7
You are comparing 3 different cell phone plans to see which is the cheapest:
Plan A costs a basic fee of $30 per month and $10 for every GB of data used
Try writing each plan as an
equation in y = mx + b form where
Plan B costs a basic fee of $80 per month with unlimited data
=GBs used and y total cost.
Plan C costs a basic fee of $50 per month and $5 for every GB of data used
You're looking to replace the m and
b in the equation. For Plan A, where
a) Write an equation for each plan that calculates the total cost (y) in terms of GB of data used (x) would the $30 go? Where would
the
Plan A:
Plan B:
Plan C:
$10 go?
b) Graph each plan on the following set of axes.
Cell Phone Plan Costs
Cost
100
c) When does Plan A cost the same as
Plan C?
80
60
d) Which plan is best if you only use 0-
4 GBs of data a month?
40:
20.
GBs of
8 10 data used
4
6
e) When does Plan B become the best
deal?

All of the mentioned hypotheses can potentially explain the cause of hypervolemia in a patient.


1. High aldosterone secretion: Increased aldosterone secretion leads to excessive salt reabsorption, causing water retention to maintain salt concentration balance.
2. Insufficient natriuretic peptides: When there are too few natriuretic peptides released, the stretching of the atria due to excess water volume does not inhibit ADH or aldosterone, causing hypervolemia.
3. Excess antidiuretic hormone secretion: Over-secretion of antidiuretic hormone results in excessive water retention and stimulation of thirst centers, leading to hypervolemia.

Hypervolemia can be caused by various factors, including increased aldosterone secretion, insufficient natriuretic peptides, and excess antidiuretic hormone secretion. Identifying the specific cause in a patient requires further examination and testing.

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A z-score of 4.334 indicates that the observation of 270 smokers who started smoking before 18 is about 4.334 standard deviations above the mean.

(a) To compute the mean and standard deviation of the random variable X, we need to know the parameters of the binomial distribution. In this case, the number of trials is 300, and the probability of success (smokers who started before 18) is 0.8.

Mean (μ) of a binomial distribution:

μ = n * p

μ = 300 * 0.8

μ = 240

The mean of the random variable X is 240.

Standard deviation (σ) of a binomial distribution:

σ = √(n * p * (1 - p))

σ = √(300 * 0.8 * (1 - 0.8))

σ = √(300 * 0.8 * 0.2)

σ = √(48)

σ ≈ 6.928

The standard deviation of the random variable X is approximately 6.928.

(b) The mean (240 in this case) represents the average number of adult smokers who started smoking before turning 18 years old in a sample of 300 trials. It provides a measure of central tendency for the distribution. In other words, on average, we would expect 240 adult smokers out of 300 to have started smoking before the age of 18.

(c) To determine if observing 270 smokers who started smoking before turning 18 years old in a random sample of 300 adult smokers is unusual, we can use the concept of z-scores. A z-score tells us how many standard deviations an observation is from the mean.

To calculate the z-score:

z = (x - μ) / σ

where x is the observed value (270), μ is the mean (240), and σ is the standard deviation (6.928).

z = (270 - 240) / 6.928

z ≈ 4.334

A z-score of 4.334 indicates that the observation of 270 smokers who started smoking before 18 is about 4.334 standard deviations above the mean. This is quite far from the mean, suggesting that it would be unusual to observe 270 smokers who started before turning 18 in a random sample of 300 adult smokers.

Note: The exact definition of what is considered "unusual" or an outlier can vary depending on the chosen significance level or threshold.

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The triangle DEF's section EF measures 24 units in length.

As per the data given in the above question are as bellow,

The provided details are as follow,

Procedure: Calculating the length that results from distorting a triangle by a scale factor

The triangle mentioned in the previous sentence is summarised in the diagram below. Using a trigonometric relationship, we discover that the following formula best describes the length of the section EF:

\($\sin a^{\circ}=\frac{E F}{D E}$\)

If we know that DE=30 and \($\sin a^{\circ}=\frac{4}{5}$\), then the length of the segment EF is:

\(E F=D E \cdot \sin a^{\circ} \\& E F=30 \cdot\left(\frac{4}{5}\right) \\\)

EF=24

Sine (sin), cosine (cos), and tangent (tan), which are defined in terms of the ratios of the sides of a right triangle, are the fundamental trigonometric functions.

