The manager of a bookstore sends a survey to 150 customers
who were randomly selected from a customer list. Nonbiased or biased?

Answer:

Darcy and Jason have $124 combined

Step-by-step explanation:

$124.

Jason- 20$ more than Darcy

Maria- Twice as much as Jason

Darcy- 20$ less than half of Maria's sum.

After I had written the page below, I came back up here and realized there was a much easier way.

268/2 = 134

Since the 20 Is added after, half is subtracted and you end up with

124!!

Now for my explanation done first, typed and read as I figured it out.

First and mostly, we need to find what Darcy starts with.

Let's say that Darcy has 5 dollars, to start somewhere easy. That would mean that Jason has 25 dollars since he has 20 more than her. That would mean that Maria would have 50 dollars, and the looted sum is 80.

Since that is less than a quarter of our end goal of 256$, I raised Darcy's initial amount of money to 15 to triple her money.

Math revised here- 15+20= (35*2) 70= 120

15+35+70

Since that is too low, I'm adding it to 30$.

Math revised again here- 30+20=(50*2)=100= 180

30+50+100

  5      15      30

 80    120    180

That is a chart determining our answers so far. There is no clear pattern, so let us continue.

Darcy starts with 50 dollars for this one.

50+20=(70*2)=140

50+70+140

260.

We are close to the sum.

Darcy starts with $52

52+20(72*2)= 144

52+72+144

268!

This means we have found how much Darcy has, and since Jason's amount depends on her, we have found both of their sums!

Answer:

5000

Step-by-step explanation:

1000 ÷ 2 = 500 x 10 = 5000

Answer:

Step-by-step explanation:

Formula for compound interest:

A= P(1+r/n)^n x t

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

We know that Serena pays annually meaning yearly (12 months or 1 year)

So after substituting all the numbers in,

A= 1000(1+0.02/12)^(12x10)

We change the rate to 0.02 because we must divide 2% by 100%. And divide the rate by number of times applied per time (n).

DISCLAIMER:

I have not done compound interest questions in a long time but if you want to confirm my answer, go to a calculator site and just input the numbers on there.

The Cartesian coordinate system is also referred to as a plane because it represents a two-dimensional space.

In mathematics, a plane is a flat surface that extends infinitely in all directions. The Cartesian coordinate system consists of two perpendicular lines, known as the x-axis and y-axis, which intersect at a point called the origin. These axes divide the plane into four quadrants.

The term "plane" in the context of the Cartesian coordinate system originates from the concept of a geometric plane, which is a fundamental concept in Euclidean geometry. In Euclidean geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions.

The Cartesian coordinate system borrows this concept and applies it to represent points, lines, curves, and shapes in a two-dimensional space.

By using the Cartesian coordinate system, we can assign coordinates (x, y) to any point in the plane, where the x-coordinate represents the horizontal position and the y-coordinate represents the vertical position.

This system allows us to precisely locate and describe objects or phenomena within the two-dimensional space, making it a valuable tool in various fields such as mathematics, physics, engineering, and computer graphics.

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Answer:9428.6

Step-by-step explanation:

To maximize his earnings, John should install 5 Secure alarms and 5 Maximum Secure alarms, and then demonstrate 5 Secure alarms and 2 Maximum Secure alarms.

Let's first consider the time constraints. Since John cannot work more than 40 hours per week, we have the following inequality:

1h(install Secure) x + 2.2h(install Maximum Secure) y + 0.25h(demo Secure) x + 0.4h(demo Maximum Secure) y <= 40

where x and y are the number of Secure and Maximum Secure alarms John installs, respectively.

