A local coffee shop is testing out new flavors of coffee: Caramel Apple Latte and Salted Minty Mocha. A poll conducted by the
coffee shop determined that 46 customers preferred only the Caramel Apple Latte, 61 customers chose only the Salted Minty
Mocha, 27 customers chose both flavors, but 18 liked neither flavor. What is the probability that a randomly selected
customer would only like the Caramel Apple Latte?

Answer:

Step-by-step explanation:

The long-run behavior of a function can be determined by examining its asymptotes and the behavior of the function near these asymptotes.

For the function f(p)=(p+1)^3(p+4)^3(p-1), there are three points to consider as possible asymptotes: p = -1, p = -4, and p = 1.

At p = -1, the factor (p-1) is equal to zero, so the function has a vertical asymptote there. This means that as p approaches -1 from either side, the function will approach infinity.

At p = -4, the factor (p+4)^3 is equal to zero, so the function also has a vertical asymptote there. Similarly, as p approaches -4 from either side, the function will approach infinity.

At p = 1, the factor (p+1)^3 is equal to zero, so the function has another vertical asymptote there. In this case, as p approaches 1 from either side, the function will approach negative infinity.

So, the long-run behavior of the function can be described as follows:

The function approaches infinity as p approaches -1 or -4 from either side.

The function approaches negative infinity as p approaches 1 from either side.

Therefore, the long-run behavior of f(p)=(p+1)^3(p+4)^3(p-1) is characterized by three vertical asymptotes at p = -1, p = -4, and p = 1.

Answer:

[tex]\text{As } p \to -\infty, f(p) \to -\infty\\\\\text{As } p \to \infty, f(p) \to \infty[/tex]

====================================================

Explanation:

Each factor is a cubic of degree 3.

The degree of the entire polynomial is 3+3+3 = 9.

Since the degree is odd and the leading coefficient is positive, this means the graph falls to the left and rises to the right.

"falls to the left" means [tex]\text{As } p \to -\infty, f(p) \to -\infty[/tex]

"rises to the right" means [tex]\text{As } p \to \infty, f(p) \to \infty[/tex]

This is verified using a graphing tool like Desmos as shown in the screenshot below. I'm using x in place of p.

The area of the shaded portion is [tex]9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex].

From the given data,

The equilateral triangle with sides 6.

Equilateral triangle: The amount of space an equilateral triangle takes up in a two-dimensional plane is its area. A triangle is said to be equilateral if all of its sides are equal and all of its interior angles measure 60 degrees. As a result, the area of an equilateral triangle can be determined if its side length is known.

In this problem

area of equilateral triangle=[tex]6^{2}*\sqrt{3}/4[/tex]----->[tex]\frac{9}{\sqrt{3} }[/tex] units²

The internal angles of an equilateral triangle are equal to 60 degrees

The area of a circle=pi*r²

for a circle with radius r=3 units

See the attached figure to better understand the problem

The area of the figure ABC is equal to the area of the circle divided by 6

Area figure ABC=[tex]9* \frac{\pi}{6}[/tex]=[tex]\frac{3}{2} *\pi[/tex]units²

the area of the shaded portion is equal to

⇒[tex]9*\sqrt{3} units^{2} -3*(\frac{3}{2} )*\pi[/tex] = [tex]9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex]

[tex]=9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex]

Therefore, the area of the shaded portion is [tex]9*\sqrt{3} units^{2} -(\frac{9}{2} )*\pi units^{2}[/tex].

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a) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05), which equals £630.

b) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05)^2, which equals £661.50.

A mathematical expression combines constants, numbers, variables, and values with mathematical operations without adding the equation symbol (=).

When the equation symbol is added to mathematical expressions, they become an equation.

In this situation, the compound interest final amount is depicted like an exponential growth function as follows:

f(x) = a(1+r)ˣ

f(x) = exponential growth function

a = initial amount

r = growth rate

x = number of time intervals

Initial amount = £600

Growth rate = 5% or 0.05

x = 1 or 2 years.

f(x) = 600 (1.05)^x

Thus, if $600 is compounded at 5% yearly for 1 or 2 years, the mathematical expressions showing the value of the account are 600 (1 + 0.05) and 600 (1 + 0.05)^2, respectively.

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The simplest form of the given expression will be  38c + 280.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

His truck is filled with cans that weigh 16 ounces each and bottles that weigh 54 ounces each. There is a combined total of 280 cans and bottles in his truck.

Let c be the number of cans in his truck. Write an expression for the combined total weight (in ounces) of the cans and bottles in his truck.

O Total weight in ounces = 38c + 280

Hence the simplest form of the given expression will be  38c + 280.

