There are x counters in a bag.
15 of the counters are blue.
Hussain takes at random 24 counters from the bag.
6 of these 24 counters are blue.
Work out an estimate for the value of x.

The volume of the rectangular prism in cubic centimeters is 3,600,000

From the question, we have the following parameters that can be used in our computation:

Dimension = 120 centimeters by 2 meters by 1.5 meters

The volume of the rectangular prism is the product of the dimensions

i.e.

Volume = Length * width * height

Substitute the known values in the above equation, so, we have the following representation

Volume = 120 * 2 * 1.5

Convert to cm

Volume = 120 * 200 * 150

Evaluate

Volume = 3600000

Hence, the volume in cubic centimeters is 3,600,000

Read more about volume at

https://brainly.com/question/463363

#SPJ1

the given solution set {-5, -1} can be obtained by substituting either of the possible solutions into the absolute value equation and verifying that it holds.

what is an equation ?

In mathematics, an equation is a statement that asserts the equality of two mathematical expressions. An equation typically consists of two expressions separated by an equal sign, with the expression on the left side of the equal sign equal to the expression on the right side of the equal sign.

In the given question,

To write an absolute value equation that satisfies a given solution set, we need to consider the definition of absolute value. The absolute value of a number is its distance from zero the number line. Therefore, an absolute value equation can be written as follows:

|expression| = distance

where the expression is the quantity whose absolute value is being taken, and distance is a non-negative value representing the distance from zero. The equation is satisfied if and only if the expression has a distance from zero that matches the given distance.

For the solution set {-5, -1}, we can write the following absolute value equations for the given figures:

A number line with -5 and -1 marked as solutions:

|x + 3| = 2

This equation is satisfied when x = -5 or x = -1, because |-5 + 3| = 2 and |-1 + 3| = 2.

A number line with -5 and -1 equidistant from zero:

|x| = 5

This equation is satisfied when x = -5 or x = 5, because |-5| = 5 and |5| = 5.

Note that for both figures, the given solution set {-5, -1} can be obtained by substituting either of the possible solutions into the absolute value equation and verifying that it holds.

To know more about equation, visit:

https://brainly.com/question/29657983

#SPJ1

Answer:

mark me as brainliest

Step-by-step explanation:

common stocks

Answer:

y intercept when x is 0, so the answer is 3

Answer: a = 5 and k = 1/2

Step-by-step explanation:

We are given that the function is defined by:

f(x) = 16 + a(3^(kx))

We need to find the real numbers a and k such that f(0) = 21 and f(4) = 61. Using the given values of f(0) and f(4), we can form a system of two equations:

f(0) = 16 + a(3^(k(0))) = 21

f(4) = 16 + a(3^(k(4))) = 61

Simplifying the first equation, we get:

16 + a(3^0) = 21

16 + a = 21

a = 5

Substituting this value of a into the second equation, we get:

16 + 5(3^(4k)) = 61

5(3^(4k)) = 45

3^(4k) = 9

We know that 3^2 = 9, therefore

4k = 2

=> k = 2/4

=> k = 1/2

Therefore, the real numbers a and k that satisfy the given conditions are a = 5 and k = 1/2. So the function is:

f(x) = 16 + 5(3^(x/2))

The solution to the equation give us an approximate that x = 1.55.

To solve this equation, we can start by subtracting 4 from both sides to isolate the exponential term:

3.5^x + 4 - 4 = 11 - 4

This simplifies to:

3.5^x = 7

Next, we can take the logarithm of both sides with base 3.5 to eliminate the exponent:

log(3.5^x) = log(7)

Using the property of logarithms that log(a^b) = b*log(a), we can rewrite the left side as:

x*log(3.5) = log(7)

Now, we can solve for x by dividing both sides by log(3.5):

x = log(7) / log(3.5)

Plugging in the values, we get:

x = 0.84509804001 / 0.54406804435

x = 1.55329475566

x ≈ 1.55.

Answered question "Solve the equation 3.5^x + 4 = 11"

Read more about equation

brainly.com/question/2972832

#SPJ1

As a result, when the entire circumference is 20 feet, the Norman window's maximum area measurements are as follows: x = 8 feet, or around 2.546 feet, is the width, Height: 9.087 feet, or about y = 16 - 16/feet.

Perimeter is the total distance around the boundary of a two-dimensional shape, such as a polygon, a circle, or a rectangle. It is the sum of the lengths of all sides or edges of the shape.

