Jerry spent ¾ of his allowance on baseball cards. If he was given S20, how mch did he spend on baseball cards.

Answer:

131ft is the amount of fencing material needed

Step-by-step explanation:

Perimeter is the distance around a shape: we have to sum all the distances

P = d1 + d2 + d3

P = 34 ft + 30 ft + 67 ft = 131 ft

Answer:

D. 131 ft.

Step-by-step explanation:

If Sarah is planning to fence in her backyard garden and one side of the garden is 34 feet long, another side is 30 feet long, and the third side is 67 feet long. The perimeter of Sarah’s garden to determine the amount of fencing material needed is 131 feet.

Answer:

4/7

Step-by-step explanation:

To find the probability, we must first find the total number of golf balls. So 99+88+44 = 231 is our total. Now we must find the number of golf balls that are not a type A ball. This is just the total number of type B balls and type C balls. So 88+44 = 132. So the probability is 132/231. This simplifies to 12/21 or 4/7.

Answer:

Step-by-step explanation:

A) Suppose that we have the complex numbers

[tex]z= x + iy \quad \text{and} \quad \\\\ \tilde{z}=\tilde{x} + i \tilde{y}[/tex]

Remember that to sum complex numbers, we sum the real parts of the two numbers to get the real part and the imaginary parts of the two numbers to get the imaginary part. Hence,  

[tex]z+\tilde{z} = (x + i y) + (\tilde{x} + i \tilde{y}) = (x + \tilde{x})+i (y+\tilde{y})[/tex]

On the other hand, if we sum the matrix visualizations of [tex]z \quad \text{and} \quad \tilde{z}[/tex] we get

[tex]\left[\begin{array}{cc}x &y\\-y&x\end{array}\right] + \left[\begin{array}{cc}\tilde{x}&\tilde{y}\\ -\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x + \tilde{x}& y + \tilde{y}\\-(y+\tilde{y})&x+\tilde{x}\end{array}\right][/tex]

which is the matrix visualization of [tex]z + \tilde{z}[/tex].

To multiply two complex numbers, we use the distributive law to multiplly and then separete the real part from the imaginary part

[tex]z \cdot \tilde{z}= (x + iy) \cdot (\tilde{x} + i \tilde{y})=(x \tilde{x} + i x \tilde{y} + i \tilde{x} y - y\tilde{y} ) = (x\tilde{x}-y\yilde{y})+i(x\tilde{y}+\tilde{x}y)[/tex]

Again, if we multiply the matrix visualizations of [tex]z \quad \text{and} \quad \tilde{z}[/tex] we get

[tex]\left[\begin{array}{cc}x&y\\-y&x\end{array}\right]\left[\begin{array}{cc}\tilde{x}&\tilde{y}\\-\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x\tilde{x}-y\tilde{y}&x\tilde{y}+y\tilde{x}\\-y\tilde{x}-x\tilde{y}&x\tilde{x}-y\tilde{y}\end{array}\right][/tex]

which is the matrix viasualization of [tex]z\cdot\tilde{z}.[/tex]

B)  Since the usual matrix operations are consisten with the usual addition and multiplication rules in the complex numbers, we can use them to find the multiplicative inverses of a complex number [tex]z=x+iy[/tex].

We are looking for the complex number [tex]z^{-1}=(x+iy)^{-1}[/tex] which in terms of matrices is equivalent to find the matrix

[tex]\left[\begin{array}{cc}x&y\\-y & x\end{array}\right]^{-1}= \dfrac{1}{x^{2}+y^{2}} \left[\begin{array}{ccc}x&-y\\y&x\end{array}\right][/tex]    

Hence,

[tex]z^{-1}=\dfrac{1}{x^2 +y^2} (x-iy)=\dfrac{1}{|z|^2}(x-iy)[/tex]

Answer:

After 25 years the amount will be $78099.34.

Step-by-step explanation:

The compound interest formula is ;

[tex]A=p(1+r/n)^{nt}[/tex]

Where p = 22000

r = 5.1% or 0.051

n = 4

t = 25

So, putting the values in formula we get;

[tex]A=22000(1+0.051/4)^{100}[/tex]

[tex]A=22000(1.01275)^{100}[/tex]

A = $78099.34

Therefore, after 25 years the amount will be $78099.34.

