Smoothie activity

The smoothie chain makes mulliole SO.15 increases to the average prices of their smoothies. The table shows the average profit of the chain compared to the number of price increases. The data models a quadratic function.

Answer:

C.

Step-by-step explanation:

x² - 36 = 0

x = 6

6² = 6 x 6 = 36

So..

36 - 36 = 0

As there are so many equations in mathematics, it is a very broad subject. These are a few illustrations of typical mathematical equations: [tex]x = -6; x = 6[/tex]. Thus, option C is correct.

To solve the equation [tex]x² - 36 = 0[/tex]  , we can use the difference of squares formula:

A, B, and C are constants in the quadratic equation: ax2 + bx + c = 0. A quadratic function, often known as a function with the form f(x) = ax2 + bx + c, can be solved using this equation to get its roots.

[tex]a² - b² = (a + b)(a - b)[/tex]

In this case, a² = x² and b² = 36, so we can write:

[tex]x² - 36 = (x + 6)(x - 6)[/tex]

Setting this expression equal to 0 and solving for x, we get:

[tex](x + 6)(x - 6) = 0[/tex]

[tex]x + 6 = 0 or x - 6 = 0[/tex]

[tex]x = -6 or x = 6[/tex]

Therefore, the solutions to the equation [tex]x² - 36 = 0[/tex] are  [tex]x = -6[/tex] and [tex]x = 6.[/tex]

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Answer:

Y intercept is (0,2) Answer D.

Step-by-step explanation:

I included a graph for equation y=2/3 x + 2.

The point estimate of the mean content of 121 bottles with the average content of 4 ounces and the standard deviation 0.22 ounces is 4. Option B is the correct answer.

A point estimate is a statistic used to predict the corresponding population parameter. In a sense, a point estimate is a guess about a parameter that uses data from a sample as the basis of the guess. Point estimates can be used to estimate population parameters such as the population mean or population standard deviation.

The point estimate is a single numerical value that represents a guess for a parameter. The sample mean and sample standard deviation are examples of point estimates for the population mean and population standard deviation. If a point estimate is a good guess, it should be fairly close to the true value of the parameter.

Thus, option B is the correct answer.

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According to a census, 3.3% of all births in a country are twins. In a month, there are 2,500 births. The census reports that 3.3% of all births result in twins, and the probability of having more than 90 twins in a month is "0.4351."

We will solve this problem using the binomial distribution formula, which is as follows:P (X > 90) = 1 - P (X ≤ 90)where P represents the probability, X represents the number of twins born in a month, and X is a binomial random variable with a sample size of n = 2,500 and a probability of success (having twins) of p = 0.033. Using the TI-83 calculator, TI-83 Plus, or TI-84 calculator, the following steps can be followed:

Press the "2nd" button followed by the "VARS" button (DISTR) to access the distribution menu. Scroll down and select "binomcdf (" from the list of options (use the arrow keys to navigate). The binomcdf ( menu will appear on the screen. The first number in the parentheses is the number of trials, n, and the second number is the probability of success, p. We want to find the probability of having more than 90 twins, so we need to use the "compliment" option. Therefore, we will subtract the probability of having 90 twins or less from 1 (using the "1 -" key). Type in "binomcdf (2500,0.033,90)" and press the "ENTER" button on your calculator.

This will give you the probability of having 90 twins or fewer in a month. Subtract this value from 1 to obtain the probability of having more than 90 twins in a month, which is the answer to our question. P(X>90) = 1 - binomcdf (2500,0.033,90)P(X>90) = 1 - 0.5649P(X>90) = 0.4351Therefore, the probability of having more than 90 twins in a month is 0.4351.

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Answer:

answer is 091 accc h na tu

Answer:

42x-27

Step-by-step explanation:

The division problem provided by the model shown here is [tex]3[/tex] ÷  [tex]\frac{1}{4}[/tex].

The first step of dividing fractions is to get the reciprocal of a second fraction, which involves flipping its numerator and denominator. Multiply all two numerators after that. Multiply the 2 denominators after that. Then finish, if required, simplify the fractions.

