At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $3.60 and a 16-ounce cup costs $4.80.


Is the linear relationship between cup size and cost also proportional? Why or why not?


Yes, the constant of proportionality is 0.3.

Yes, there is no constant of proportionality.

No, the constant of proportionality is 0.3.

No, there is no constant of proportionality.

Note that given the temperature values, the average low temperature for the week is 1° (Option A).

It is important to remember that the average of a set of data values is calculated by adding the values and dividing by the number of values.

Thus, the Average Low temperature is given as:

Average (A) = sum of data values / no of data values

⇒ Average (A)  = [8+7+(-3)+(-8)+(-5)+3+5]/7

A = 7/7

A = 1

Thus, the  Average Low temperature is given as 1° (Option A)

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Full Question:

See the attached table

Answer: False.

Step-by-step explanation:

       We will compute the different expressions to see if the equations are true.

16 + 1 = 17

17 = 17 ✓

(16 + 1) -1 = 17 - 2

(17) -1 = 15

16 ≠ 15 ✗

       The second equation is incorrect. We can tell right away because 2 is being subtracted from 2, but nothing is being taken away from the 16 (1 - 1 = 0).

Answer:

a) 12

b) 56

Step-by-step explanation:

In this problem we are asked to plug the given a and b values into the expressions [tex]3b \div (2a - 1) + b[/tex] and [tex]9b+a^4\div8[/tex] then evaluate them.

[tex]a = 2[/tex], [tex]b=6[/tex]

a) [tex]3b \div (2a - 1) + b[/tex]

↓ plug in the given [tex]a[/tex] and [tex]b[/tex] values

[tex]3(6) \div (2(2) - 1) + 6[/tex]

↓ simplify value inside parentheses

[tex]3(6) \div 3 + 6[/tex]

↓ execute multiplication

[tex]18 \div 3 + 6[/tex]

↓ execute division

[tex]6 + 6[/tex]

↓ execute addition

[tex]12[/tex]

b) [tex]9b+a^4\div8[/tex]

↓ plug in the given [tex]a[/tex] and [tex]b[/tex] values

[tex]9(6)+2^4\div8[/tex]

↓ simplify exponent

[tex]9(6)+16\div8[/tex]

↓ execute multiplication

[tex]54+16\div8[/tex]

↓ execute division

[tex]54+2[/tex]

↓ execute addition

[tex]56[/tex]

The final expression is

sqrt (39y9) = y4 • sqrt(39y) assuming y as positive.

Rewrite

39 y ^9 as ((y^2)^2)^2 . 39 y

Factor out y^8.

√39(y^8 . y).

Rewrite   [tex]y^8 as (y^4)^2[/tex]

 √39(y^4)^2 . y).

Rules for simplifying variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

    sqrt(x8)=x4

    sqrt(x-6)=x-3

  (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     sqrt(x5)=x2•sqrt(x)

     sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

SQRT(y9) = y4 • SQRT(y)

Therefore, sqrt (39y9) = y4 • sqrt(39y)

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The laptop worth after five halves years will be $1,543. Then the correct option is E.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

You purchase a new laptop today. The value of that laptop depreciates based on the function is given below.

f(x) = 4,300(0.83)ˣ.

Where 'x' is the number of years.

The laptop worth after five halves years will be given as,

[tex]\rm f(x) = \$4,300 \times (0.83)^{5.5}[/tex]

f(x) = $4,300 × 0.35886

f(x) = $1,543

The laptop worth after five halves years will be $1,543. Then the correct option is E.

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The missing options are given below.

$2,105

$1,601

$2,699

$3,215

$1,543

The worth of the laptop after 2.5 years is $2,699.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(t) = 4,300 [tex](0.83)^t[/tex]

Now,

For t = 5/2,

t = 2.5

f(5) = 4300 x [tex]0.83^{2.5}[/tex]

f(5) = 2699

Thus,

The laptop is worth $2,699 after 2.5 years.