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Answer: First, let's find out how many times a 100-pound person would take the antihistamine in a week:

Every 6 hours * 24 hours/day = 4 times a day

4 times a day * 7 days/week = 28 times a week

Next, let's find the number of 13.2 mg chewable tablets taken in a week:

A typical dose of 19 mg * 28 doses/week = 532 mg

532 mg / 13.2 mg/tablet = 40 tablets

So, a 100-pound person would take 40 chewable tablets in a week following the prescribed dosage.

Now, let's find the amount of liquid antihistamine to be taken in a week:

A typical dose of 19 mg * 28 doses/week = 532 mg

532 mg / 13.2 mg/10 mL = 40.15 mL

So, a 100-pound person would take 40.15 mL of liquid antihistamine in a week following the prescribed dosage.

Step-by-step explanation:

The percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.

What is the Percent of change?

The percent of change is a measure that compares the difference between two values to the original, or initial, value. It is usually expressed as a percentage and indicates how much a value has increased or decreased from its initial value.

To find the percent of change from 9 points to 4 points, we need to first calculate the amount of change, which is the difference between the final value (4 points) and the initial value (9 points):

Amount of change = Final value - Initial value = 4 - 9 = -5

The negative sign indicates a decrease in value.

Next, we can calculate the percent of change using the formula:

Percent change = (Amount of change / Initial value) x 100%

Substituting the values we get:

Percent change = (-5 / 9) x 100% ≈ -55.6%

Hence, the percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.

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The number of students who either play hockey or football is given by the equation n ( A ∪ B ) = 45 students

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the total number of students in the class be n ( U ) = 50 students

Let the number of students who play hockey be n ( A ) = 20 students

Let the number of students who play football be n ( B ) = 35 students

Let the number of students who play hockey and football n ( A ∩ B ) = 10

So , from the set theory n(A∪B) = n(A) + n(B) - n(A⋂B)

Substituting the values in the equation , we get

The number of students who play hockey or football = 20 + 35 - 10

On simplifying the equation , we get

The number of students who play hockey or football = n( A ∪ B ) = 45 students

And , the number of students who do not play hockey or football is given by the equation = n ( U ) - n ( A ∪ B )

On simplifying the equation , we get

The number of students who do not play hockey or football = 50 - 45 = 5 students

Hence , the number of students who play hockey or football is 45 students

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Answer:

154.3° (to the nearest tenth)

Step-by-step explanation:

1 exterior angle=360/number of sides

360/14=25.714285

To get the one angle within the 14 sided polygon, take 1 exterior angle away from 180, as they are on a straight line

180-25.714285=154.285714

To the nearest tenth:

154.3°

Using de Morgan’s laws to rewrite a statement : It is true that April is not a spring month OR August is not a spring month

This refers to a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan. He was a 19th-century British mathematician. De Morgan's laws can also be called De Morgan's theorem.

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The x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.

In physics and mathematics, a vector is a mathematical object that has both magnitude and direction. Vectors are often represented by arrows, with the length of the arrow indicating the magnitude of the vector, and the direction of the arrow indicating the direction of the vector.

For example, the velocity of a moving object is a vector quantity, because it has both a magnitude (the speed of the object) and a direction (the direction in which the object is moving).

To find the x-components and y-components of the vector [tex]\mathbf{\hat d }[/tex] = (5.0 km, 29° left of +y-axis), we can use trigonometry.

The magnitude (or length) of the vector is given by the first component, which is 5.0 km.

The angle between the vector and the positive y-axis is 29° left of +y-axis, which means it forms a 61∘ angle with the negative y-axis (since 29∘ + 61° = 90°).

The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:

x-component = magnitude x cos(angle) = 5.0 km x cos(61°) ≈ -2.25 km

The negative sign indicates that the x-component is in the opposite direction of the positive x-axis.

The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:

y-component = magnitude x sin(angle) = 5.0 km x sin(61°) ≈ 4.30 km

Therefore, the x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.

Expressed as an ordered pair, the components are (-2.25 km, 4.30 km).

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Answer:  Choice C)  [tex]7i\sqrt{2}[/tex]

Work Shown:

[tex]\sqrt{-98} = \sqrt{-1*49*2}\\\\\sqrt{-98} = \sqrt{-1}*\sqrt{49}*\sqrt{2}\\\\\sqrt{-98} = i*7*\sqrt{2}\\\\\sqrt{-98} = 7i\sqrt{2}\\\\[/tex]

Answer:

x    y

0    -2

4    -1

graph: should look like the picture attached

explanation:

Answer:

Step-by-step explanation:

<1 + <4 = 180 supplementary angles

180 - 95 = 85 degrees

Answer:

  27.5 square units

Step-by-step explanation:

You want to know the area of the composite shape shown in the graph.

The shape can be decomposed into a parallelogram and a triangle. Each has the same base, 5 units.

