A pound of chocolate costs 8 dollars. Leila buys p pounds. Write an equation to represent the total cost c that Leila pays.

The company profit is decreasing by 1/3 thousand dollars per year.

An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the initial value of y.

Let y represents a company's profit in thousands of dollars, and x represents the time in years.

From the graph, using the point (-3, 4) and (3, 2):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Substituting:

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

The company profit is decreasing by 1/3 thousand dollars per year.

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Answer: The coordinates of the image of a figure after a rotation of 0.25 degrees about the x-axis can be found using the following formulas:

x' = x

y' = y * cos(θ) - z * sin(θ)

z' = y * sin(θ) + z * cos(θ)

where (x, y, z) are the original coordinates and (x', y', z') are the new coordinates. In this case, we only need to find the y' coordinate because the rotation is about the x-axis and the x coordinate will not change.

For each point, we can use the formula to find the y' coordinate:

A (2, 6) -> y' = 6 * cos(0.25) - 0 * sin(0.25) = 5.99911... ~ 6

B (0, 0) -> y' = 0 * cos(0.25) - 0 * sin(0.25) = 0

C (-5, 8) -> y' = 8 * cos(0.25) - 0 * sin(0.25) = 7.99823... ~ 8

D (-2, 10) -> y' = 10 * cos(0.25) - 0 * sin(0.25) = 9.99649... ~ 10

So, the new coordinates after rotating 0.25 degrees about the x-axis are:

A (2, 6) -> (2, 6)

B (0, 0) -> (0, 0)

C (-5, 8) -> (-5, 8)

D (-2, 10) -> (-2, 10)

The coordinates of the points have not changed after the rotation because the rotation angle is very small.

Step-by-step explanation:

A. 10 cm radius: 2 * pi * 10 cm = 62.83 cm

B. 2.7 cm radius: 2 * pi * 2.7 cm = 16.94 cm

C. 1.2 mm radius: 2 * pi * 1.2 mm = 7.54 mm

D. 9.01 cm radius: 2 * pi * 9.01 cm = 56.76 cm

A. The circumference of a circle with a radius of 10 cm is 62.83 cm.

B. The circumference of a circle with a radius of 2.7 cm is 16.94 cm.

C. The circumference of a circle with a radius of 1.2 mm is 7.54 mm.

D. The circumference of a circle with a radius of 9.01 cm is 56.76 cm.

The circumference of a circle is the distance around its edge. It can be calculated using the formula 2πr, where r is the radius of the circle. The radius is the distance from the center of the circle to any point on its edge. To find the circumference of a circle, we need to multiply the radius by 2 and then by pi (π), which is roughly 3.14.

For example, if the radius of the circle is 10 cm, then the circumference of the circle is 2πr = 2π x 10 cm = 62.83 cm. Similarly, if the radius of the circle is 2.7 cm, then the circumference of the circle is 2π x 2.7 cm = 16.94 cm. If the radius of the circle is 1.2 mm, then the circumference of the circle is 2π x 1.2 mm = 7.54 mm. Finally, if the radius of the circle is 9.01 cm, then the circumference of the circle is 2π x 9.01 cm = 56.76 cm.

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We are 90% confident that the true weekly return of the index portfolio is between 1.186% and 1.214%.

One important concept in statistics is a confidence interval, which is a range of values that is likely to contain the true value of a parameter, such as a population mean or proportion.

The analyst has a sample of 28 observations of the weekly return, which is assumed to be normally distributed. The sample mean is 1.2% and the sample variance is 0.00175. With this information, we can calculate the standard error of the mean, which measures the variability of the sample mean from one sample to another. The formula for the standard error is:

standard error = sample standard deviation / square root of sample size

In this case, the sample standard deviation is the square root of the sample variance, which is approximately 0.0418%. The square root of the sample size is 5.2915. Therefore, the standard error of the mean is:

standard error = 0.0418 / 5.2915 = 0.0079%

To construct a 90% confidence interval for the weekly return, we need to use the t-distribution, which is a probability distribution that takes into account the sample size and the level of confidence. The t-distribution has more variability than the normal distribution, which results in wider confidence intervals for smaller sample sizes.