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Answer:

1.2 grams (or) 1200 mg per day

Step-by-step explanation:

The amount needed for 1 hour,

→ 200 mg ÷ 4 hour

→ 200 ÷ 4

→ 50 mg

Patient will receive in one day is,

→ 1 day = 24 hours

→ 50mg × 1 day

→ 50 × 24

→ 1200 mg

Converting mg into grams,

→ 1 g = 1000 mg

→ 1200 mg

→ 1200 ÷ 1000

→ 1.2 grams

Hence, the answer is 1.2 grams.

Answer:

1.2 grams

Step-by-step explanation:

There are 24 hours in one day.

Therefore, if the medication is to be taken every 4 hours, the patient receives:

Given that the doctor prescribes 200 mg of medication every 4 hours, the amount in milligrams that the patient will receive in one day is:

There are 1000 milligrams in one gram.

Therefore, to convert milligrams to grams, divide by 1000:

Therefore, the patient should receive 1.2 grams of medication in one day.

Answer: 1.68

Step-by-step explanation: Okay, to find this we need to use this formula:

Amount = Part percent * whole number / 100

So, now let's plug in the numbers:

Amount = 14 * 12 / 100

= 168/100

= 1.68

Therefore the amount of gold in the rock is 1.68 oz out of the 12 ounces.

I hope this helped!

Answer: 1.68

Step-by-step explanation: So, if we want to find how much gold is in the rock, it's a good idea to set up a proportion. So, it would be like this:

[tex]\frac{14}{100} = \frac{?}{12}[/tex]

Now, we would cross-multiply the 12 and the 14, which is 168, and then divide it by 100. That can be found by moving the decimal 2 places left of 168.00. So, that would be 1.68. Therefore, there are 1.68 ounces of gold in the rock. I hope this helped!

As a result, when a park's size is 3/5 square miles and its length is 7/8 miles, the park's width is equal to 24/35.

A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.

given

Area of a park with a rectangular shape is equal to 3/5 of a mile squared.

A rectangular park is 7/8 of a mile long.

3/5 = 7/8 * Park's rectangular width

As a result, when a park's size is 3/5 square miles and its length is 7/8 miles, the park's width is equal to 24/35.

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The probability that the entire batch will be accepted, 0.981

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Given that,

A sample of items is randomly selected without replacement

Entire batch is accepted if every item in the sample is okay

The ABC Electronics Company has just manufactured 2100 write-rewrite CDs

Defective CDs = 180

Probability of entire batch selected = ?

Probability of selecting a first non-defective item = 2087/2100

Probability of selecting a second non-defective item = 2086/2099

Probability of selecting a third non-defective item = 2085/2098

Probability of entire batch selected = 2087/2100×2086/2099×2085/2098

Probability of entire batch selected =   0.981

Hence, the probability will be 0.981

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Answer:were are the lists ? Pls include the lists.

Step-by-step explanation:

The Sun's rays hit the Earth most directly close to the equator, whereas near the poles they hit at a sharp angle.

This indicates that the tropics are warmer than the poles and that higher latitudes absorb less solar radiation per square centimeter (or inch) of surface area than lower latitudes do.

The incoming solar energy is more direct (almost perpendicular or closer to a 90° angle) when the sun's rays hit the surface of the Earth close to the equator. Warmer temperatures result from the solar radiation being concentrated over a smaller surface area.

Near the equator, the incoming solar radiation impacts the Earth's surface more directly (nearly perpendicular or closer to a 90° angle). Because the sun radiation is concentrated over a smaller surface area, it leads to warmer temperatures.

Since less surface area receives sunlight at the equator than at the poles, it warms up more quickly. Less atmosphere needs to be traveled through at the equator than at the poles.

As a result, the Earth's surface receives more solar heat. The variance in solar energy received at various latitudes affects atmospheric circulation.

