This recipe makes 12 portions of potato soup. Richard follows the recipe but wants to make 4 portions. Complete the amounts of each ingredient that he needs. Recipe: Serves 12 72 ml oil 180 g onions 1.2 kg potatoes 1.32 litres milk ml oil g onions g potatoes ml milk​

Answer:

x² + 2x + y² + 4y = 20

(x² + 2x + 1) - 1 + (y² + 4y + 4) - 4 = 20

(x + 2)² + (y + 4)² - 5 = 20

(x + 2)² + (y + 4)² = 25

Therefore, the center is (-2, -4) and the radius is √25 = 5.

Answer: 2/90 = 1/45

Step-by-step explanation:

The multiplicative rate of change for the function  is approximately.

To find the multiplicative rate of change for the exponential function f(x) = , we need to calculate the derivative of the function. However, it's important to note that the function you provided is not an exponential function. An exponential function has a base raised to a variable exponent.

The given functioncan be rewritten as. Now, we can proceed to find the multiplicative rate of change by taking the derivative of f(x) with respect to x.

Using the chain rule, the derivative of is:

Here, ln(2/5) is a constant representing the natural logarithm of 2/5. The multiplicative rate of change is given by the derivative, which is

The value of ln(2/5) is approximately -0.916.

It's important to note that the multiplicative rate of change is not constant for this function. It depends on the value of x and decreases exponentially as x increases.

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Answer:

w<13

Step-by-step explanation:

Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.

Answer:

w < 1`3

Step-by-step explanation:

Isolate the variable w on one side of the inequality sign.

w+7<20

w<20 - 7

w<13.

Answer:

11.25minutes

Step-by-step explanation:

From the question we are told that lifts unloads 576 skiers per hour at the top of the slope, this is expressed as;

576skiers = 1hr

To determine the time it will take 108skier, we can write

108skier = x

Divide both expressions

576/108 = 1/x

576x =108

x = 108/576

x = 0.1875hr

Convert to minute

x = 0.1875×60

x = 11.25minutes

Hence it took the ride 11.25minutes

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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Answer:

The probability that a randomly chosen widget weighs more then 19 grams is 0.468.

Step-by-step explanation:

X = Widget weights produced at Acme Widget Works

It is provided that X is normally distributed with mean 17.46 grams and variance 375.67 grams.

Compute the probability that a randomly chosen widget weighs more then 19 grams as follows:

\(P(X>19)=P(\frac{X-\mu}{\sqrt{\sigma^{2}}}>\frac{19-17.46}{\sqrt{375.67}})\)

                  \(=P(Z>0.08)\\\\=1-P(Z<0.08)\\\\=1-0.53188\\\\=0.46812\\\\\approx 0.468\)

Thus, the probability that a randomly chosen widget weighs more then 19 grams is 0.468.

Answer: 1/3, "I THINK"

Step-by-step explanation: You already had your cursor on it lol, Sorry if im wrong.

Using permutation we calculate that the number of ways "generally" can be written is 90720 .

A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

Nearly every area of mathematics as well as many other scientific disciplines use permutations. They are applied to the analysis of sorting algorithms in computer science, the description of particle states in quantum physics, and the description of RNA sequences in biology.

The sum of all positive integers less than or equal to n, sometimes represented as n!, is the number of permutations of n different objects.

Total number of letters in the word "GENERALLY"  = 9

There are 2 E and 2 L in the word , all the other words are different.

Hence the total number of ways in which it can be formed using permutation is  

= 9! ÷ (2!×2!)

Cancel the factorials: \($\frac{n !}{(n-m) !}=n \times(n-1)$\)timess \($(n-m+1), \quad n > m$\) \($\frac{9 !}{2 !}=9 \times 8 \times 7 \times 6 \times 5 \times 4 \times$\)\($=\frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}{2 !}$\)

\(\frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}{2 !}=90720$$\)

=90720

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The ball can take 3/2 seconds in the air before it hits the ground.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ h (t) = - 16t² + 48t + 28

Which models the height (in feet) of a ball where t is the time (in seconds).

Now,

Find the time to the ball in the air before it hits the ground as;

The function is,

⇒ h (t) = - 16t² + 48t + 28

Make derivative zero after differentiation as;

⇒ h' (t) = 0

⇒ h' (t) = - 32t + 48 = 0

⇒ - 32t + 48 = 0

⇒ 32t = 48

⇒ t = 48/32

⇒ t = 3/2 seconds

Thus, The ball can take 3/2 seconds in the air before it hits the ground.

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Answer: 7/2

Step-by-step explanation:

Answer:

36000 inches

Step-by-step explanation:

Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Answer:

55°

Step-by-step explanation:

Total: 90°

90° - 35°

55°

The required equation for number of miles and years for the car is given as; y = 19000x + 41000

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The parameters are;

Suppose the year 2020 represents x = 0.

The distance travelled per year can be taken as the slope of the linear  equation. Thus, slope = 19000.

And, the distance travelled by January 1, 2020 is 41000.

This tells us that for x = 0, y = 41000.

The linear equation in slope intercept form is given as;

y = mx + c

where;

m is slope

c is y-intercept

Substitute the corresponding values in the above equation to obtain,

y = 19000x + c

At x = 0, y = 41000

41000 = (19000 × 0) + c

c = 41000

Now, the equation can be written as,

y = 19000x + 41000

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Answer:

2,808

Step-by-step explanation:

since 117 = d then we would just plug that into the equation of s = 24d and get s = 24(117), after that you would just solve.