John is required to work a minimum of 20 hours per week as an installer and a maximum of 20 hours as a demonstrator. So we have the following constraints:

1h(install Secure) x + 2.2h(install Maximum Secure) y >= 20 (minimum hours as installer)

0.25h(demo Secure) x + 0.4h(demo Maximum Secure) y <= 20 (maximum hours as demonstrator)

Now, we can set up the objective function to maximize John's earnings:

E(x,y) = 3(install Secure) x + 3(install Maximum Secure) y + 2(demo Secure) x + 2(demo Maximum Secure) y

= 5x + 5.6y

Using linear programming techniques, we can solve for the optimal values of x and y that maximize the objective function and satisfy the constraints. The optimal values turn out to be x=5 and y=5 for installing alarms, and x=5 and y=2 for demonstrating alarms. Therefore, John should install 5 Secure alarms and 5 Maximum Secure alarms, and then demonstrate 5 Secure alarms and 2 Maximum Secure alarms, to maximize his earnings.

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Answer:

Step-by-step explanation:

I'll rewrite 2x-y-4=0 to make it in slope-intercept form:

2x-y-4=0

-y = -2x + 4

y = 2x -4

This line has a slope of 2 and a y-intercept of -4.

See the attached graph.

Answer:

0.20×6

1.2

Step-by-step explanation:

boom

bam

pow

baba beep bum

P O W

We can conclude that C. the neighborhood is significantly less likely to be Democrat.

The null hypothesis was that there is no difference between the proportion of Democrats in the sample and the population. Since the null hypothesis has been rejected, it means that there is a significant difference between the sample and the population proportions. In this case, 60% of the respondents in the random sample are Democrats, which is lower than the 75% Democrat proportion in the community as a whole. Therefore, we can conclude that the neighborhood from which the sample was drawn is significantly less likely to be Democrat compared to the overall community.

The other options are not supported by the given information:

A type I error might or might not have occurred. We cannot determine this based on the information provided. A type I error refers to the incorrect rejection of a true null hypothesis. Without knowing the true proportions of the neighborhood, we cannot determine if a type I error has been committed. Whether a one-tailed test or a two-tailed test was used is not specified in the question.

However, the conclusion that the neighborhood is significantly less likely to be Democrat can be derived from either type of test. Therefore, the correct option is C.

The question was incomplete, Find the full content below:

sixty percent of the respondents in a random sample drawn from a neighborhood are democrats. the community as a whole is 75% democrat. the difference between sample and population has been tested and the null hypothesis has been rejected. what might we conclude? select one:

a. a type i error has been committed

b. a one-tailed test has definitely not been used

c. the neighborhood is significantly less likely to be democrat

d. the difference is not significant

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The width of the rectangle is 5 meters, and the length is 12 meters.

Let's denote the width of the rectangle as "W" (in meters) and the length as "L" (in meters).

According to the given information:

The length is 2 meters more than 2 times the width:

L = 2W + 2

The area of the rectangle is 60 square meters:

A = L * W

= 60

Substituting the expression for L from equation 1 into equation 2, we get:

(2W + 2) * W = 60

Expanding and rearranging the equation:

\(2W^2 + 2W - 60 = 0\)

Dividing the equation by 2 to simplify:

\(W^2 + W - 30 = 0\)

Now we can solve this quadratic equation. Factoring or using the quadratic formula, we find:

(W + 6)(W - 5) = 0

This equation has two solutions: W = -6 and W = 5.

Since the width cannot be negative, we discard the solution W = -6.

Therefore, the width of the rectangle is W = 5 meters.

To find the length, we can substitute the value of W into equation 1:

L = 2W + 2

= 2 * 5 + 2

= 10 + 2

= 12 meters

So, the width of the rectangle is 5 meters and the length is 12 meters.

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To find the size of the largest subset $s$ of $\{1,2,3,...,50\}$ such that no pair of distinct elements of $s$ has a sum divisible by 7,

we can use the pigeonhole principle.The set of integers $\{1,2,3,...,50\}$ can be partitioned into six subsets such that the sum of any two integers in the same subset is divisible by

7:$$ \{1, 8, 15, 22, 29, 36, 43, 50\},

$$$$ \{2, 9, 16, 23, 30, 37, 44\},

$$$$ \{3, 10, 17, 24, 31, 38, 45\},

$$$$ \{4, 11, 18, 25, 32, 39, 46\},$$$$ \{5, 12, 19, 26, 33, 40, 47\},

$$$$ \{6, 13, 20, 27, 34, 41, 48\}.

$$

Since there are six subsets, we can pick at most one element from each subset to form our subset $s$. Thus, the largest subset $s$ that satisfies the given condition has $8+7+7+7+7+7=43$ elements. Therefore, the size of the largest subset $s$ is $\boxed{43}.$

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Option C is the correct answer because the probability of having a hand with two pairs is given as approximately 24%

What is cumulative distribution function ?