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Complete Question -

How is the heat energy per area received from sunlight different at the equator than at the poles?

On solving the provided question, we can say that from the graphs the equation we have [tex]f(x) = y^2 + 5y -9[/tex]  => f(1/3) = -29/9

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

here,

from the graphs the equation we have

[tex]f(x) = y^2 + 5y -9\\f(1/3) = 1/9 + 5/3 - 9\\f(1/3) = 1 + 15 - 45 / 9\\f(1/3) = -29/9[/tex]

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The 34% would be considered a statistic.

A statistic is a numerical measurement of a characteristic of a population.

It is calculated by taking the number of individuals in the sample with a certain characteristic, such as preferring charcoal to gas grills, and dividing it by the total number of individuals in the sample.

For example, in the survey of 1000 adults, if 340 of them prefer charcoal to gas grills, then the statistic would be calculated as 340/1000 = 0.34 = 34%. This statistic can then be used to make inferences about the entire population. In this case, it can be inferred that 34% of the population prefers charcoal grills to gas grills.

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option D 3,125!/(3,125-10)! is the correct expression, because it represents the number of ways to choose 10 people from a group of 3,125 people (without regard to order) and accounts for the fact that each person can win only once.

A. (3,125-10)!/3,125! is not the correct expression, because this would represent the number of ways that 10 people can be chosen from a group of 3,115 people (without regard to order) and doesn't account for the fact that each person can win only once.

B. (3,125-10)! 10!/3,125! is also not the correct expression, because this is the number of ways to choose 10 people out of 3,115 and then arrange them in a specific order of 10 gift cards, and this doesn't account that each person can win only once.

C. (3,125)!/(3,125-10)!10! is also not the correct expression, because this represents the number of ways to arrange 3,125 people, regardless of the fact that only 10 can win, and this doesn't account for the fact that each person can win only once.

Therefore, the correct expression is D. 3,125!/(3,125-10)!

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The probability of randomly selecting a can that is not of grape is:

P =  0.67

We know that on the ice chest there are:

For a total of 6 + 9 + 8 + 4 = 27

The probability of selecting a can that is not of grape juice is equal to the quotient between the numbers of cans that are not of grape, and the total number of cans.

There are 27 cans in total and 18 of these aren't of grape, then the probability is:

P = 18/27 = 0.67

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The population will reach 100,000 in 2047 and the population will reach 200,000 in 2082.

Total population of the city = 50,000

Growth annual rate = 2%

Using the formula of compound growth -

A = P ( 1 +r)^t

Substituting the values -

P=50,000, r =2% = 0.02 and A=100,000

Thus,

1,00,000 = 50,000 ( 1 + 0.02)^t

= 1.02^t = 1,00,000/50,000

= 1.02^t = 2

Taking ln both sides, thus -

= In( 1.02^t) = In (2)

t = In( 1.02^t)/ In (2)

t = 35

The population will reach 100,000 in the year -

= 2012+35

= 2047

Similarly,

P=50,000, r =2% = 0.02 and A=2,00,000

Thus,

2,00,000 = 50,000 ( 1 + 0.02)^t

= 1.02^t = 2,00,000/50,000

= 1.02^t = 4

Taking ln both sides, thus -

= In( 1.02^t) = In (4)

t = In( 1.02^t)/ In (4)

t = 70

The population will reach 100,000 in the year -

= 2012 + 70

= 2082

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Answer:

x =1,69 or x= -0,44

In the case where v1 and v2 are two vectors in the vector space V and v1 is a scalar multiple of v2, let's say v1 = k * v2, where k is a scalar, we can write:

v1 = k * v2

Linearly dependent vectors are a set of vectors that can be expressed as a linear combination of the other vectors in the set. In other words, one vector in the set can be written as a scalar multiple of the other vectors in the set.

As a result, v1 can be expressed as the linear combination of v2 and k, where k is a scalar. Thus, v1 and v2 are linearly dependent on one another.