Answer:

Step-by-step explanation:

X= quarts of sauce # 1 ( 17% of sugar)

Y= quarts of sauce # 2( 30 % of sugar )

General Balance

[tex]X+Y=2.6[/tex]      EQ (1)

[tex]Y=2.6-X\\[/tex]

SUGAR BALANCE

[tex]0.17X+0.3Y=2.6*0.24\\[/tex]   EQ (2)

replace Y from eq(1) into eq(2)

[tex]0.17X+0.3(2.6-X)=0.624\\0.17X+0.78-0.3X=0.624\\-0.13X=0.624-0.780\\X=\frac{-0.156}{-0.13} \\X= 1.2\\Y=2.6-1.2=1.4[/tex]

Answer:

296 cubic feet

Step-by-step explanation:

First and foremost, you have to have everything in either feet or inches.  Right now they are in both.  Since the answer is asked for in feet, let's convert everything to feet.  The width is already in feet, so that's good.

However, even though the length is 49 feet, we still have to convert the 4 inches part of that to feet.  Using the fact that there are 12 inches in a foot:

[tex]4in.*\frac{1ft}{12in.}=\frac{1}{3}ft[/tex] so we have

[tex]49\frac{1}{3}ft[/tex]

Convert that to improper to make the multiplication easier in the end:

[tex]49\frac{1}{3}=\frac{148}{3}ft[/tex]

Now we have to convert the 8 inches to feet using the same reasoning:

[tex]8in.*\frac{1ft}{12in.}=\frac{2}{3}ft[/tex]

Now everything is in terms of feet.  The volume is found by multiplying length times width times height:

[tex](\frac{148}{3} )(\frac{9}{1})(\frac{2}{3})=  \frac{2664}{9}ft[/tex]

Divide that and it comes out to an even 296 cubic feet

To evaluate the triple integral, set up the limits of integration based on the given bounds. The parabolic cylinder and the planes define the limits for x, y, and z. Evaluate the triple integral using appropriate integration techniques.

To evaluate this triple integral, we need to set up the limits of integration based on the given bounds of the parabolic cylinder and the planes. The parabolic cylinder is defined by the equation z = 25 - y^2, so we need to find the limits for x, y, and z. Since the plane z = 0 is a boundary, the lower limit of integration for z is 0. The other boundary planes, x = 5 and x = -5, set the limits for x. For y, we need to find the limits based on the parabolic cylinder equation. By rearranging the equation, we have y = ±sqrt(25-z), which gives us the upper and lower limits for y.

Now, we can set up the triple integral as follows:

∫-55 ∫-sqrt(25-z)sqrt(25-z) ∫025-y^2 x^6e^y dzdydx

We can then evaluate this triple integral using the appropriate integration techniques, such as using the power rule and integration by parts for the x^6e^y term.

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To evaluate the triple integral, we need to find the limits of integration for each variable. Given the given bounds, the limits for x and y can be determined, and then the integral can be solved using standard techniques.

To evaluate the triple integral, we need to find the limits of integration for each variable.

Given that E is bounded by the parabolic cylinder z = 25 - y^2 and the planes z = 0, x = 5, and x = -5, the limits for y will be -√(25-x^2) to √(25-x^2), the limits for x will be -5 to 5, and the limits for z will be 0 to 25 - y^2.

The integral becomes: ∫∫∫ x^6e^y dz dx dy, with the limits as mentioned above. You can now solve this triple integral using standard integration techniques.

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The value of  X  is 55.

The detailed answer explains how to solve the equation for x by following a step-by-step process.

Solve the equation for x:

Answer:  The correct option is (C) 38.

Step-by-step explanation:  Given that a polyhedron has 20 vertices and 20 faces.

We are to find the number of edges of the polyhedron using Euler's formula.

Euler's formula :

For any polyhedron, the number of vertices and faces together is exactly two more than the number of edges.

Mathematically, V − E + F = 2, where V, E and F represents the number of vertices, number of edges and number of faces of the polyhedron.

For the given polyhedron, we have

number of vertices, V = 20,

number of faces, F = 20

and

number of edges, E = ?

Therefore, from Euler's formula

[tex]V-E+F=2\\\\\Rightarrow 20-E+20=2\\\\\Rightarrow 40-E=2\\\\\Rightarrow E=40-2\\\\\Rightarrow E=38.[/tex].

Thus, the required number of edges of the given polyhedron is 38.

Option (C) is CORRECT.

Using Euler's formula V - E + F = 2 for a polyhedron with 20 vertices and 20 faces, we find that the number of edges (E) is 38.