The formula for a t-confidence interval is:

sample mean ± t-value x standard error

The t-value depends on the sample size and the level of confidence. For a sample size of 28 and a 90% confidence level, the t-value is 1.699. Therefore, the confidence interval is:

1.2 ± 1.699 x 0.0079 = [1.186%, 1.214%]

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Answer:

26

Step-by-step explanation:

56/2 -2

The solution of the given system of equations 6x+3y=8 and 8x+4y=-1 is x=0 and y==-8/9

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system. (5, 4) is a solution of the first equation, but not the second.

We are given that;

The equation 1;  6x+3y=8

The equation 2; 8x+4y=-1

Now,

In equation 1

6x=8-3y

x=(8-3y)/6

Substituting the value of x in equation 2

8((8-3y)/6)+4y=-1

4((8-3y)/3)+4y=-1

(8-3y)/3)+4y=-1/4

8-3y+12y=-3/4

8+9y=-3/4

9y=-3/4-8

9y=-3-32/4

9y=-35/4

y=-32/36=-8/9

Putting the value of y in equation 1

6x+3(-8/9)=8

54x-8=8

x=0

Therefore, the solution of the equations will be x=0, y=-8/9.

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The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

Function 1 is given as,

y = - 2x - 4

The slope is -2 and the y-intercept is -4.

From the graph, the equation of function 2 is given as,

x / 2 + y / 4 = 1

2x + y = 4

y = - 2x + 4

The slope is -2 and the y-intercept is 4.

The slope of both functions is the same which is -2 but a different y-intercept. Thus, function 1 is parallel to function 2.

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The missing graph is attached below.

Type I error would be weather remains dry, but school is needlessly canceled. Type II error would be don't cancel school, but the snow storm hits. The correct option is B.

In hypothesis testing, the null hypothesis is the default assumption that is being tested. In this case, the null hypothesis is that the weather will remain dry. The school superintendent must decide whether to reject or accept this null hypothesis based on the evidence available.

There are two types of errors that can occur in hypothesis testing: Type I and Type II errors.

Type I error occurs when the null hypothesis is rejected, even though it is actually true. In other words, the school superintendent decides to cancel school due to a snowstorm, but the weather remains dry. This can result in unnecessary school closures, which can disrupt students, teachers, and parents' schedules.

Type II error occurs when the null hypothesis is accepted, even though it is actually false. In other words, the school superintendent decides not to cancel school because of the assumption that the weather will remain dry, but a snowstorm hits. This can put students, teachers, and parents in danger as they try to commute to school in hazardous conditions.

The consequences of a Type I error and a Type II error can be significant in this scenario. The school superintendent must weigh the potential risks of making each type of error to make the best decision for the safety and well-being of the school community.

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Complete question is:

A school superintendent must make a decision whether or not to cancel school because of a threatening snow storm. What would the results be of Type I and Type II errors for the null hypothesis: The weather will remain dry?

A. Type I error: don't cancel school, but the snow storm hits.

Type II error: weather remains dry, but school is needlessly canceled.

B. Type I error: weather remains dry, but school is needlessly canceled.

Type II error: don't cancel school, but the snow storm hits.

C. Type I error: cancel school, and the storm hits.

Type II error: don't cancel school, and weather remains dry.

D. Type I error: don't cancel school, and snow storm hits.

Type II error: don't cancel school, and weather remains dry.

E. Type I error: don't cancel school, but the snow storm hits.

Type II error: cancel school, and the storm hits.

If LA Galaxy has won 36% of their soccer matches, this means that they have won 36/100 * 50 = 18 matches.

So, they have won 18 matches out of 50.

Step-by-step explanation:

percentage of soccer matches won = 36%

total matches = 50

matches won = 36/100 * 50

=18

The correct option is C which is out of 30000 there will be 27000 deaths.

According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.