The parallelogram has a height of 3 units, so its area is ...

  A = bh

  A = (5)(3) = 15 . . . . square units

The triangle has a height of 5 units, so its area is ...

  A = 1/2bh

  A = 1/2(5)(5) = 12.5 . . . . square units

The total area of the figure is the sum of the areas of its parts:

  total area = (15 units²) +(12.5 units²) = 27.5 units²

The area of the polygon is 27.5 square units.

==========================================================

Explanation:

Let's go through each answer choice to see which are true and which are false.

A.

The fractions for advertising and rent are 1/6 and 7/12 respectively. The LCD is 12, so let's get 1/6 to have a denominator of 12. Multiply top and bottom by 2 to get 1/6 = 2/12.

Now we can compare the fractions 2/12 (aka 1/6) and 7/12. Clearly 7/12 is larger. It's like saying "having 7 slices of pizza is more than 2 slices of pizza". Therefore, the claim that more was spent on advertising compared to rent is false.

----------------------

B.

1/4 = 3/12 when multiplying top and bottom by 3

3/12 was spent on supplies and 2/12 was spent on advertising

We see that more was spent on supplies, so claim B is true

----------------------

C.

This claim is false because it contradicts claim B.

Another way to see why it's false is to use a calculator to get these decimal values

Since 0.17 is not larger than 0.25, this means 1/6 is not larger than 1/4.

----------------------

D.

We could use any of the methods mentioned in the previous sections, but I'll go another route.

For now assume that the fractions for supplies and rent (1/4 and 7/12 respectively) are equal.

Let's use cross multiplication to say the following:

1/4 = 7/12

1*12 = 4*7

12 = 28

Clearly the two sides are different so the original fractions aren't equal. To fix this error, replace each equal sign with a "less than" sign like so

1/4 < 7/12

1*12 < 4*7

12 < 28

Think of it like working backward up the chain. Start with 12 < 28 which is clearly true, and you can work backwards to end up with 1/4 < 7/12.

The fact we end up with 1/4 < 7/12 shows the claim "The bookstore spends more on supplies than rent" is false. It's the other way around: the bookstore spent more on rent compared to supplies.

----------------------

Summary: We found only choice B to be true. The other statements were false.

Each worker would take home a net pay of $586.71.

What is the net pay?

The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.

To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.

To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.

For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:

Gross Pay for 40 hours = $15.90/hour x 40 hours = $636

For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:

Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88

Therefore, their total gross pay would be:

Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88

Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:

Total Deductions = 28% x $814.88 = $228.17

Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:

Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71

Therefore, each worker would take home a net pay of $586.71.

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The 'L' shape is reflected over the y axis is shown by figure B.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

As, we have to reflect the image over the y axis.

That means that the image gets flipped across the y-axis.

So, the rule reflect over y axis is  (x, y) -> (-x, y).

Then, among all the option the figure that satisfies the rule is Figure B.

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Answer:

Step-by-step explanation:

We can start by finding how much money Carlos spent on clothes. To do this, we simply multiply the original amount of $400 by 40%:

Clothes = $400 * 40% = $400 * 0.40 = $160

Next, we find how much money Carlos has left after spending on clothes. To do this, we subtract the amount spent on clothes from the original amount:

Remaining Money = $400 - $160 = $240

Finally, we find how much money Carlos spent on video games. To do this, we multiply the remaining money by 50%:

Video Games = $240 * 50% = $240 * 0.50 = $120

So, in total, Carlos spent $160 on clothes and $120 on video games, for a total of $160 + $120 = $280.

And Carlos has $400 - $280 = $120 left.

After spending 40% of the $400 on clothes, Carlos has $400 x (100 - 40) / 100 = $240 left.

Next, he spent 50% of the remaining $240 on video games, which is $240 x 50 / 100 = $120.

Therefore, Carlos spent a total of $400 - $240 = $160.

Finally, Carlos has $240 - $120 = $120 left.

On solving the provided question, we can say that from the graphs The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.

Prior to technological advancement, the opportunity cost of treating HIV/AIDS rises as the world deviates from its PPF. The potential cost of treating more HIV/AIDS cases falls as a result of technological advancements since less other commodities and services must be sacrificed in order to treat more HIV/AIDS patients. Alternatively, the world might treat more HIV/AIDS patients right now by forgoing the same number of other commodities and services.

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The correct question is -

More than 50 years after it jumped the species barrier and became one of the most devastating viruses to affect​ mankind, HIV remains a stubborn adversary. Treatment has improved dramatically over the past 20 years and​ now, a cure could be in sight.

​Source: The Guardian​, November​ 30, 2018

Make a graph of the production possibilities frontier with​ HIV/AIDS cases treated on the x​-axis and other goods and services on the y​-axis before and after the advance in technology.