The question pertains to finding the number of edges of a polyhedron using Euler's formula, which states V - E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. Given that the polyhedron has 20 vertices (V = 20) and 20 faces (F = 20), we can rearrange Euler's formula to solve for the number of edges (E): E = V + F - 2. Plugging in the values we get E = 20 + 20 - 2, which simplifies to E = 38. Therefore, the polyhedron has 38 edges.

Answer:

5.92 per cheesecake.

Step-by-step explanation:

The initial number cherry cheesecakes = 280,

Also, the cost of each cheesecakes = $ 2.51,

So, the total cost price = 280 × 2.51 = $ 702.8,

Markup = 65 %,

Thus, the total selling cost = 702.8 + 65% of 702.8 = $ 1159.62,

Now, the spoilage rate = 30 %,

So, the total new number of cheesecakes = 280 - 30% of 280 = 280 - 84 = 196,

Hence, the selling cost of each cheesecake = [tex]\frac{1159.62}{196}[/tex]

[tex]=\$ 5.91642857143[/tex]

[tex]\approx \$ 5.92[/tex]

Answer:

r(q(-4)) = -10

Step-by-step explanation:

q(x) = -x - 2

r(x) = -2x^2 -2

r(q(-4))

First find q(-4)

Let x=-4

q(-4) = -(-4) - 2

q(-4) = +4 -2 = 2

q(-4) =2

We substitute this value in for x in r(x)

r(2) = -2(2)^2 -2

     = -2 (4) -2

     = -8 -2

     = -10

For this case we have the following functions:

[tex]q (x) = - x-2\\r (x) = - 2x ^ 2-2[/tex]

We must find [tex]r (q (x))[/tex]. So:

We substitute [tex]q (x)[/tex]in [tex]r (x).[/tex]

[tex]r (q (x)) = - 2 (-x-2) ^ 2-2[/tex]

Now we substitute[tex]x = -4[/tex]

[tex]r (q (-4)) = - 2 (- (- 4) -2) ^ 2-2\\r (q (-4)) = - 2 (+ 4-2) ^ 2-2\\r (q (-4)) = - 2 (2) ^ 2-2\\r (q (-4)) = - 2 (4) -2\\r (q (-4)) = - 8-2\\r (q (-4)) = - 10[/tex]

Answer:

[tex]r (q (-4)) = - 10[/tex]

a)

[tex]6\cdot5\cdot2\cdot2=120[/tex]

b)

[tex]4\cdot5\cdot2\cdot2 +2\cdot5\cdot1\cdot1=80+10=90[/tex]

Answer:

Step-by-step explanation:

37

Final answer:

In the political party's survey example, the population is all registered voters in the community, the sample is the 1500 randomly selected voters, and the situation is an example of a survey with nonresponse bias.

Explanation:

Understanding Population and Sample in Surveys

When it comes to surveys, it's important to differentiate between a population and a sample. For the political party's mail survey:

The population refers to all registered voters in the community since they are the entire group of individuals the survey is designed to understand and represent.

The sample is the 1500 randomly selected voters who received the questionnaire, as they are a manageable number intended to represent the larger population of all registered voters in the community.

This example is of a survey containing nonresponse bias, because a significant portion of the surveys were not returned, which could skew the results and not accurately represent the overall population.

Nonresponse is an issue that affects the reliability and accuracy of survey results because those who do not respond could have systematically different views from those who do. This is an example of nonsampling error, as the error arises not from the method of selecting the sample but from the lack of responses.

Final answer:

The population in the survey is all registered voters in the community, and the sample is the 1500 randomly selected voters. This scenario is an example of a survey containing nonresponse bias.

Explanation:

In the scenario described, the population is Option C) all registered voters in this community, since the study seeks to understand an attribute (opinion on the president's job performance) of this entire group. The sample is Option B) the 1500 randomly selected voters receiving the questionnaire, as they are the portion of the population supposed to represent the larger group's opinions. The issue described is an example of B) a survey containing nonresponse bias, which occurs when the subset of the sample that responds (480 returned surveys) is different in some way from those who do not respond, which can potentially skew the survey results. Finally, nonresponse bias is a critical challenge in survey methods since response rates can affect the representativeness of the sample and hence the accuracy of the survey's conclusions.

Answer: 0.0081

Step-by-step explanation:

Let X be the number of rafts.

Given : The mean number of rafts floating : [tex]\lambda=0.4[/tex] rafts per day .