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Note: The correct question would be as bellow,

A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees

15.5 units

24 units

30 units

37.5 units

Answer:

B) -4, - 1, 2, 5, 8

Step-by-step explanation:

Hope it helps you in your learning process

Step-by-step explanation:

A confounding variable is a variable that affects the independent and dependent variables and may cause a false association between them. Therefore, in this case:

A. Giving males a different sports drink than females could be a confounding variable since gender may affect their performance.

C. The timing of the sports drink consumption could also be a confounding variable since it may affect the athlete's performance.

D. Giving different brands of sports drinks to the athletes can be a confounding variable since the different formulas in the sports drinks might affect the results.

Therefore, options A, C, and D represent confounding variables. Option B does not represent a confounding variable since allowing athletes to choose their preferred drink from a cooler is a valid way to ensure that each athlete is comfortable with their sports drink.

Answer:

\(r^4 * r^3\\r^7\)

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

the second option

Step-by-step explanation:

i got this question before

There is not evidence that the population mean waiting time is different from 3.6 ​minutes.

What is the p-value?

A statistical measurement known as a p-value is employed to check a hypothesis' validity against actual data. A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct. The statistical significance of the difference that was found increases with decreasing p-value.

From the question, we know that the size (n), the mean (x), and the standard deviation (s) of the sample are 81, 3.45 minutes and 0.9 minutes. Additionally, we are going to decide if the waiting time is different or not from 3.6 minutes, so the null and alternative hypotheses are:

H0: m=3.6

H1:  m≠3.6

Where m is the mean of the population.

Then, we don't need to be concerned about the shape of the population distribution because the value of the n is bigger than 30 and we can use the statistic z as:

\(z = \frac{x-m}{\frac{a}{\sqrt{n} } }\)

So, replacing the values, the test statistic is:

\(z = \frac{3.45 - 3.6}{\frac{0.9}{\sqrt{81} } }\)

= 2.50

On the other hand, the p-value for this test is calculated as:

p-value = 2P(z >2.50) = 2(0.0668) = 0.134

Taking into account that the p-value is bigger than the level of significance 0.01, the null hypothesis is not rejected, and there is not evidence that the population mean waiting time is different from 3.6 ​minutes.

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The interest rate your friend is charging you for the $20,000 loan is 20% per year.

The simple interest is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is the interest rate and t is time.

Given that;

The Principal P = $20,000

Accrued amount A = $40,000

Elapsed time t = 5 years

Interest rate r =?

Plug these values into the above formula and solve for the interest rate r:

\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)

Converting r decimal to R a percentage

Rate R = 0.2 × 100%

Rate r = 20% per year

Therefore, the interest rate is 20% per year.

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A C - chart is used for Number of defects per unit.

What is C - chart?

In statistical quality control, the c-chart is a sort of control chart used to track "count"-type data, often the total number of nonconformities per unit. On rare occasions, it is also used to keep track of all the events that take place in a given period of time.

C-charts are used to assess if a process is predictable and stable as well as to track the results of process improvements before and after they have been made. The C - chart is particularly useful when there are few actual flaws in the subgroup but many potential for defects exist.

Count type data, such as the number of non-conformities per unit, are monitored using a statistical quality control chart known as a C-Chart.

Hence, a C - chart is used for Number of defects per unit.

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The completing the square method is a method for solving a quadratic equation in the form of ax2 + bx + c = 0.

To solve a quadratic equation by completing the square, the equation must first be written in the form of ax2 + bx = -c. The next step is to add (b/2)2 to both sides of the equation. This will give the equation (ax2 + bx + (b/2)2 = -c + (b/2)2. Then, factor the left side of the equation as a perfect square. The equation should now be in the form of (x + (b/2a))2 = -c + (b/2)2 + (b/2a)2. The final step is to take the square root of both sides of the equation, resulting in x = -(b/2a) ± √(-c + (b/2)2 + (b/2a)2). This is the solution to the quadratic equation.

For example, consider the equation 2x2 + 8x = -4.