Given, according to the website, 90% of the 30,000 deaths caused by unsafe water and filthy living conditions that occur every week around the world involve children under the age of five. All of the following interpretations of this statistic are accurate.

The percentage of deaths will be calculated as:-

Percentage = 30000 x 90%

Percentage = 30000 x 0.9

Percentage = 27000

Therefore, the number of deaths will be 27000.

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Option B : The market for DVDs is described by a downward sloping demand curve and an upward sloping supply curve. The price ceiling of $12 per DVD will result in a shortage of DVDs.

In a competitive market, the market price of a good will be set at the intersection of the demand curve and the supply curve. This is the point where the quantity of the good that consumers are willing to buy at a given price is equal to the quantity that producers are willing to sell. At this market price, producer surplus is equal to the area above the supply curve and below the market price, up to the quantity supplied.

In this scenario, the producer surplus will be equal to the area between the supply curve and the price ceiling, up to the quantity that is supplied. Based on the diagram, the producer surplus will be equal to $900,000.

So, the answer to the question is $900,000.

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The above figure shows the market for DVDs. The government decides that all citizens deserve to watch affordable DVDs so a price ceiling of $12 per DVD is placed on DVDs. After this price ceiling is in effect, producer surplus equals ________.

A. $1,800,000

B. $900,000

C. $400,000

D. $200,000

E. $100,000

Answer:

14.737

Step-by-step explanation:14 divided by .95 = 14.7368… then rounded to nearest hundred is 14.737

There will be 350 different haiku that can be made with the given words.

In this case, there are 5 syllables in the first line, 7 syllables in the second line, and 5 syllables in the last line, so the number of different haiku is given by the number of combinations of 3 elements taken from the set containing 5 elements (for the first and last lines) and 7 elements (for the second line), respectively.

This can be calculated as:

C(5,3) * C(7,3) = 10 * 35

= 350

So, there are 350 different haiku that can be made with the given words.

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If , Pete is saving $0. 45 each week to buy a video game that cost $9.0. Pete will have to save for 20 weeks to have enough money to buy the video game.

The problem asks us to find out how many weeks Pete will have to save to buy a video game that costs $9.0 if he is saving $0.45 each week. To solve this problem, we can use division to find out how many times $0.45 goes into $9.0.

We first divide the total cost of the game by the amount Pete saves each week, which gives us the number of weeks he will need to save.

In this case, the division of $9.0 by $0.45 yields 20, which means that Pete will have to save for 20 weeks to buy the video game. This calculation is important for Pete because it helps him plan his savings and gives him a goal to work towards. By saving $0.45 every week, he can keep track of his progress and stay motivated to reach his goal.

This problem highlights the importance of basic arithmetic skills, specifically division, in practical situations like budgeting and financial planning. By applying mathematical concepts to everyday situations, we can make informed decisions and manage our resources more effectively.

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Answer:

Right cylinder

Step-by-step explanation:

Right cylinder

a) The sampling distribution of p can be approximated as a normal distribution with mean μp = .17 and standard deviation σp = .0203.

b) The probability that the sample proportion will be within ±.02 of the population proportion is 0.6778

In statistics, sampling distribution plays a crucial role in estimating the parameters of a population. The sampling distribution helps us to understand the probability distribution of sample statistics that we obtain by taking random samples from a population.

a) In this case, we are interested in the proportion of households that spend more than $100 per week on groceries, denoted by p. We know that the population proportion is p = .17, and a sample of 800 households will be selected from the population.

The central limit theorem states that if the sample size is large enough (in this case, n = 800), then the sampling distribution of p will be approximately normal with a mean of p and a standard deviation of:

σp = √(p(1-p)/n)

where p is the population proportion, and n is the sample size. Plugging in the values, we get:

σp = √(.17(1-.17)/800) = .0203

b) Now, we want to find the probability that the sample proportion will be within ±.02 of the population proportion. That is, we want to find P(.15 ≤ p ≤ .19).