Simple Division: Little numbers can be divided into groups and pieces using the simple division method in mathematics. Divide easy and basic division problems into terms that can be divided using simple division sums. Arithmetic, subtraction, multiplying, & division are the four fundamental mathematical operations.

Given:

We have three section [tex]1+ 1 + 1= 3[/tex]

[tex]= \frac{4}{12}[/tex]

[tex]= \frac{1}{3}[/tex]

In this case, the model yields the division issue.

[tex]3[/tex] ÷ [tex]\frac{1}{4}[/tex]

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1.4m/s is the rate that Roberto is walking. We know the formula for calculating the time i.e. t= d/r.

The term "distance" refers to how far we move. The rate is a measurement of our trip speed. Time is measured by how far we travel. The distance an object will travel over time and at a specific average rate is the subject of rate problems.

Given,

Distance = D

D= 1.4t

Rate= ?

Substituting the given values in the formula t= d/r

where,

t= time in seconds

d= distance

r= rate

We get,

t= 1.4t/r

t/1.4t= 1/r

t gets cancelled

so we have,

1/1.4= 1/r

r= 1.4m/s

Therefore, 1.4m/s is the rate at which Roberto is walking.

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The complete question is as follows:

Roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds.

What is the rate that Roberto's walking in meters per second?

The answers are a) ASA congruence rule b) SSS congruence rule c) it is not necessary congruent.

Congruent refers to having the same height and shape. Congruent therefore involves comparing two numbers, and equivalent denotes the equality of two expressions. Therefore, to state two line segments are congruent implies that the two lines have equal measures.

a) ∠GIH is corresponding to ∠LJK

GH = KL

∠IHG = ∠KLJ

By ASA congruence rule

ΔGIH ≅ ΔJKL

b) AB  = DF

AC = DE

BC = EF

By SSS congruence rule

ΔABC ≅ ΔDEF

c) Two Corresponding sides are congruent, which is not enough to make them congruent.

So, it is not necessary congruent.

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As a result, f(x) changes at a rate of 1/2 on average over the range [0, 1/2].

A function is a mathematical formula that relates every element in one set, known as the domain, to a single element in another set, known as the range. The most prevalent way to represent a function is as f(x), where f(x) stands for the output or dependent variable and "x" stands for the input or independent variable. There is a value of f(x) in the range for each value of x in the domain. Consider the function f(x) = 2x + 1 as an illustration. This function's range and scope possibilities are both limited to the real numbers.

given

We must determine the slope of the secant line that goes through the interval's endpoints in order to determine the average rate of change of a function over the interval. Since the range in this instance is [0, 1/2], we must determine the slope of the secant line that connects (0, f(0)) and (1/2, f(1/2)).

Let's first assess the function at the interval's endpoints:

f(0) = 0² + 2(0) + 1 = 1

f(1/2) = (1/2)² + 2(1/2) + 1

= 5/4

Next, we can calculate the slope of the secant line using the slope formula:

slope is equal to (f(1/2)-f(0)) / (1/2 - 0)

= ((5/4)-1) / (1/2)

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

= 1/2.

As a result, f(x) changes at a rate of 1/2 on average over the range [0, 1/2].

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The order of events from least likely to most likely are as follows:

The reason for this order is because of the chances of each event occurring. Event D has the least chance of occurring because no numbers in the set have a value less than or equal to 0. Event A is the next least likely because only one number in the set is greater than 0, which is the number 1. Event C is the next least likely because only two numbers in the set are at least 2 (2 and 3). Event B is the next least likely, as there are only five even numbers in the set (2, 4, 6, 8, and 10). Events E, F, G, and H are the most likely to occur, because of the number of numbers that are divisible by 3, and 5, and are prime numbers.

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The length of WX is greater than the length of YZ, and that the sides are neither parallel nor perpendicular.

Quadrilateral WXZY has four vertices: W(-1,4), X(4,0), Y(-5,1), and Z(0,-3). We are asked what is true about the sides WX and YZ.