Then , for 7 days the number of rafts = [tex]\lambda_1=\lambda\times 7=0.4\times7=2.8[/tex] rafts per day .

The formula to calculate the Poisson distribution is given by :_

[tex]P(X=x)=\dfrac{e^{-\lambda_1}\lambda_1^x}{x!}[/tex]

Now, the  probability that they will have to wait more than a week is given by :-

[tex]P(X>7)=1-P(X\leq7)\\\\=1-(P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(5)+P(6)+P(7))\\\\=1-(\dfrac{e^{-2.8}2.8^{0}}{0!}+\dfrac{e^{-2.8}2.8^{1}}{1!}+\dfrac{e^{-2.8}2.8^{2}}{2!}+\dfrac{e^{-2.8}2.8^{3}}{3!}+\dfrac{e^{-2.8}2.8^{4}}{4!}+\dfrac{e^{-2.8}2.8^{5}}{5!}+\dfrac{e^{-2.8}2.8^{6}}{6!}+\dfrac{e^{-2.8}2.8^{7}}{7!})\\\\=1-0.991869258012=0.008130741988\approx0.0081[/tex]

Hence, the required probability : 0.0081

Answer:0.0206

Step-by-step explanation:

Using Binomial distribution for a sample of 20 adults

Let r denotes the no of correct answers out of 20

Probability that fewer than 6 people will guess correctly is P(r<6)

P(r<6)=P(r=0)+P(r=1)+P(r=2)+P(r=3)+P(r=4)+P(r=5)

[tex]P(r=0)=^{20}C_0\left ( 0.5\right )^{0}\left ( 0.5\right )^{20}=\left ( 0.5\right )^{20}[/tex]

[tex]P(r=1)=^{20}C_0\left ( 0.5\right )^{1}\left ( 0.5\right )^{19}=20\left ( 0.5\right )^{20}[/tex]

[tex]P(r=2)=^{20}C_0\left ( 0.5\right )^{2}\left ( 0.5\right )^{18}=190\left ( 0.5\right )^{20}[/tex]

[tex]P(r=3)=^{20}C_0\left ( 0.5\right )^{3}\left ( 0.5\right )^{17}=1140\left ( 0.5\right )^{20}[/tex]

[tex]P(r=4)=^{20}C_0\left ( 0.5\right )^{4}\left ( 0.5\right )^{16}=4845\left ( 0.5\right )^{20}[/tex]

[tex]P(r=5)=^{20}C_0\left ( 0.5\right )^{5}\left ( 0.5\right )^{15}=15,504\left ( 0.5\right )^{20}[/tex]

[tex]P(r<6)=\left ( 0.5\right )^{20}\left [ 1+20+190+1140+4845+15504\right ][/tex]

[tex]P(r<6)=\left ( 0.5\right )^{20}\times 21,700[/tex]

P(r<6)=0.02069

Answer:

210

Step-by-step explanation:

In 2005 the employee was tripple of 1995 which is 50×3=150. So number of employees in 2005=150.

In 2015 number of employees were 40% of employees in 2005.

40% of 150 =150×40÷100 = 60,

Therefore number of employees in 2015 =150+60= 210 employees.

Answer:

210 employees in 2015

Step-by-step explanation:

In order to solve this we first have to calculate the number of employees that there were in 2005, since the problem says that they tripled their employees from 1995, that meas three times 50, meaning 150 employees in 2005, if by 2015 the number of employees had increase in 40% we just do a simple rule of three, 150 being the 100% and trying to calculate the 140%:

[tex]\frac{150}{100}= \frac{x}{15} \\x=\frac{150*15}{100}\\ x= 210[/tex]

So now we know that there were 210 employees in 2015.

Answer: 95.45 %

Step-by-step explanation:

Given : The distribution is bell shaped , then the distribution must be normal distribution.

Mean : [tex]\mu=\ 16[/tex]

Standard deviation :[tex]\sigma= 1.5[/tex]

The formula to calculate the z-score :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x = 13

[tex]z=\dfrac{13-16}{1.5}=-2[/tex]

For x = 19

[tex]z=\dfrac{19-16}{1.5}=2[/tex]

The p-value = [tex]P(-2<z<2)=P(z<2)-P(z<-2)[/tex]

[tex]0.9772498-0.0227501=0.9544997\approx0.9545[/tex]

In percent, [tex]0.9545\times100=95.45\%[/tex]

Hence, the percentage of data lie between 13 and 19 = 95.45 %

Answer: the technicians have 19 hours to correct the problem.