In contrast, if variables v1 and v2 are linearly dependent, v1 can be expressed as a linear combination of variables v2, and vice versa. That is, scalars k1 and k2 can exist such that:

v2 = k2 * v1 and v1 = k1 * v2.

This suggests that v1 = k1 + k2 + v1. We can divide both sides by v1 because it is not a zero vector, and the result is:

1 = k1*k2

Therefore, let's argue that v1 is a scalar multiple of v2, the other vector.

In conclusion, if and only if one of the vectors is a scalar multiple of the other, v1 and v2 are linearly dependent.

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525 millimeters of compound A are needed.

What is a mixture?

Combining two or more substances and identifying a property of the ingredients or the resulting combination is the focus of mixture problems. For instance, we could need to figure out how much water to add to a saline solution to make it more diluted, or we might need to know how much of an orange juice bottle is concentrated.

Here, we have

Given: A certain drug is made from only two ingredients: compound A and compound B. There are 7 millimeters of compound A used for every 5 millimeters of compound B. If a chemist wants to make 900 millimeters of the drug.

Given the following ratio

A : B = 7 : 5

Mixture = 900 millimeters

To calculate the amount of compound A needed, we make use of the following formula:

A = A/(A+B)×mixture

A = 7/(7+5)×900

A = 525 millimeters.

Hence, 525 millimeters of compound A are needed.

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The image point of.tge given pair of coordinates; (12, -12) after a dilation by a scale factor of 1/3 centered at the origin is; (4, -4).

It follows from transformations that; when a point (x, y) is dilated by a scale factor of 1 / 3 centered at the origin, the resulting image point is; ( kx , ky ).

On this note, since the transformation in discuss is such that; the scale factor is 1/3 centered at the origin; the resulting image point is;

( 1/3 • 12 , 1/3 • -12 )

= ( 4, -4 ).

Ultimately, the image point which results from the dilation is; ( 4, -4 ).

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Answer:

12

Step-by-step explanation:

Divide the numbers

(48/2)-1x4^2+2x2

(24)-1x4^2+2x2

*Evaluate the exponent

24-1x4^2+2x2

24-1x16+2x2

*multiply the numbers*

24-1x16+2x2

24-16+2x2

*Again*

24-16+2x2

24-16+4

*add the numbers*

24-16+4=12

Answer:

-4

Step-by-step explanation:

Since this equation uses order of operations, you should solve what's in the parenthesis first.  

48 ÷ 2 = 24

Now you have 24 - 4²2 + 2 × 2.  The next thing to solve in order of operations is exponents, so square 4.  

4² = 16

Now you should have 24 - 16 (2) +2 × 2.  Next is multiplication, so multiply 16(2) and 2 × 2.  

16 × 2 = 32, and 2 × 2 = 4

Now you have 24 - 32 + 4.  This should look a lot more simple now.  Simply do the math from here; doesn't matter how.  

24 - 32 = -8

-8 + 4 = -4

I hope this helped you!  :)

5.62% percentage of his adjusted gross income is he paying in property tax.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Jimmy paid $8,200 in property taxes.

His adjusted gross income is $146,000.

The percentage of his adjusted gross income is he paying in property tax is, (8200/146000)*100%

 =5.62%

Hence, 5.62% percentage of his adjusted gross income is he paying in property tax.

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for the given scenario the distribution is applicable, (a) negative binomial (b) binomial (c) normal (d) exponential (e) Poisson (f) uniform, (g) geometric.

The waiting process is frequently a part of geometric, negative binomial, and exponential random variables; in these cases, the waiting process is continuous until something occurs, rather than a count of trials. (Exponential). Large numbers of independent quantities that are averaged and summed typically have distributions that are close to normal. For observed counts, there are two models: Poisson and binomial. For binomial, there is a predetermined number of trials, leading to a clearly defined maximum count; for Poisson, there is no clearly defined maximum potential count. When there is no evident preference for one interval of distance or time over another such equal-length interval, the distribution is continuous.