2x2 + 8x + (8/2)2 = -4 + (8/2)2

(2x + 4)2 = -4 + 16

2x + 4 = ±√20

x = -4 ± √20/2

Therefore, the solutions to the equation are x = -4 ± √5.

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AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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To prove the properties of the projection matrix, we'll assume that p is the projection matrix corresponding to a subspace S of \(R^{m}\).

(a) p² = p

To show that p² = p, we need to demonstrate that applying the projection matrix p twice is equivalent to applying it once.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, if we apply the projection matrix p again to p(x), we have:

p(p(x)) = projection of p(x) onto S

Since p(x) is already the projection of x onto S, applying the projection matrix p once more won't change the result. Hence, we can write:

p(p(x)) = p(x)

This equation holds for any vector x in \(R^{m}\), meaning that p² = p.

(b) \(p^{T}\) = p

To prove that \(p^{T}\) = p, we need to show that the transpose of the projection matrix p is equal to p.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, let's compute the transpose of p(x):

\((p(x))^{T}\) = \((projection of x onto S)^T\)

The transpose of a projection onto a subspace doesn't change the result because it only affects the column vectors of the projection matrix. The transpose of p(x) is still the projection of x onto S. Hence, we can write:

\((p(x))^T\) = p(x)

Since this equation holds for any vector x in \(R^{m}\), we can conclude that \(p^T\) = p.

Therefore, we have shown that (a) p² = p and (b) \(p^T\) = p, proving the properties of the projection matrix corresponding to a subspace S of \(R^{m}\).

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Answer:

The slope is -5/2 as a fraction

or -2.5 as a decimal.

Step-by-step explanation:

First we have to get it into this format y = mx + b

5x + 2y = 6 (subtract 5x on both sides)

2y = -5x + 6 (divide by 2 on both sides)

y = -5/2x + 3

The slope is -5/2 or -2.5

Hope this helps ya!!

Answer: 402.1

Step-by-step explanation:

Answer:

$141,557.76

Step-by-step explanation:

Chao bought a boat for 160,000

The value of the boat reduces by 4% every year

Therefore the value of the most at the end of three years can be calculated as follows

= 100%- 4%

= 96%

= 160,000 × 96/100^3

= 160,000 × 0.96^3

= 160,000 × 0.884736

= 141,557.76

Hence the price of the boat after 3 years is 141,557.76

Answer:

not B

Step-by-step explanation:

I took the test

Substitute the variables for the numbers. Then solve.

b⁵ = 3⁵ = 243

c⁶ = 4⁶ = 4096

b³ = 3³ = 27

c³ = 4³ = 64

(243)(4096)/(27)(64) = 576

Answer:

simplify the powers, so b^(5-3) * c^(6-3) =

b^2 * c^3 = 3^2 * 4^3 =

9 * 64 = 576

Answer:

graph 1: f(x) = 3*x^2 - 5*x

graph 2: f(x) = 3*x^2 + 5

graph 3: f(x) = -3*x^2 - 5

Step-by-step explanation:

This is ratter easy if we know some of the main rules for quadratic equations.

For a quadratic equation:

y = f(x) = a*x^2 + b*x + c

if a > 0, then the arms of the graph will open upwards.

if a < 0, then the arms of the graph open downwards.

With this in mind we can look at the graphs, only one of them have arms that open downwards, then the function that matches with this graph should be the only one with a leading coefficient smaller than zero, which is:

f(x) = -3*x^2 - 5

Now, when we have functions like:

y = f(x) = a*x^2 + c

c is the value of y at the vertex.

In graph 2 we can see that the arms open upwards, and that the y-value at the vertex is positive (it is above the horizontal axis)

Then the function of graph 2 should have a positive leading coefficient and a positive constant term.

The function is:

f(x) = 3*x^2 + 5

Then the remaining function is the one that corresponds to graph 1

f(x) = 3*x^2 - 5*x

Then we have:

graph 1: f(x) = 3*x^2 - 5*x

graph 2: f(x) = 3*x^2 + 5

graph 3: f(x) = -3*x^2 - 5

The method has statistical significance but does not have practical significance, and therefore should not be used to make conclusions.