The cumulative distribution function (CDF) is a function that gives the cumulative probability that a random variable X is less than or equal to a certain value x. It is denoted by F(x) and is defined as:

F(x) = P(X ≤ x)

where P(X ≤ x) is the probability that the random variable X takes a value less than or equal to x.

The CDF is used to describe the probability distribution of a random variable, which is a variable that takes on different values with certain probabilities. The CDF provides information about the probability that the random variable X takes a value less than or equal to a specified value x.

According to the question:
A geometric probability density function should not be used because it is used to model the number of trials needed to get the first success in a sequence of independent Bernoulli trials, which does not apply to this situation.

A cumulative distribution function (CDF) should be used to determine the probability that a player is dealt two pairs in the first hand. The CDF gives the probability that a random variable takes a value less than or equal to a specified value. In this case, the CDF would be used to find the probability that a player is dealt two pairs or fewer in the first hand.

Option C is the correct answer because the probability of having a hand with two pairs is given as approximately 24%, which implies a cumulative probability distribution function would be appropriate to use. The cumulative probability distribution function would give the cumulative probability of having two pairs or fewer in the first hand.

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Answer:

y + (1/4)(x + 4)

Step-by-step explanation:

One point on the graph is (-4, 0); another is (4, 2).

The change in x from the first point to the second is 8; this is the 'run.'

The change in y is 2 (which is 2 - 0).  This is the 'rise.'

Thus, the slope of the line is m = rise / run = 2/8 = 1/4

Let's use the point-slope form of the equation of a straight line:

y  - k = m(x - h).  Substituting 0 for k and -4 for h, we get:

y - 0 = (1/4)(x + 4), or

y + (1/4)(x + 4)

Answer:

58 =x

Step-by-step explanation:

The exterior angle is the sum of the opposite interior angles

114 = 56+x

114 -56 =x

58 =x

False. The statement that a cone and cylinder with the same height and bases of equal radius have equal volumes is incorrect.

The volume of a cone is given by the formula \(V_{cone}\) = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. On the other hand, the volume of a cylinder is given by the formula \(V_{cylinder }\) = πr²h, where r is the radius of the base and h is the height of the cylinder.

Comparing the formulas, we can see that the volume of the cone is one-third of the volume of the cylinder. Since the factor of one-third exists in the volume formula for the cone, the volumes of a cone and a cylinder with the same height and bases of equal radius are not equal. The cone will always have a volume that is one-third of the volume of the corresponding cylinder.

Therefore, the statement that the volumes of a cone and a cylinder with the same height and bases of equal radius are equal is false.

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Answer:

Step-by-step explanation:

\(18a ^{2} (c−8)÷27ab(c−8)\)

Answer:

15(a)(b)(c)

Step-by-step explanation:

I don't know what your asking for

Answer:

500=D 100=M

Step-by-step explanation:

I hope that helps :D

The initial value, base, domain and the range of the function are given in the explanation below.

Consider the exponential function: f(x) = 3(Five-fourths) Superscript x

The initial value for this function is 3

The base for this function is 5/4

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

The domain for this function is all real numbers.

The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range for this function is  y>0.

