cavity of radius R/2, as seen in the picture. Now, the cavity-filled sphere exerts gravitational force F2 on the same particle P.

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sin

Answer:

SOH CAH TOA

Step-by-step explanation:

This means SIN tietha is equal to opposite over adjacent CAH COStetha is equal to adjacent over hypotenoys TOA TAN tetha is equal to opposite over adjacent