Question content area bottom left

Part 1

The opportunity cost of treating​ HIV/AIDS cases increases as more​ HIV/AIDS cases are treated.

Draw a curve that shows the production possibilities for the world economy that produces​ HIV/AIDS treatments and other goods and services. Label the curve PPF0.

Then draw the PPF that shows the effect of an advance in technology on​ HIV/AIDS treatments. Label the curve PPF1.

Answer: The profit function P(x) can be found by subtracting the cost function C(x) from the revenue function R(x), so:

P(x) = R(x) - C(x) = (-0.5(x-80)^2 + 3,200) - (30x + 200)

The domain of P(x) is the set of all possible values of x for which the profit calculation makes sense. In this case, the company has a maximum capacity of 130 items, so the domain of P(x) is 0 <= x <= 130.

To calculate the profit when producing 50 items and 60 items, we simply plug in these values for x in the profit function:

Profit when producing 50 items = P(50) = (-0.5(50-80)^2 + 3,200) - (30 * 50 + 200) = $2350

Profit when producing 60 items = P(60) = (-0.5(60-80)^2 + 3,200) - (30 * 60 + 200) = $2280

Since the profit is higher for producing 50 items, the company should choose to produce 50 items.

From our model, we can see that as the production increases, the cost also increases linearly with a slope of 30, while the revenue increases parabolically but with a negative slope, meaning that after reaching a certain point, the increase in revenue becomes slower compared to the increase in cost. This is why the profit decreases as the production increases, and therefore the company makes less profit when producing 10 more units.

Step-by-step explanation:

If the r-value, or correlation coefficient, of a data set is 0.934, the

coefficient of determination to three decimal places is:  A. 0.872.

The coefficient of determination (R-squared) is the square of the correlation coefficient (r) and represents the proportion of the variance in the dependent variable (y) that can be explained by the independent variable (x).

So, to find the coefficient of determination, we need to square the correlation coefficient:

R-squared = r^2

= 0.934^2

= 0.872 (Rounded to three decimal places)

Therefore, the answer is (A) 0.872.

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Answer:

Hence x= 8 should be added to the terms of 49:68 to get the ratio 3:4.

Step-by-step explanation:

have a nice day.

Using subtraction operator, the distance between the house and the ducks is 21 feet

Trigonometric ratios are mathematical ratios that relate the sides of a right triangle to its angles. The three primary trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan.

In this case, we don't need to use trigonometric ratio since the duck and house with the tree are on the same length. We can simply use a basic arithmetic operation to find the distance between the ducks from the house.

Using subtraction, the distance between the ducks and the house will be

distance = 47 - 26

distance = 21 feet

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Answer: 4(45x^(3)-1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 out of the 5 people are adults (since 2 women and 2 men) therefore 80% of people are adults.

Answer:

80%

Step-by-step explanation:

Its either too easy or too hard. 2+2=4 obviously, and 4/5=8/10. 8/10, 0.80, or 80% is the answer. If I got this right I don't know how lol.

Answer:

  EF = 18

Step-by-step explanation:

Given similar triangles DEF and JHI, midpoints G and K of sides DE and HI, with sides marked GF=9, EF=x+8, KI=14, HI=3x-2, you want to know the length of EF.

Corresponding sides in similar triangles are proportional. This means ...

  EF/GF = HI/KI

  (x+8)/9 = (3x-2)/14 . . . . substitute given values

  14(x +8) = 9(3x -2) . . . . multiply by 14·9

  14x +112 = 27x -18 . . . . eliminate parentheses

  130 = 13x . . . . . . . . . . . add 18-14x

  10 = x . . . . . . . . . . . . . divide by 13

Now, we can find EF:

  EF = x+8 = 10 +8

  EF = 18

Answer:

5

Step-by-step explanation:

We can assume ∠KLJ ≅ MLJ. So we put them equal to each other.

[tex]42=9x-3\\45=9x\\5=x[/tex]

The value of x when an angle of the given figure is given as 9x - 3 is x = 5.

Given a figure.

It is required to find the value of x.

Here, consider the two triangles which are split up in the figure.

Consider the triangles JKL and JML.

Comparing the sides and angles:

JK = JM

KL = ML

JL = JL

So, they are similar.

Each corresponding angles are equal.

Here, the angle corresponding to ∠JLK is ∠JLM.

So, they are equal.

∠JLM = ∠JLK

9x - 3 = 42

Add 3 on both sides.

9x = 45

Divide both sides by 9.

x = 5

Hence, the value of x is 5.

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Answer:

range = 33

Step-by-step explanation:

the range of a data set is the difference between the largest and smallest values in the set.

largest value = 163 and smallest value = 130 ( from diagram ), then

range = 163 - 130 = 33