To calculate this probability, we need to standardize the distribution using the z-score formula:

z = (p - μp) / σp

Plugging in the values, we get:

z = (.15 - .17) / .0203 = -0.9867

z = (.19 - .17) / .0203 = 0.9867

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:

P(z ≤ -0.9867) = 0.1611

P(z ≤ 0.9867) = 0.8389

Therefore, the probability that the sample proportion will be within ±.02 of the population proportion is:

P(.15 ≤ p ≤ .19) = P(z ≤ 0.9867) - P(z ≤ -0.9867) = 0.8389 - 0.1611 = 0.6778

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Complete Question:

The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population.

a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries.

b. What is the probability that the sample proportion will be within ±.02 of the population proportion?

The given probability distribution for the random variables is valid

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The equation will be

The probability = Number of favorable outcomes / Total number of outcomes

The probability distribution is the probabilities of the each random event

From the table we can see that the probability distribution of each random events are

0.20, 0.15, 0.25, 0.40

Add the probability distributions of each random events

= 0.20 + 0.15 + 0.25 + 0.40

= 1

Here the sum of the probability distribution of the random events is 1

Therefore, the probability distribution is valid

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Answer:

Simple Interest

SI=PRT/100

P=€100

SI=€300-€100 = €200

T=10 years

rate = unknown

Rate = SIx100/(pxt)

Rate = 200x100/(100x10)

= 20%

b)Compound interest

CI = P(1+i)ⁿ

CI= €300

P =€100

n = 10

€300 = €100(1+i)¹⁰

take the tenth root of both sides

€1.77 = €1.58(1+i)

divide both sides by 1.58

1.12 = 1 + i

i = 1.12 - 1

i = 12%

c)si=prt/100

=(100x20x15)/100

= €300

total = 300+100

€400

CI = P(1+i)ⁿ

= 100(1+0.12)¹⁵

=€547.35

It is gathering more money with annual compound interest

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The trees will be the same height in 2 years and the height of these trees will be 22 ft.

A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=x+10. Where:

m= the slope.

b= the constant term that represents the y-intercept

For the given example: m=1 and b=10.

For solving the question you should convert the given text into an algebraic expression.

Tree01= 18+2*y

Tree02= 20.5+0.75*y (Note that  3/4=0.75)

y= number of years

Therefore,

18+2*y=20.5+0.75*y

2y-0.75*y=20.5-18

1.25y=2,5

y=2

Thus, at 2 years the trees will be the same height.

When y=2, you have:

Tree01= 18+2*y= 18+2*2=18+4=22

Tree02= 20.5+0.75*y =20.5+1.5=22

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The ordered pair (2,10) means that the cost to feed 200 animals is of $10,000.

The general format of an ordered pair is given as follows:

(x,y).

The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.

The variables for this problem are given as follows:

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The value of x for the trapezoid quadrilateral is equal to 5.

The quadrilateral is an isosceles trapezoid, with a line parallel to both opposing lines splitting the other two unparallelly going lines into equal halves. Hence, according to normal relations, the mid length is 5x-1.

The lengths of the opposing sides are 21 and 27 respectively. As a result, we may write 2(5x - 1) = 21 + 27.

Growing further, 10x - 2 = 48

10x = 48 + 2

10x = 50

Divide all sides by ten.

x = 50/10

x = 5

As a result, the value of x is 5.

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The equivalent expression with combined like terms is -5.5t + 6.3.

What is Equivalent expression?

Equivalent equations are algebraic equations with the same roots or solutions. We get an analogous equation by adding or subtracting the same number or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same non-zero value.

To combine like terms, we can group the terms with the variable t together, and group the constant terms together:

(-3.6t) + (-1.9t) + (1.2 + 5.1)

We can simplify the constant terms:

(-3.6t) + (-1.9t) + 6.3

Finally, we can combine the terms with the same variable by adding their coefficients:

-5.5t + 6.3

Therefore, the equivalent expression with combined like terms is -5.5t + 6.3.

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The student can combine like terms in the given expression by adding and subtracting the corresponding pairs. This gives the equivalent expression as 3.2t - 2.4.