Area is a measure of the size or extent of a two-dimensional surface or region. It is the amount of space enclosed within a closed shape or boundary.

Let's assume that the width of the rectangular part of the window is x and the height is y.

The perimeter of the window is given by:

Perimeter = width + height + semicircle circumference

Perimeter = x + y + πx/2

We are given that the total perimeter is 20 feet, so we can write:

x + y + πx/2 = 20

We can solve for y in terms of x:

y = 20 - x - πx/2

The area of the window is given by:

Area = rectangular part area + semicircle area

Area = xy + πx^2/8

We can substitute the expression we obtained for y into the equation for the area:

Area = x(20 - x - πx/2) + πx^2/8

Simplifying this expression, we get:

Area = 20x - (π/2)x^2 + πx^2/8

Area = 20x - (π/2)x^2/4

To find the maximum area, we can take the derivative of the area function with respect to x and set it equal to zero:

d/dx (Area) = 20 - (π/2)x/2 = 0

Solving for x, we get:

x = 8/π

Substituting this value back into the expression for y that we obtained earlier, we get:

y = 20 - 8/π - π(8/π)/2 = 20 - 4π/π - 16/π = 20 - 4 - 16/π = 16 - 16/π

Therefore, the dimensions of the Norman window of maximum area when the total perimeter is 20 feet are:

Width: x = 8/π feet (approximately 2.546 feet)

Height: y = 16 - 16/π feet (approximately 9.087 feet)

To know more about Area visit:

https://brainly.com/question/27683633

#SPJ1

The dimensions of the Norman window of maximum area when the total perimeter is 20 feet are:

Width: x = 8/π feet (approximately 2.546 feet)

Height: y = 16 - 16/π feet (approximately 9.087 feet)

Perimeter is the total distance around the boundary of a two-dimensional shape, such as a polygon, a circle, or a rectangle. It is the sum of the lengths of all sides or edges of the shape.

Area is a measure of the size or extent of a two-dimensional surface or region. It is the amount of space enclosed within a closed shape or boundary.

Let's assume that the width of the rectangular part of the window is x and the height is y.

The perimeter of the window is given by:

Perimeter = width + height + semicircle circumference

Perimeter = x + y + πx/2

We are given that the total perimeter is 20 feet, so we can write:

x + y + πx/2 = 20

We can solve for y in terms of x:

y = 20 - x - πx/2

The area of the window is given by:

Area = rectangular part area + semicircle area

[tex]Area = xy + \pi x^{2/8[/tex]

We can substitute the expression we obtained for y into the equation for the area:

[tex]Area = x(20 - x - \pi x/2) + \pi x^{2/8[/tex]

Simplifying this expression, we get:

[tex]Area = 20x - (\pi /2)x^2 + \pi x^{2/8[/tex]

[tex]Area = 20x - (\pi /2)x^{2/4[/tex]

To find the maximum area, we can take the derivative of the area function with respect to x and set it equal to zero:

d/dx (Area) = 20 - (π/2)x/2 = 0

Solving for x, we get:

x = 8/π

Substituting this value back into the expression for y that we obtained earlier, we get:

y = 20 - 8/π - π(8/π)/2 = 20 - 4π/π - 16/π = 20 - 4 - 16/π = 16 - 16/π

Therefore, the dimensions of the Norman window of maximum area when the total perimeter is 20 feet are:

Width: x = 8/π feet (approximately 2.546 feet)

Height: y = 16 - 16/π feet (approximately 9.087 feet)

To know more about Area visit:

brainly.com/question/27683633

#SPJ1

For the functions, f(x) = −x+2, and g(x)=5x²,

a) f∘g(x) =  5x² + 2

b) g(f(x)) = 5x² -20x + 20

c) f∘(g(x))² = 25x⁴

d) g(x - 1)    = 5x² - 10x + 5

Here, the functions are: f(x) = −x+2, and g(x)=5x²

a) f∘g(x)

We know that composite function f∘g(x) means f(g(x))

For function f(x) substitute x = g(x)

i.e., f(g(x)) = -(g(x)) + 2

                = -(5x²)  +2

                = 5x² + 2

b) g(f(x))

For function g(x) substitute x = f(x)

i.e., g(f(x)) = 5x²

                = 5(-x + 2)²

                = 5(x² -4x + 4)

                 = 5x² -20x + 20

c) f∘(g(x))²

First we find the (g(x))²= (5x²)²

                                     = 25x⁴

Now the composite function  f∘(g(x))² would be,

 f∘(g(x))² = f((g(x))²)

              = -(g(x))²+ 2

              = -(g(x))² + 2

d) g(x - 1)

Substitute x = x -1 in function g(x)

g(x - 1) = 5(x - 1)²

           = 5(x² - 2x + 1)

           = 5x² - 10x + 5

Learn more about the function here:

https://brainly.com/question/28193995

#SPJ1

The correct option A: 2 complex roots will be obtained from the given quadratic equation.