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Answer:

1) 3

2) 5/4

3) All real numbers

4) y>0

Step-by-step explanation:

Answer:

d. multiply the second equation by 4

Answer:

p(b|a) =5/7

Step-by-step explanation:

hello :

note : p(b|a) = p(a and b)/p(a)

p(b|a) = 25/35 =5/7

The value of the probability of the event B given A, symbolically P(B|A), when it is known that P(A) = 0.35, P(B) = 0.45 and P(A∩ B) =0.25 is found as: P(B|A) = 5/7

For two events A and B, by chain rule, we have:

\(P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)\)

where P(A|B) is probability of occurrence of A given that B already occurred.

We're given that:

Using the chain rule of probability, we get:

\(P(A \cap B) = P(A)P(B|A) \\\\P(B|A) = \dfrac{P(A \cap B)}{P(A)} = \dfrac{0.25}{0.35} = \dfrac{5}{7}\)

Thus, the value of the probability of the event B given A, symbolically P(B|A), when it is known that P(A) = 0.35, P(B) = 0.45 and P(A∩ B) =0.25 is found as: P(B|A) = 5/7

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Answer:

Step-by-step explanation:

Rap music is generally more popular with young blacks than young whites, during the 80s-90s when rap was becoming more popular with artists such as 2pac, BIG, Dr. Dre, etc they were more popular among young blacks than whites

Sale tax rate = 6.85%

To calculate the sale tax on a $14,000 Car, multiply 14,000 by the sale tax rate in decimal form ( divided by 100)

14,000 x (6.85/100) = 14,000 x 0.0685= $959

To find the final cost, add the sale tax amount to the price:

14,000 + 959 = $14,959

The total activity of the sample 12 days later is about 4.102 GBq, while the total activity of the sample 29.12 years later is about 4 GBq.

To determine the total activity of the sample 12 days later, we need to understand radioactive decay. Both 90Sr and 90Y are radioactive isotopes, meaning they decay over time.

The decay of a radioactive substance can be described using its half-life, which is the time it takes for half of the atoms in the substance to decay.

The half-life of 90Sr is about 28.8 years, while the half-life of 90Y is about 64 hours.

First, let's calculate the activity of the 90Sr after 12 days.

Since the half-life of 90Sr is much longer than 12 days, we can assume that its activity remains almost constant. So, the total activity of 90Sr after 12 days is still 4 GBq.

Next, let's calculate the activity of the 90Y after 12 days.

We need to convert 12 days to hours, which is 12 * 24 = 288 hours.

Using the half-life of 90Y, we can calculate that after 288 hours, only \(1/2^(288/64) = 1/2^4.5 = 1/34\) of the 90Y will remain.

So, the activity of the 90Y after 12 days is 3.48 GBq / 34 = 0.102 GBq.

Therefore, the total activity of the sample 12 days later is approximately 4 GBq + 0.102 GBq = 4.102 GBq.

To determine the total activity of the sample 29.12 years later, we can use the same logic.

The 90Sr will still have an activity of 4 GBq since its half-life is much longer.

However, the 90Y will have decayed significantly.

We need to convert 29.12 years to hours, which is 29.12 * 365.25 * 24 = 255,172.8 hours.

Using the half-life of 90Y, we can calculate that only \(1/2^(255172.8/64) = 1/2^3999.2 = 1/(10^1204)\) of the 90Y will remain.

This is an extremely small amount, so we can consider the activity of the 90Y to be negligible.

Therefore, the total activity of the sample 29.12 years later is approximately 4 GBq.

In summary, the total activity of the sample 12 days later is about 4.102 GBq, while the total activity of the sample 29.12 years later is about 4 GBq.

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Answer:

reciprocals

Step-by-step explanation:

HAVE A GOOD DAY AND BE SAFE WIT THIS RONA

Every positive integer can be expressed as the sum of distinct Fibonacci numbers.

To prove that every positive integer can be expressed as the sum of distinct Fibonacci numbers, we can use mathematical induction.

First, we establish the base cases:

1 is a Fibonacci number and is equal to itself, so it can be expressed as the sum of one Fibonacci number. Similarly, 2 is a Fibonacci number and can be expressed as the sum of one Fibonacci number.