Step-by-step explanation:

The countdown started at "T-minus 27 hours" that means that the clock starts ticking backwards and if an hour passes away the lime left for the launch will be 26 hours and the limit the technicians have is T minus 8 hours so the problem can be solved with a simple substraction 27 hours minus 8 hours equals 19 hours.

Answer:

R indicates Random Assignment

Step-by-step explanation:

In designing an experiment, R is the symbol used for assigning the subjects randomly to different groups through randomization. It is called random assignment and It is the option (d) random assignment. It is achieved by using chance procedure ( random number generator, by flipping coin, throwing ). This ensures that all the subjects have equal chance of placing in all the groups.

Option (a) Symbol O is used for Observations. (So option (a) is wrong answer)

Option (b) Symbols x , y are used as Observational variables (So option (b) is wrong answer)

Option (c) Comparison groups is wrong answer as R is not used for that.

The symbol R in experimental design represents random assignment, a technique used to ensure that groups in an experiment are initially equivalent and thereby allow researchers to make causal inferences.

In experimental design, the symbol R indicates random assignment. Random assignment is a process used to create initial equivalence between the groups in an experiment, which is crucial for allowing researchers to draw causal conclusions. In this process, participants are assigned to different groups or conditions on a random basis, such as by drawing numbers or using a random number generator.

Random assignment minimizes the effects of lurking variables, ensuring that before the experimental manipulation occurs, the groups can be considered equivalent on various potential confounding factors. When individuals are selected into groups denoted by R, we can generally classify these designs as experimental, as opposed to nonexperimental designs where nonrandom assignment (NR) is indicated.

For example, in a study where the size of tableware is manipulated to see its effect on food consumption, the psychologist would use random assignment to ensure that both treatment groups are comparable prior to the intervention, which is the manipulation of the independent variable.

Answer:

wow that school has alot of test don't it lol

Step-by-step explanation:

anyway what's the question

After calculating the Z-scores for the student's performance in each class, we found that she performed closer to the top of her class in statistics. Thus, she did relatively better on the statistics exam compared to the chemistry exam.

To determine relative performance in each class, we need to calculate the number of standard deviations the student's score is from the mean (also known as a

Z-score

).

For the chemistry exam, where the mean was 90 and the standard deviation was 64, the student's Z-score is: (102 - 90) / 64 = 0.1875.

For the statistics exam, with a mean of 70 and standard deviation of 16, the student's Z-score is: (77 - 70) / 16 = 0.4375.

Comparing these Z-scores, we can conclude that the student did relatively better in the statistics class because her Z-score (0.4375) was higher there than in her chemistry class (0.1875). This indicates she performed closer to the top of her class in statistics. Therefore, the answer would be selection C: the student did relatively better on the statistics exam than on the chemistry exam, compared to the other students in the two classes.

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Answer:

[tex]P =0.3998[/tex]

Step-by-step explanation:

Let [tex]{\displaystyle {\overline{x}}}[/tex] be the average of the sample, and the population mean will be [tex]\mu[/tex]

We know that:

[tex]\mu = 4095[/tex] gr

Let [tex]\sigma[/tex] be the standard deviation and n the sample size, then we know that the standard error of the sample is:

[tex]E=\frac{\sigma}{\sqrt{n}}[/tex]

Where

[tex]\sigma=569[/tex]

[tex]n=130[/tex]

In this case we are looking for:

[tex]P(|{\displaystyle{\overline{x}}}- \mu|>42)[/tex]

This is:

[tex]{\displaystyle{\overline{x}}}- \mu>42[/tex] or [tex]{\displaystyle{\overline{x}}}- \mu<-42[/tex]

[tex]P=P({\displaystyle{\overline{x}}}- \mu>42)+ P({\displaystyle{\overline{x}}}- \mu<-42)[/tex]

Now we get the z score

[tex]Z=\frac{{\displaystyle{\overline{x}}}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]P=P(z>\frac{42}{\frac{569}{\sqrt{130}}}) + P(z<-\frac{42}{\frac{569}{\sqrt{130}}})[/tex]

[tex]P=P(z>0.8416) + P(z<-0.8416)[/tex]

Looking at the tables for the standard nominal distribution we get

[tex]P =0.1999+0.1999[/tex]

[tex]P =0.3998[/tex]

The [tex]n[/tex]-th term in the series is 6 multiplied by the [tex](n-1)[/tex]-th power of 5/6:

[tex]a_1=6=6\left(\dfrac56\right)^{1-1}[/tex]

[tex]a_2=5=6\left(\dfrac56\right)^{2-1}[/tex]

[tex]a_3=\dfrac{25}6=6\left(\dfrac56\right)^{3-1}[/tex]

and so on.