To determine the length of WX, we can use the distance formula: d = √((x2-x1)² + (y2-y1)²). So, d(W,X) = √((4-(-1))² + (0-4)²) = √(5² + 4²) = √41. Similarly, d(X,Z) = √((0-4)² + (-3-0)²) = √16 + 9 = √25 = 5.

To determine the length of YZ, we can use the same formula: d(Y,Z) = √((-3-(-5))²+ (0-1)²) = √4 + 1 = √5.

Now, we need to compare the lengths of WX and YZ to determine what is true about them. √41 is greater than √5, so we know that WX is longer than YZ.

However, this does not tell us whether WX and YZ are parallel, perpendicular, or neither. To determine this, we need to examine the slopes of the sides.

The slope of WX is (0-4)/(4-(-1)) = -4/5. The slope of YZ is (0-(-3))/(-5-0) = 3/5. Since the slopes are not equal, we know that the sides are not parallel.

To determine if the sides are perpendicular, we can multiply their slopes. If the product is -1, then the sides are perpendicular. So, (-4/5) * (3/5) = -12/25, which is not equal to -1. Therefore, we can conclude that the sides WX and YZ are neither parallel nor perpendicular.

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The slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.

An equation is an expression that states the equality of two things. It typically consists of an equal sign (=) and two expressions on either side of the equal sign that represent the same thing. Equations are used to describe relationships between different variables and can be used to solve mathematical problems. They can also be used to show the relationships between different quantities in physics and chemistry.

a)The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 6, and the run is 2, so the slope is 3.

b) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 3, and the run is -7, so the slope is -3/7.

c) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 4, and the run is 6, so the slope is 2/3.

Finding slope in tables and graphs is a common mathematical skill that is used to identify the rate of change of a linear equation. This is determined by finding the change in the dependent variable (the y-axis) divided by the change in the independent variable (the x-axis). This is what is referred to as the slope of the equation. To find the slope in tables and graphs, you must look at the differences between the points on the x-axis and y-axis, and divide the change in the y-axis by the change in the x-axis. This will give you the slope of the equation. Finding the slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.

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Perimeter of a regular pentagon = side + side + side + side + side

A polygon is a two-dimensional shape with straight sides that are connected to form a closed figure. The perimeter of a polygon is defined as the total distance around the exterior of the shape.

To calculate the perimeter of a polygon, you add up the lengths of all its sides. For example, a regular pentagon has five sides that are all the same length. To find the perimeter of this pentagon, you would add up the length of all five sides:

Perimeter of a regular pentagon = side + side + side + side + side

= 5 × side

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PCA (Principal Component Analysis) is an unsupervised learning technique used to reduce dimensionality. It is a commonly used dimensionality reduction technique. This technique is used to discover patterns in data that have multiple features. PCA is used to reduce the dimensionality of data.

Compute the mean of each feature. For every feature, compute the mean μ=1/nΣxi where n is the number of data points and xi is the feature vector. Calculate the covariance matrix compute the covariance matrix from the mean-adjusted data: X=X−μ,Covariance matrix: C=1/nXTX where X is the mean-adjusted data matrix.

Now find the eigenvectors and eigenvalues of the covariance matrix. Sort the eigenvectors in order of decreasing eigenvalues. These eigenvectors represent the principal components. The first eigenvector represents the direction of the maximum variance.

Create the projection matrix. Only the top k principal components are used for dimensionality reduction. The projection matrix can be computed by stacking the eigenvectors of the top k principal components: W=[u1u2…uk]where ui represents the eigenvector.

Project the data onto the lower-dimensional subspace. The original data can be projected onto the lower-dimensional subspace using the projection matrix: Z=X×WPCA is a commonly used dimensionality reduction technique that involves computing the principal components of a dataset. This technique can be used to find the most important patterns in the data.

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The conclusion we can draw from the circle graph is (2) Jazz is the preferred music for 56 students.

From the circle graph, we can draw the following conclusions:

Pop is the preferred music for 35% of the sample, which is equivalent to 0.35 x 400 = 140 students.