Answer:

53

Step-by-step explanation:

The remainder you got when 3x³ - 5x² - 23x + 24 is divided by x - 3 is -9.

Polynomials are expressions in algebra which consist of both variables and coefficients. Sometimes, variables are also known as indeterminates. Polynomials are classified as monomials, binomials, and trinomials based on the degree of the variables in the expression.

Variables in the monomials, binomials and trinomials have the highest degree equals 1, 2 and 3 respectively.

By doing the long division method, we will bet the quotient as 3x² + 4x - 11 and the remainder equals -9.

Let's check this using division algorithm.

Dividend = 3x³ - 5x² - 23x + 24

Divisor = x - 3

Quotient = 3x² + 4x - 11

Remainder = -9

By division algorithm,

Dividend = (Divisor × Quotient) + Remainder

3x³ - 5x² - 23x + 24  = [(x - 3) (3x² + 4x - 11)] + -9

                                 = [3x³ + 4x² - 11x - 9x² - 12x + 33] + -9

                                 = 3x³ + 4x² - 9x² - 11x - 12x + 33 - 9

                                 = 3x³ - 5x² - 23x + 24

Hence -9 is the remainder of this division process.

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Answer:

Theater B.

Step-by-step explanation:

Find out each theatre's percentage of seats taken.

Theater A =

100% = 60

1% = 60 ÷ 100 = 0.60

36 ÷ 0.60 = 60% of the seats taken.

Theater B =

81 + 9 = 90

100% = 90

1% = 90 ÷ 100 = 0.90

81 ÷ 0.90 = 90%

Theater C =

100% = 80

1% = 80 ÷ 100 = 0.80

80 - 12 = 68

68 ÷ 0.80 = 85%

Theater B have the greatest percentage of seats taken out of all 3.

Answer:

624 pounds

Step-by-step explanation:

If 10 boxes of paper weigh 260 pounds, one box of paper is equal to 26 pounds because 260 divided by 10 is equal to 26. If one box equals 26 pounds, 24 boxes times 26 pounds each is equal to 624 pounds.

What is Function?

Function is the relationship between inputs where each input is related to exactly one output. It is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

"y is a function of x" (denoted y = f(x)) means that y varies according to whatever value x takes on.

How to determine

Where F(x) = 2x^4 + x^2 - 10x + 1

So, to calculate f(-10)

f(x) = y

Where x = -10

f(-10) = 2(-10)^4 + (-10)^2 -10(-10) + 1

f(-10) = 2(10000) + 100 + 100 + 1

f(-10) = 20000 + 100 + 100 + 1

f(-10) = 20201

For f(2),

f(x) = y

Where x = 2

f(2) = 2(2)^4 +2^2 -10(2) + 1

f(2) = 2(16) + 4 -20 + 1

f(2) = 32 + 4 -20 + 1

f(2) = 17

For f(3)

f(x) = y

Where x = 3

f(3) = 2(3)^4 + 3^2 -10(3) + 1

f(3) = 2(81) + 9 -30 + 1

f(3) = 162 + 9 - 30 + 1

f(3) = 142

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The value of the variable x = 21/32

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.

These expressions are also made up of certain arithmetic or mathematical operations.

These operations includes;

From the information given, we have that;

3/8=4/7x

cross multiply the values, we have;

7x(3) = 8(4)

multiply the values and expand the brackets, we get the values;

21x = 32

Divide both sides by the coefficient of the variable x, we get;

x = 32/21

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Answer:

option C

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

divide both sides by 3 s+1=2

subtract both sides by 1 s=1

Answer:

-30 feet

Step-by-step explanation:

it is -30 feet because that one is closest to sea level because -42 feet is -12 feet more than -30 feet. plsss give me brainliest plssss

Answer: yx (4)(12) / 8

Step-by-step explanation:

Answer:

1. What is an inverse proportion equation that represents this situation?

y=48/k

2. How many crackers will each person get if 8 people are sharing the crackers?

6 crackers

Step-by-step explanation:

1. What is an inverse proportion equation that represents this situation?

The number of crackers, y, is inversely proportional to the number of people, x. In mathematical terms, this is y=k/x, where k is some number.

When there are 4 people, each person gets 12 crackers:

y=k/x

12=k/4

48=k

Therefore, our equation is y=48/x

2. How many crackers will each person get if 8 people are sharing the crackers?

y=48/x, where y is the number of cracker and x is the number of people.

y=48/8

y=6

Answer:

Difference = 250 students

Step-by-step explanation:

Let the total number of students be x.

Given the following data;

% driving = 30%

% riding = 60%

% walking = 10%

Number of students driving = 375

First of all, we would determine the total number of students.

Total = 30/100 * x = 375

0.3x = 375

Total, x = 375/0.3

Total, x = 1250 students.

Next, we determine the number of students walking;

Walking = 10/100 * 1250

Walking = 12500/100

Walking = 125 students

Finally, we would determine many more students drive to school than walk to school;

Difference = 375 - 125

Difference = 250 students

Answer:

Step-by-step explanation:

the point (-3,1) is on the graph of G

meaning G(-3)=1

so the correct answer is G(x) =

   \((x+3)^2+1\)

hope this helps

Answer:

The first one is exponential, the second one is linear, and the last one is quadratic.

Step-by-step explanation:

The first one is exponential, because the values are increasing at an increasing rate. In other words, the difference between any consecutive x-values yield a bigger difference.

The second one is linear, because the values are increasing at a constant rate.

The last one is quadratic, because the values decrease, and then increase, which can be represented by a parabola for a quadratic equation.