The quadratic formula's section under square root is the discriminant.

The number of solutions to the given quadratic equation depends on the discriminant, which can be positive, zero, or negative.

Given quadratic equation:

x² - 3x + 7 = 0  ..eq 1

standard form of quadratic equation:

ax²  + bx + c = 0  ..eq 2

On comparing eq 1 and eq 2

a = 1, b = -3 and c = 7

Check the value of discriminant:

D = b² - 4ac

D = (-3)² - 4*1*7

D = 9 - 28

D = - 19

D < 0 (No real roots)

As, rational as well as irrational both are real number, so only option that satisfy the obtained condition is:

A: 2 complex roots.

Know more about the discriminant:

https://brainly.com/question/30727612

#SPJ1

The probability of selecting 3 boys for the relay team given that the first selection was a girl is approximately 0.055945 or 8/143.

Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.

Let's start by calculating the probability of selecting a girl first. Since there are 7 girls and 14 team members in total, the probability of selecting a girl first is:

P(Girl first) = 7/14 = 1/2

Now, we need to calculate the probability of selecting 3 boys from the remaining 13 team members (6 boys and 7 girls). We can do this using combinations:

Number of ways to select 3 boys from 6 = C(6,3) = 20

Number of ways to select 1 girl from 7 = C(7,1) = 7

Total number of ways to form a relay team of 4 from 13 = C(13,4) = 715

Therefore, the probability of selecting 3 boys from the remaining 13 team members is:

P(3 boys from 13) = (20*7)/715 = 4/143

Finally, we can use conditional probability to calculate the probability of selecting 3 boys given that the first selection was a girl:

P(3 boys | Girl first) = P(3 boys from 13)/P(Girl first)

= (4/143)/(1/2)

= 8/143

= 0.055944...

Rounded to the nearest millionth, the probability is 0.055945.

Therefore, the probability of selecting 3 boys for the relay team given that the first selection was a girl is approximately 0.055945 or 8/143.

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

Answer: Let's start by finding out the time it takes for Gerald to jog from Point A to Point B. We can use the formula:

distance = rate x time

to do this. Since the distance between Point A and Point B is 24 km and Gerald's speed is 6 km/h, we have:

24 = 6t

where "t" is the time it takes for Gerald to jog from Point A to Point B. Solving for "t", we get:

t = 4

So Gerald takes 4 hours to jog from Point A to Point B.

Now, let's look at Shaun's journey. We know that he starts 30 minutes after Gerald and reaches Point A 30 minutes earlier than Gerald. This means that the time it takes for Shaun to travel from Point B to Point A is 3.5 hours (i.e., 4 hours - 0.5 hours + 0.5 hours).

Using the formula distance = rate x time again, we can find out Shaun's average speed:

24 = rate x 3.5

simplifying, we get:

rate = 6.857 km/h

So Shaun's average speed is 6.857 km/h (or approximately 6.86 km/h rounded to two decimal places).

Answer:

  8 km/h

Step-by-step explanation:

You want to know Shaun's average speed on a 24 km jogging track if Gerald jogged at 6 km/h for the distance, while Shaun left half and hour later and arrived half an hour earlier than Gerald.

The time it took Gerald to complete the distance is found from ...

  time = distance/speed

  time = (24 km)/(6 km/h) = (24/6) h = 4 h

Shaun left half an hour later than Gerald, and completed the trip half an hour before Gerald did. Shaun's time was 1 hour less than Gerald's, so was ...

  4 h -1 h = 3 h

Shaun's average speed can be found from ...

  speed = distance/time

  speed = (24 km)/(3 h) = 8 km/h

Shaun's average speed was 8 km/h.

Answer: a

Step-by-step explanation:

Answer:

G(x) = (x - 2)^2 + 1, so A is correct.

The  area of triangle ABC is 6cm²

A triangle is a three-sided polygon that consists of three edges and three vertices.  It is also known as the trigon and has special names such as the hypotenuse (opposite the right angle) and legs (the other two sides). It can also refer to a percussion instrument consisting of a rod of steel bent into the form of a triangle open at one angle.