Therefore, conclusion (1) is incorrect.

Jazz is the preferred music for 14% of the sample, which is equivalent to 0.14 x 400 = 56 students.

Therefore, conclusion (2) is correct.

The combined percentage of Hip Hop, Rock, and Jazz is 13% + 25% + 14% = 52%, which is more than half of the sample.

Therefore, conclusion (3) is incorrect.

Hip Hop and Pop are the preferred music for 25% + 35% = 60% of the sample, which is equivalent to 0.6 x 400 = 240 students.

Therefore, conclusion (4) is incorrect.

Therefore, the only correct conclusion that can be drawn from the circle graph is that Jazz is the preferred music for 56 students.

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One way to determine whether a point is a solution to a two-variable inequality is to substitute the values of the variables in the inequality and determine whether the inequality is true or false. If the inequality is true, the point is a solution, and if the inequality is false, the point is not a solution.

For example, consider the inequality 2x + 3y > 7. Let’s see if the point (1,2) is a solution. To do so, substitute x=1 and y=2 into the inequality:2(1) + 3(2) > 7 Simplify to get:2 + 6 > 7 This is true, so the point (1,2) is a solution to the inequality. Conversely, let’s see if the point (4,-1) is a solution. To do so, substitute x=4 and y=-1 into the inequality:2(4) + 3(-1) > 7 Simplify to get:8 - 3 > 7 This is false, so the point (4,-1) is not a solution to the inequality .There are some general rules that can be followed to help determine which side of a line is shaded in an inequality. If the inequality is greater than or less than, the line should be dashed, and the shading should be above or below the line, respectively. If the inequality is greater than or equal to or less than or equal to, the line should be solid, and the shading should be above or below the line, respectively.

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Answer:

Cost price of 5 orange=(60/50)*5=6k

Now to get 50% profit

Selling price of group of 5 orange

=6*1.5=9k.

The true statements regarding the plot of normal distributions A and B are B has the larger mean, and B has the larger standard deviation; options 2 and 3.

A plot of a normal distribution is a bell-shaped curve that represents the probability distribution of a continuous random variable that follows a normal distribution.

The plot shows the frequency of occurrence of values of the variable, with the most common values near the mean and the less common values near the tails of the distribution.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the location of the center of the distribution, while the standard deviation determines the spread or width of the distribution.

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Answer:

b×h ÷2 esa es la fórmula para el área

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

we see that the baseline is 4 units long.

and the height from the top vertex down to that baseline is 5 units.

so, the area is

4 × 5 / 2 = 20/2 = 10 units²

Answer:

270 students dislike carrots.

Step-by-step explanation:

Therefore, the 2-liter bottle is the more cost-effective option as it has a lower cost per milliliter.

Millimeters (mm) is a unit of length in the metric system. It is a subunit of a meter, with one meter being equal to 1000 millimeters. Millimeters are commonly used to measure small distances such as the thickness of paper, the width of a fingernail, or the diameter of a small object. The abbreviation for millimeters is "mm".

by the question.

To evaluate which option is the most cost-effective, we need to compare the cost per milliliter of each option.

Calculate the price per liter: To compare the cost of the two options, you'll need to calculate the price per liter of each. You can do this by dividing the price of the bottle by its volume in liters. For example, if the 2-liter bottle costs $4, the price per liter would be $2 ($4/2 liters). If the 750ml bottle costs $2.50, the price per liter would be $3.33 ($2.50/0.75 liters).

Compare the price per liter: Once you have the price per liter for each option, you can compare them. In this example, the 2-liter bottle is cheaper at $2 per liter compared to the $3.33 per liter for the 750ml bottle.

Consider the convenience: While the 2-liter bottle may be cheaper, you should also consider if it's more convenient for you. If you won't be able to use all the 2-liters before it goes bad, or if it's difficult to carry around, then multiple 750ml bottles may be a better option for you despite the higher cost per liter.