Now, assume that every positive integer up to n can be expressed as the sum of distinct Fibonacci numbers. We want to show that n+1 can also be expressed in this way.

Let Fm be the largest Fibonacci number less than or equal to n+1. We know that Fm-1 is less than n+1, so we can express n+1 as the sum of Fm-1 and some smaller Fibonacci numbers (which are all less than Fm-1 because the Fibonacci sequence is increasing).

Because we assumed that every positive integer up to n can be expressed as the sum of distinct Fibonacci numbers, we know that Fm-1 can be expressed in this way. And because we are adding smaller Fibonacci numbers to Fm-1 to get n+1, we know that these smaller Fibonacci numbers are also distinct from the ones used to express Fm-1.

Therefore, we have shown that every positive integer can be expressed as the sum of distinct Fibonacci numbers

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Okay so we have 18 ppl we want 4 cookies per person

in one batch we can make 24

first multiple 18 by 4 or vice versa

answer is 72

now divide 72 by 24

answer is 3

we need 3 batches to make 4 cookies per person

The equation of the ellipsoid is\(\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1\)

The equation of an ellipsoid is represented as:

\(\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1\)

Given that the ellipsoid passes through the points (±6,0,0),(0,±7,0) and (0,0,±5)

It means that:

(±a,0,0)  = (±6,0,0)

(0,±b,0) = (0,±7,0)

(0,0,±c) = (0,0,±5)

By comparison, we have:

±a=±5

±b=±6

±c=±7

So, the equation of the ellipsoid becomes:

\(\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1\)

By substituting the values, the equation of the ellipsoid becomes is

\(\frac{x^{2} }{36}+\frac{y^{2} }{49} +\frac{z^{2} }{25} =1\)

.An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant. In an ellipse, there are two radius measures, one horizontally along the x-axis, the other vertically along the y-axis.For  a circle both these have the same value.

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Answer:

x = 6

Step-by-step explanation:

12x+252=324

Subtract 252 from each side

12x+252-252=324-252

12x =72

Divide each side by 12

12x/12 = 72/12

x =6

Answer:

the answer is attached to the picture

After solving the question by Pythagorean theorem we have: OM = PR(cos(ß) - sin(ß)) = cos(a + ß)(cos(ß) - sin(ß)) as the expression for the length of segment OM.

You may determine the right angled triangle's missing length using Pythagoras' Theorem. The triangle has three sides: the adjacent, which doesn't touch the hypotenuse, the opposite, which is always the longest, and the hypotenuse. Pythagoras' formula is: \(a^{2} + b^{2} = c^{2}\)

There seems to be a typo in the question, as "segment ON =" is not followed by an expression or value. However, I will provide an explanation based on the given information.

We start with the point (1,0) on the unit circle and rotate it counterclockwise by an angle of a + ß. This brings us to the point P on the circle, which has coordinates (cos(a + ß), sin(a + ß)).

Next, we draw a perpendicular segment PN from point P to the line ON, where O is the origin (0,0) and N is the foot of the perpendicular from P to ON. We also draw another perpendicular segment PR from point P to the x-axis.

From the right triangle ONP, we see that ON = sin(a + ß) (since sin is the y-coordinate of a point on the unit circle) and NP = cos(a + ß) - 1 (since the x-coordinate of P is cos(a + ß) and we started with the point (1,0)).

Using the Pythagorean theorem, we have:

\(OM^2 + NP^2 = ON^2\)

where OM is the segment from point O to the foot of the perpendicular from P to the x-axis (which we called R). Since OR is perpendicular to PR, we have OR = PR cos(90 - ß) = PR sin(ß), and since OP is perpendicular to PR, we have OP = PR cos(ß).

Thus, OM = OP - OR = PR cos(ß) - PR sin(ß) = PR(cos(ß) - sin(ß)).

Substituting this into the Pythagorean theorem equation, we have:

(PR(cos(ß) - sin(ß))) + (cos(a + ß) - 1) = sin(a + ß)

This is the expression for the length of segment OM.

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