[tex]\displaystyle\sum_{n=1}^\infty6\left(\frac56\right)^{n-1}[/tex]

Consider the [tex]N[/tex]-th partial sum,

[tex]S_N=\displaystyle\sum_{n=1}^N6\left(\frac56\right)^{n-1}[/tex]

[tex]S_N=6\left(1+\dfrac56+\cdots+\dfrac{5^{N-2}}{6^{N-2}}+\dfrac{5^{N-1}}{6^{N-1}}\right)[/tex]

Multiplying both sides by 5/6 gives

[tex]\dfrac56S_N=6\left(\dfrac56+\dfrac{5^2}{6^2}+\cdots+\dfrac{5^{N-1}}{6^{N-1}}+\dfrac{5^N}{6^N}\right)[/tex]

and substracting this from [tex]S_N[/tex] gives

[tex]\dfrac16S_N=6\left(1-\dfrac{5^N}{6^N}\right)[/tex]

[tex]S_N=36\left(1-\left(\dfrac56\right)^N}\right)[/tex]

As [tex]N\to\infty[/tex], it's clear that the sum converges to 36.

The geometric series in the question is convergent with a common ratio of 5/6. Using the formula for the sum of an infinite geometric series, the sum of the series is found to be 36.

In mathematics, specifically in series, determining whether a geometric series is convergent or divergent is centered around the common ratio value. In terms of this particular series: 6 + 5 + 25/6 + 125/36 + ..., the common ratio is 5/6. Given this common ratio, it's clear that it falls between -1 and 1. Hence, this geometric series is convergent.

Once we establish it is a convergent series, we can calculate its sum using the formula for the sum of an infinite geometric series: S = a / (1 - r), where 'a' is the first term and 'r' is the common ratio. Inserting the respective values a = 6 and r = 5/6, we get: S = 6 / (1 - 5/6) = 36. Hence, the sum of this infinite geometric series is 36.

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Answer:

  1.  n = 40

  2.  

Step-by-step explanation:

The ordinary annuity formula can be written as ...

  PV = PMT(1 -(1+r)^-n)/r

where PMT is the payment per period, r is the interest rate per period, and n is the number of periods.

This formula can be solved explicitly for n, but not for r. Iterative or other methods can be used to find r.

__

1. Filling in the given information, we have ...

  15000 = 650(1 -1.03^-n)/0.03

  450/650 = 1 - 1.03^-n . . . . . divide by the coefficient of the stuff in parens

  1.03^-n = 4/13 . . . . . . . . . . . solve for the exponential term

  -n·log(1.03) = log(4/13) . . . . take logarithms

  n = log(13/4)/log(1.03) ≈ 39.87 . . . . . solve for n

  n ≈ 40

__

2. We can rewrite the annuity formula to make it be a function of i that is zero at the desired value of i.

  f(i) = PV -PMT(1 -(1+i)^-n)/i

If we want i as a percentage, then we can replace i with i/100 and fill in the given values to get ...

  f(i) = 9000 -500(1 -(1 +i/100)^-35)/(i/100)

  f(i) = 1000(9 -50(1 -(1 +i/100)^-35)/i) . . . . multiply the fraction by 100/100

Since we're seeking a value of f(r) that is zero, we can eliminate the factor of 1000.

  f(i) = 9 -50(1 - (1+i/100)^-35)/i

The attached graph shows the solution to f(i)=0 is near i=4.27%. As a decimal rounded to 3 decimal places, this is ...

  i ≈ 0.043

Proof:

Given any functions [tex]f_{1}(x),f_{2}(x),f_{3}(x)[/tex] they are linearly dependent if we can find values of [tex]c_{1},c_{2},c_{3}[/tex] such that

[tex]c_{1}f_{1}(x)+c_2f_{2}(x)+c_{3}f_{3}(x)=0[/tex]