For the 750ml bottle:

[tex]Cost per milliliter = R28 /750ml[/tex]

[tex]Cost per milliliter = R0.0373/ml[/tex]

For the 2-liter bottle:

[tex]Cost per milliliter = R63 / 2000ml[/tex]

[tex]Cost per milliliter = R0.0315/ml[/tex]

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The Sale price is C. $260.63.

Selling price is the price at which a product or service is sold by a business or seller to a customer. It is the amount of money that a customer must pay in order to purchase the product or service. The selling price is typically determined by factors such as production costs, competition, supply and demand, and profit margins.

Sale price is the discounted price at which a product or service is sold for a limited period of time. It is usually a lower price than the regular price, and it is offered to customers as an incentive to make a purchase. Sale prices can be determined by applying a discount or markdown to the regular selling price.

In the given question,

To find the sale price, we need to first calculate the amount of the markdown:

Markdown = Regular Price x Markdown Rate

Markdown = $389 x 0.33

Markdown = $128.37

The sale price is then the regular price minus the markdown:

Sale Price = Regular Price - Markdown

Sale Price = $389 - $128.37

Sale Price = $260.63

Therefore, the answer is C. $260.63.

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Answer:

Step-by-step explanation:

To solve this problem, we need to use the formula for compound interest:

A = P*e^(rt)

where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).

For Sophie's account, we have:

P = $92,000

r = 6 1/8% = 0.06125 (as a decimal)

t = 14 years

A = 92000*e^(0.06125*14)

A = $219,499.70 (rounded to the nearest cent)

For Damian's account, we have:

P = $92,000

r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)

t = 14*12 = 168 months

A = 92000*(1+0.005521)^168

A = $288,947.46 (rounded to the nearest cent)

Now we can subtract Sophie's final amount from Damian's final amount to find the difference:

Difference = $288,947.46 - $219,499.70

Difference = $69,447.76

Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.

There are 27 different ways for Sam to color the sides of the equilateral triangle, accounting for rotations and reflections.

We have,

To calculate the number of different ways Sam can color the sides of the equilateral triangle, we need to consider the symmetry of the triangle.

Since two colorings are considered the same if one coloring can be rotated and/or reflected to obtain the other coloring, we need to account for these symmetries.

Let's analyze the possibilities:

- All three sides have the same color:

There is only one way to color the triangle in this case.

- Two sides have the same color, and the third side has a different color: Sam can choose the color for the two sides in 5 ways and the color for the remaining side in 4 ways (since it must be different from the other two colors).

However, we need to divide this by 3 to account for the different rotations of the equilateral triangle.

Thus, there are (5 x 4) / 3 = 20 / 3 = 6.67 (approx) ways to color the triangle in this case.

Since the number of colorings must be a whole number, we consider this as 6 ways.

- All three sides have different colors:

Sam can choose the color for the first side in 5 ways, the color for the second side in 4 ways (since it must be different from the first), and the color for the third side in 3 ways (since it must be different from the first two).

However, we need to divide this by 6 to account for the different rotations and reflections of the equilateral triangle.

Thus, there are (5 x 4 x 3) / 6 = 20 ways to color the triangle in this case.

In total, the number of different ways Sam can color the sides of the equilateral triangle is:

= 1 + 6 + 20

= 27.

Thus,

There are 27 different ways for Sam to color the sides of the equilateral triangle, accounting for rotations and reflections.

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Answer:

27.18

Step-by-step explanation:

Firstly, you must label the triangle.

r- opposite

13.85- adjacent

We know that tan θ = opposite/ adjacent so we substitute our numbers into the equation.

tan (63) = r/13.85

Then, times 13.85 on both sides so we only have our unknown on one side.

(x13.85)  tan(63)= r/13.85   (x13.85)

r= tan (63) x 13.85

r=27.18

:)

Answer:

Step-by-step explanation:

Answer:

y = 2x/15 + 6

Step-by-step explanation:

3y/2 = x/5 + 9

3y = (x/5 + 9) (2)    The 2 that was dividing goes on to multiply on the other side.

3y= 2x/5 + 18

y = (2x/5 + 18) / 3   The 3 that was multiplying goes on to divide on the other side.

y = 2x/15 + 6