1. The statement mentions that there is a % chance of getting that many babies born female if the method had no effect.
2. Since the method increases the likelihood of a baby born female from the approximately 50% rate expected by chance to 51%, it has statistical significance.
3. However, not many couples would likely use a procedure that only slightly raises the likelihood of a baby born female, so it does not have practical significance.

In conclusion, the method has statistical significance but does not have practical significance, and therefore should not be used to make conclusions.

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The percentage of attorneys in given range is approximately 50%.

The boxplot below represents the salaries of attorneys in Los Angeles.

We can estimate the percentage of attorneys who have salaries between $55,000 and $80,000 by counting the number of boxes between the range (called the interquartile range, or IQR), which is from $55,000 to $80,000.

There are two boxes within the range, and two boxes that are not within the range (called the lower and upper outliers).

Thus, the percentage of attorneys with salaries between $55,000 and $80,000 is approximately 50%.

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The rule for a rotation by 270 ° about the origin is (x,y) ⇒ (y,-x)

Rotating the triangle PQR to create an image of the triangle involves moving the triangle PQR in a circular direction.

The coordinates of the given triangle are:

Using the rule, the coordinates now are:

In the attatchment, the answer is in pictoral form.

Given:

Rule of transformation is rule R x-axis ∘ T⟨–5, 3⟩.

The point is (-3,-2).

To find:

The image of given point after the transformation.

Solution:

Consider the given point be P(-3,-2).

Rule of transformation is rule R x-axis ∘ T⟨–5, 3⟩. If means first we have apply translation T⟨–5, 3⟩ after that we have to apply reflection R x-axis.

If a figure translated by T⟨–5, 3⟩, then

\((x,y)\to (x-5,y+3)\)

\(P(-3,-2)\to P'(-3-5,-2+3)\)

\(P(-3,-2)\to P'(-8,1)\)

If a figure reflected by R x-axis, then

\((x,y)\to (x,-y)\)

\(P'(-8,1)\to P''(-8,-1)\)

Therefore, the image of given point after transformation is (-8,-1).

Answer:

58

Step-by-step explanation:

i think

Answer:

1 gallon : 25.6 miles

Step-by-step explanation:

So, the way we can find the rate, or ratio between 2 units is to divide one unit by the other unit.

So basically, we see the first set of units is:

2 gallons - 51.2 miles

So basically, for every 2 gallons, there are 51.2 miles.

To find the ratio, or rate, we must find the miles per gallon.

We can do that by dividing both sides by 2:(g=gallons, m=miles)

2g/2=51.2/2m

=

g=25.6

So for every gallon, there is 25.6 miles.

We can write this as:

1 : 25.6

Hope this helps!

Answer:

25.6

Step-by-step explanation:

51.2/2=25.6

Answer:

perimeter of rectangles = 2 ( l + b)

34 = 2 ( x + 2 + 3x - 4 )

34 = 2 ( 4x - 2 )

34 = 8x - 4

38 = 8 x

38/ 8 = x

thus , x = 4.75 inches

Answer:

x=19/4

Step-by-step explanation:

perimeter is the sum of all sides

so

perimeter given is 34 = (x+2)+(x+2)+(3x-4)+(3x-4)

34=8x-4

34=8x

x=34/8 which reduces to 19/4

The true statement is (d) the product of c and b could be multiplied by one-third.

The variation equation can be represented as:

\(a = \frac{bc}{d}\)

When the value of d is tripled, the equation becomes

\(a = \frac{bc}{3d}\)

This means that: the product of c and b could be multiplied by one-third.

Hence, the true statement is (d)

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The median and quartiles fall in the middle age classes.

The median is the middle value in a set of data, meaning that half of the data falls below the median and half falls above it. The quartiles divide the data into four equal parts, with the first quartile (Q1) being the 25th percentile, the second quartile (Q2) being the median or 50th percentile, and the third quartile (Q3) being the 75th percentile.

In terms of age classes, the median and quartiles would fall in the middle age classes. For example, if the age classes were 0-10, 11-20, 21-30, 31-40, 41-50, 51-60, 61-70, 71-80, and 81-90, the median and quartiles would fall in the 21-30, 31-40, and 41-50 age classes.

It is important to note that the specific age classes that the median and quartiles fall in will depend on the distribution of the data. However, they will always fall in the middle age classes, as they represent the middle values of the data set.

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