The area of the triangle is given as

Area= 1/2absinC

But the CosB = Adj/Hypo

Cos60 = Adj/12

1/2 = Adj/12

corss and multiply to have

2A = 12

Therefore Adj = 6

Therefore base = 6*2 = 12

Applying the formula we have Area= 1/2acsinB

Area = 1/2* 12*12*Cos60

Area = 12*1/2 =6cm²

Learn more about the area of a triangle on https://brainly.com/question/19305981

#SPJ1

Given that the coordinates of the three vertices of a square are (4, 14), (10, 14), and (4,8).

The missing coordinate will be at (10,8) on the coordinate plane for the given square.

A vertex is a location in geometry where two or more line segments converge. Vertices are the corners of two-dimensional forms such as squares and triangles. Vertices are the places where three or more faces of a three-dimensional shape, such as a cube or a pyramid, meet.

Four of a square's vertices have the coordinates (4,14), (10,14), and (4,8).

The length of one of the square's sides may be determined using the distance formula, and the length can then be used to determine the coordinates of the missing vertex.

We know that one side of the square has a length of 6 units since the distance between (4,14) and (10,14) is 6 units.

We know that the missing vertex must be 6 units away from (4,8) in the y-direction since the square is symmetric.

The missing vertex therefore has the coordinates (10,8).

To know more about vertex visit:

brainly.com/question/30940247

#SPJ1

The missing coordinate will be at (10,8) on the coordinate plane for the given square.

A vertex is a location in geometry where two or more line segments converge. Vertices are the corners of two-dimensional forms such as squares and triangles. Vertices are the places where three or more faces of a three-dimensional shape, such as a cube or a pyramid, meet.

Four of a square's vertices have the coordinates (4,14), (10,14), and (4,8).

The length of one of the square's sides may be determined using the distance formula, and the length can then be used to determine the coordinates of the missing vertex.

We know that one side of the square has a length of 6 units since the distance between (4,14) and (10,14) is 6 units.

We know that the missing vertex must be 6 units away from (4,8) in the y-direction since the square is symmetric.

The missing vertex therefore has the coordinates (10,8).

To know more about vertex visit:

brainly.com/question/30940247

#SPJ1

Part A: Number of servings  is  1.24 servings/person

Part A: To determine the number of complete servings of fruit salad, we need to divide the total amount of fruit salad Mrs. Harris made (31 cups) by the amount she wants each person to get (25 cup/person). Using the formula:

Number of servings = Total amount of fruit salad / Amount per serving

Number of servings = 31 cups / 25 cups/person

Number of servings = 1.24 servings/person

Since we cannot have a fraction of a serving, we round down to the nearest whole number, as we cannot serve a fraction of a fruit salad. Therefore, Mrs. Harris will be able to serve 1 complete serving of fruit salad with the amount she made.

art B:

If each cup of fruit salad contains 1/4 cup of fruit and each serving is 1/4 cup, then each serving contains 1 cup of fruit.

To calculate the number of bananas Mrs. Harris needs, we first need to determine how many cups of bananas are in 31 cups of fruit salad:

31 cups × 1/4 cup of banana per cup of fruit salad = 7.75 cups of bananas

Since each cup of banana contains 14 of a banana, we can multiply the number of cups of bananas by 14 to find the total number of bananas needed:

7.75 cups of bananas × 14 bananas per cup = 108.5 bananas

So Mrs. Harris needs to buy approximately 109 bananas for the fruit salad.

Learn more about servings from

https://brainly.com/question/29801416

#SPJ1

Answer:

Step-by-step explanation:

Answer:

x = 67.4°

y = 22.6°

Step-by-step explanation:

The tangent ratio is a trigonometric ratio that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the side adjacent to that angle.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

The side opposite angle x is 7.2, and the side adjacent angle x is 3.

Use the tangent trigonometric ratio to find the measure of angle x:

[tex]\begin{aligned}\tan(x)&=\dfrac{7.2}{3}\\x&=\tan^{-1}\left(\dfrac{7.2}{3}\right)\\x&=\vphantom{\dfrac12}67.380135...^{\circ}\\x&=67.4^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, x = 67.4°.

The side opposite angle y is 3, and the side adjacent angle y is 7.2.