To combine like terms in the equation -3.6 - 1.9t + 1.2 + 5.1t, you need to group together the like terms. The two like terms we have are the terms with the variable t, -1.9t and +5.1t, and the two constant terms -3.6 and +1.2 without the variable t.

When you add and subtract these pairs accordingly, you get:
-1.9t + 5.1t = 3.2t
-3.6 + 1.2 = -2.4

So, the equivalent expression that combines these like terms is: 3.2t - 2.4.

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The presented statement states that a square pyramid has a surface area of 340 cm².

For instance, we may calculate the area of a rectangle by multiplying its length by its width. The area of the rectangle seen above is 24 or 8. There are eight little squares in all if you count them.

The following formula may be used to determine a square pyramid's surface area:

(Base Area) + Surface Area (Area of 4 triangular faces)

The base area of the pyramid would have been 10 cm x 10 cm, or 100 cm2, as the pyramid's base is a squares with a diameter of ten centimeters.

Each triangle face's area may be calculated using the formula for

Area = (1/2)bh

where b denotes the bottom and h the top.

The area of each triangle face will be (1/2) x 10 cm x 12 cm = 60 cm², given that the pyramid's height is 12 cm.

As a result, the pyramid's total surface area would be as follows: 100 cm² + (4 x 60 cm²) = 100 cm² + 240 cm² = 340 cm².

So, the correct response is B) 340 cm².

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The point of intersection of two lines implies a system has one solution, therefore, Darnell should conclude that: B. there is exactly one solution to the system of equations.

If the two lines in a system of equations intersect when graphed, then there is exactly one solution to the system of equations. This is because the point of intersection represents the values of the variables that satisfy both equations simultaneously.

If the two lines in a system of equations are parallel and do not intersect when graphed, then there are no solutions to the system of equations. If the two lines are the same and coincide when graphed, then there are infinitely many solutions to the system of equations.

Therefore, Darnell should conclude that: B. there is exactly one solution to the system of equations.

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The fraction of income spent on cleaning is 71/50.

A fraction is represented by the ratio in the form -

{x} : {y} = {x}/{y}

In terms of numbers, we can write -

2 : 3 = 2/3

Given is that 2/5 of the income of a community of neighbors they are used in fuel, 1/8 in electricity, 1/12 in garbage collection, 1/4 in maintenance of the building and the rest is used for cleaning.

Assume the fraction to be {x}. Then, we can write -

2/5 + 1/8 + 1/12 + 1/4 + x = 1

0.4 + 0.125 + 0.083 + 0.25 + x = 1

x = 0.142

x = 142/100

x = 71/50

Therefore, the fraction of income spent on cleaning is 71/50.

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{Question in english -

2/5 of the income of a community of neighbors

they are used in fuel; 1/8 in electricity, 1/12

in garbage collection, 1/4 in maintenance of the

building and the rest is used for cleaning.

What fraction of the income is spent on cleaning?}

Limits function lim p(x) can be calculated if p is a polynomial function by:

To calculate the limits of a polynomial function, p(x), first identify the degree of the polynomial. Then, use the formula Lim p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₀, where an is the leading coefficient. For example, if the polynomial is of degree 3, then the formula would be:

Lim p(x) = a₃ x³ + a₂ x² + a₁ x + a₀.

Next, we need to subtitute the variable x with the defined limits. For example, if the defined limit of the function is 2, then the limit function would be:

Lim p(2) =  a₃ (2)³ + a₂ (2)² + a₁ (2) + a₀

Then, we just need to simplify our finding:

Lim p(2) =  8a₃ + 4a₂ + 2a₁ + a₀

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Answer:

25°

Step-by-step explanation:

look at the picture, that's the ans

Answer:

x = 25.4

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

139° is an exterior angle of the triangle, then

5x - 25 + 37 = 139

5x + 12 = 139 ( subtract 12 from both sides )

5x = 127 ( divide both sides by 5 )

x = 25.4