We have to identify the best described as binomial, geometric, negative binomial, Poisson, uniform distribution and so on.

(a) X is the sum of the numbers obtained by rolling a die 500 times.

in that case negative binomial distribution suitable choice.

(b)  X is the number, out of the next 15 customers at a clothing store, who are women. the binomial is the best distribution for this condition.

(c) X is the number of murders committed in a city during a week.

 normal distribution.

(d) X is the time of day (measured in hours after midnight) that a meteor strikes Earth.

exponential distribution.

(e)  X is the amount of time that it will take until a call center receives a phone call

Poission distribution.

(f) X is the number of times we drive through an intersection before getting one red light. uniform distribution.

(g)X is the average GPA of 60 randomly chosen UC San Diego students.

 geometric distribution.

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Answer:

6n+2

Step-by-step explanation:

So if you own 10,000 shares of the company, you would receive $4,500 in dividends.

A dividend is a portion of a company's profits and retained earnings that it distributes to its shareholders and owners. When a company makes a profit and accumulates retained earnings, those earnings can be reinvested in the company or distributed to shareholders as a dividend.

The amount of dividends you will receive if you own 10,000 shares can be calculated as follows:

Dividend per share = Share price * dividend yield

Dividend per share = $18 * 0.025

Dividend per share = $0.45

Total dividends received = number of shares * dividend per share

Total dividends received = 10,000 * $0.45

Total dividends received = $4,500

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The value of the fucntion after differentiating is [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

Differentiation is the ratio of a slight change in one quantity to a little change in another that depends on the first quantity. Calculus' major emphasis on the differentiation of a function makes it one of the subject's key ideas. Differentiation is the process of determining the maximum or lowest value of a function, the speed and acceleration of moving objects, and the tangent of a curve. If y = f(x) and f(x) is differentiable, then f'(x) or dy/dx is used to indicate the differentiation.

The function is [tex](x^{2} - 4x - 1)\x^{-\frac{2}{3} }[/tex]

After differentiating

[tex]\frac{d}{dx}(x^{2} - 4x - 1)\x^{-\frac{2}{3} }[/tex] = [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }\frac{d}{dx}(x^{2} - 4x - 1)[/tex]

= [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]

The value of the fucntion after differentiating is [tex]-\frac{2}{3} (x^{2} - 4x - 1)\x^{-\frac{5}{3} }(2x - 4)[/tex]

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The mean of the population can be calculated by finding the sum of all the heights and dividing it by the total number of observations.

This is also known as the arithmetic mean and can be represented by the formula:

Mean = (Sum of Observations) / (Number of Observations)

In this case, the sum of all the heights is 10,800 and the total number of observations is 100. Therefore, the mean of the population is:

Mean = 10,800 / 100 = 108 inches

To verify this result, we can also look at the histogram. Since the heights are grouped into intervals of 10 inches, the mean should be around the midpoint of the tallest bar, which is 108 inches. This confirms our calculation of the mean.

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The function that best represented by this graph is f(x) = −x² + 1.

The correct option is C.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

A graph of a function is given in the image.

The parent function of the graph is g(x) = x².

And the graph is negative of the parent function.

And shifted upwards to 1 point.

That means, the function is f(x) = −x² + 1.

Therefore, the function is f(x) = −x² + 1.

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The plot of both lines is given below.

y = 2r-5,

r + y = -8.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

The system of equations,

y = 2r-5,

r + y = -8.

And the intersection point is the solution of the equation.

The plot of the lines is given in the attached image.

Therefore, plots are given in the attached image.

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Answer: 18000 cm^2

Step-by-step explanation:

1.5 meters = 150 cm

1.2 meters = 120 cm

Area = length * width

        = 150 cm * 120 cm

        = 18000 cm^2