Use the tangent trigonometric ratio to find the measure of angle y:

[tex]\begin{aligned}\tan(y)&=\dfrac{3}{7.2}\\y&=\tan^{-1}\left(\dfrac{3}{7.2}\right)\\y&=\vphantom{\dfrac12}22.6198649...^{\circ}\\y&=22.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, y = 22.6°.

Answer:

153.94 cm2

Step-by-step explanation:

Circle area = π * r² = π * 49 [cm²] ≈ 153.94 [cm²]

π ≈ 3.14159265 ≈ 3.14

d = r * 2 = 7 [cm] * 2 = 14 [cm]

MARK AS BRAINLIEST PLS I TOOK 3 HOURS THINKING ABOUT THIS

The likelihood that the average tariff rate of 400 shipments of ethanol picked at random will be inside $80 of the average tariff rate of all shipments is roughly 0.789, or 78.9%.

The probability that an event will occur or that a proposition is true is quantified by probability theory, a branch of mathematics. A number from zero to one, where 0 approximately indicates how likely the event will happen and 1 generally indicates certainty, is the probability given an occurrence. In mathematics, probability is a measure of how likely an event is to take place. Probability levels can also be expressed as percent between 0 and 100 percent in addition to the numerals 0 to 1. the percentage of all outcomes out of all equally likely alternatives that lead to a specific occurrence, represented as a ratio.

given,

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means is approximately normal, with mean equal to the population mean and a standard deviation determined by dividing the population's standard deviation by the sample size square root.

We are given that the standard deviation of the population of tariff rates is $1200. Let mu be the population mean tariff rate, and x-bar be the sample mean tariff rate. We want to find the probability that the sample mean is within $80 of the population mean, i.e., |x-bar - mu| <= $80.

Using the formula for the standard error of the mean, we have:

SE = sigma/sqrt(n) = $1200/sqrt(400) = $60

Now, we can standardize the variable z = (x-bar - mu)/SE, and find the probability of |z| <= 80/60 = 4/3 using a standard normal distribution table or calculator.

P(|z| <= 4/3) = 0.7887

Therefore, the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.789 or 78.9% (rounded to three decimal places).

Interpretation: Sampling error refers to the natural variation in sample statistics (such as the sample mean) that occurs due to chance, even when the sample is randomly selected and representative of the population. In this case, the probability of the sample mean tariff rate being within $80 of the population mean is high (78.9%), which suggests that the amount of sampling error in estimating the population mean using a sample of 400 observations is relatively small.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

Answer:

The odds that are less generous are 19:1, 14:1, and 15:1.

Step-by-step explanation:

You have to see which numbers are greater than 11.

The vertical line at x=0 represents the boundary of the inequality, and the shaded region to the left of the line represents the solution set of the inequality, x < 0.

Explain the term inequality

Inequality refers to the unequal distribution of resources, opportunities, and rewards among individuals or groups within a society. It can be based on factors such as race, gender, income, education, and social status, leading to disparities in outcomes and experiences.

According to the given information

Start by simplifying the inequality using the distributive property and combining like terms:

4(x-1) - 2x < 6 - 5(x+2)

4x - 4 - 2x < 6 - 5x - 10

2x - 4 < -5x - 4

2x + 5x < 4 - 4

7x < 0

x < 0

So the solution to the inequality is x < 0.

To know more about inequality visit

brainly.com/question/30228778

#SPJ1

The measure of an inscribed angle of a circle is 1/2 the measure of its intercepted arc. In this case, arc OM is the intercepted arc, and 1/2 of 120 degrees is 60 degrees.

Therefore, the basketball needs an additional 2,016π cubic centimeters of air to be fully inflated.

In physics and mathematics, volume refers to the amount of space occupied by a three-dimensional object or region of space. The volume of a solid object can be calculated using various formulas, depending on the shape of the object. The concept of volume is used in many areas of science and engineering, including physics, chemistry, architecture, and manufacturing. It is particularly important in fields such as fluid mechanics and thermodynamics, where the flow and behavior of liquids and gases are often analyzed in terms of their volume and the changes in volume that occur during various processes.

Here,

The volume of a fully inflated basketball is given by the formula V = (4/3)πr³, where r is the radius of the ball. In this case, the radius is 12 cm, so the volume of a fully inflated basketball is:

V = (4/3)π(12 cm)³

V = (4/3)π(1728 cm³)

V = 2,304π cm³

To find the volume of a basketball that is only inflated halfway, we need to find the radius of the half-inflated ball. Since the volume of a sphere is proportional to the cube of its radius, we can use the following proportion:

(Volume of half-inflated ball) / (Volume of fully inflated ball) = (Radius of half-inflated ball)³ / (Radius of fully inflated ball)³

Let Vh be the volume of the half-inflated ball, then:

Vh / 2,304π cm³ = (6 cm)³ / (12 cm)³

Simplifying this equation, we get:

Vh = (1/8) * 2,304π cm³

Vh = 288π cm³

Now we can find the additional volume of air needed to fully inflate the ball:

Volume of fully inflated ball - Volume of half-inflated ball = Additional volume of air needed

2,304π cm³ - 288π cm³ = 2,016π cm³

To know more about volume,

https://brainly.com/question/12237641

#SPJ1

Answer:

x = 81.5°

Step-by-step explanation:

the secant- tangent angle x is half the difference of the measures of the intercepted arcs.

the sum of the arcs in a circle = 360°, then

unknown intercepted arc = 360° - (215 + 93)° = 360° - 308° = 52°

then

x = [tex]\frac{1}{2}[/tex] (215 - 52)° = [tex]\frac{1}{2}[/tex] × 163° = 81.5°

The closest answer is 3xLn3 which is (B).

If k(x) = 3x, then f(x) can be expressed as the integral of k(x) with respect to x:

f(x) = ∫ k(x) dx = ∫ 3x dx = (3/2)x² + C

where C is the constant of integration.

To find f'(x), the derivative of f(x) with respect to x, we simply differentiate the expression for f(x):

f'(x) = d/dx [(3/2)x² + C] = 3x

A differential equation is a mathematical equation that relates a function and its derivatives. Specifically, a differential equation describes how a quantity changes as a function of its own rate of change.

Differential equations are commonly used in physics, engineering, and other sciences to model and analyze natural phenomena.

For example, the motion of a simple pendulum can be described using a differential equation that relates the position and velocity of the pendulum to its acceleration and the forces acting upon it.

Learn more about differentiation here:

https://brainly.com/question/954654

#SPJ1

The least number of packages of plates and spoons will be 12 and 9 respectively so she should order to have an equal number of plates and spoons.

What is inequality?

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

Given that, a restaurant owner will use the data below to place new orders for plates and spoons. Packages of nine plates and twelve spoons are available for purchase. Equal quantities of plates and spoons are ordered by the restaurant owner.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

If the plates are sold in packages of 9 and there are 12 packages the number of plates will be 108.

If the plates are sold in packages of 12 and there are 9 packages the number of plates will be 108.

Thus, the least number of packages of plates and spoons will be 12 and 9 respectively so she should order to have an equal number of plates and spoons.

Learn more about inequality here:

brainly.com/question/19491153

brainly.com/question/29001724

It should be noted that to determine the amplitude of a sinusoidal function from a graph:

Identify the highest point (peak) and the lowest point (valley) of the graph of the sinusoidal function.

Find the vertical distance between the peak and the midline of the graph (the line halfway between the highest and lowest points).

The amplitude of the sinusoidal function is half of this vertical distance.

Identify the highest point (peak) and the lowest point (valley) of the graph of the sinusoidal function.

Find the vertical coordinate of the midline of the graph (the line halfway between the highest and lowest points).

Write the equation of the midline as y = the vertical coordinate of the midline.

To determine the maximum value of a sinusoidal function from a graph:

Identify the highest point (peak) of the graph of the sinusoidal function.

The maximum value of the sinusoidal function is the vertical coordinate of this peak.

To determine the minimum value of a sinusoidal function from a graph:

Identify the lowest point (valley) of the graph of the sinusoidal function.

The minimum value of the sinusoidal function is the vertical coordinate of this valley.

To determine the period of a sinusoidal function from a graph:

Identify two consecutive peaks or valleys of the graph of the sinusoidal function.

Find the horizontal distance between these two points.

The period of the sinusoidal function is twice this horizontal distance.

Learn more about graph on

https://brainly.com/question/19040584

#SPJ1

Answer:

No

Step-by-step explanation:

to determine if (- 5, 3 ) is a solution substitute the x- coordinate into both equations and if the value of y is equal to the y- coordinate then the point is a solution to the system.

y = x - 6 = - 5 - 6 = - 11 ≠ 3

y = - 2x - 7 = - 2(- 5) - 7 = 10 - 7 = 3

since both equations are not satisfied , then

(- 5, 3 ) is not a solution to the system