Using the given functions in the above equation we get

[tex]c_{1}f_{1}(x)+c_2f_{2}(x)+c_{3}f_{3}(x)=0\\\\c_{1}x^{2}+c_{2}(1-x^{2})+c_{3}(2+x^{2})=0\\\\\Rightarrow (c_{1}-c_{2}+c_{3})x^{2}+c_{1}+c_{2}+2c_{3}=0[/tex]

This will be satisfied if and only if

[tex]c_1-c_2+c_3=0,c_1+c_2+2c_3=0[/tex]

Solving the equations we get

[tex]c_1+2c_3=-c_2\\\\c_1+c_1+2c_3+c_3=0\\2c_1+3c_3=0[/tex]

Since we have 3 variables and 2 equations thus we will get many solutions  

one being if we put [tex]c_3=1[/tex] we get

[tex]c_1+2c_3=-c_2\\\\c_1+c_1+2c_3+c_3=0\\2c_1+3c_3=0\\\\c_1=\frac{-3}{2}\\\\c_2=\frac{-1}{2}[/tex]

Thus we have [tex]c_1=\frac{-3}{2},c_2=\frac{-1}{2},c_3=1[/tex] as one solution. Hence the given functions are linearly dependent.

Answer: AD = 7.5

Step-by-step explanation: A midpoint is halfway between 2 points, which is AB. AB = 15. To find AD, which is half of the line, divide 15 by 2.

15/2 = 7.5

AD is 7.5

Answer:

AD = 7.5 units

Step-by-step explanation:

It is given in the question, a segment AB having measure = 15 units

If D is the midpoint of the segment AB, then we have to find the measure of segment AD.

Since D is the midpoint of AB then length of segment AD = [tex]\frac{1}{2}\times AB[/tex]

= [tex]\frac{1}{2}\times 15[/tex]

= 7.5 units

Therefore, AD = 7.5 units will be the answer.

Answer:

n = 23

x = 17

p = 0.50

Step-by-step explanation:

For a binomial experiment we have the following variables:

1) Number of trials or Sample size:

The number of trials is represented by n. In the given scenario 23 adults were asked about their favorite pizza, so the number of trials in this will be 23. Thus

n = 23

2) Number of success

The number of success is denoted by x. Number of success indicates that how many trials resulted in the favorable outcome. In the given case, choosing a sausage pizza is a success. Since 17 adults chose the sausage, so

x = 17

3) Probability of success on single trial

This is represented by p. It is stated that 50% adults say sausage is their favorite pizza. So,

p = 50% = 0.50

In a binomial probability experiment, n represents the size of the random sample, p represents the probability of success, and x represents the number of successes. In this given scenario, n=23, p=0.50 and x=17.

In a binomial probability experiment, the parameters n, p, and x are designated as follows: 'n' is the size of the random sample which in this case is 23. 'p' is the probability of success on a single trial, here it is the percentage of adults who indicated that sausage is their favorite pizza, which in decimal form is 0.50. 'x' is the number of successes, in this scenario, the number of adults in the sample of 23 who prefer sausage on their pizza, which is 17. So, in this experiment, n=23, p=0.50 and x=17. Success in this context is defined as an individual person preferring sausage on their pizza.

To ensure the binomial experiment is valid, and can be approximated by a normal distribution, the quantities np and nq (where q is 1-p, the probability of failure) must both be greater than five (np > 5 and nq > 5). In this case, np = 23*0.50 = 11.5 and nq = 23*0.50 = 11.5, thus the experiment is valid.

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Answer: 0.4

Step-by-step explanation:

Given : The number of candidates are equally qualified for President = 5

The number of candidates are members of a minority group =2

Since , to avoid bias in the selection of the candidate, the company decides to select the president by lottery. Here the chances of each candidates is same.

The probability one of the minority candidates is hired is given by :-

[tex]\text{P(Minority)}=\dfrac{\text{Number of minority candidates}}{\text{Total candidates}}\\\\=\dfrac{2}{5}=0.4[/tex]

Hence, the  probability one of the minority candidates is hired =0.4

Final answer:

The probability that one of the minority candidates is hired is 0.4, or 40%, since there are 2 minority candidates out of a total of 5 candidates.

Explanation:

Since there are five equally qualified candidates and two of them are minority candidates, we can calculate the probability by considering the ratio of the number of minority candidates to the total number of candidates.

The probability (P) that one of the minority candidates is hired can be calculated using the formula P = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes).

Here, the Number of Favorable Outcomes is 2 (since there are two minority candidates) and the Total Number of Possible Outcomes is 5 (since there are five candidates in total).

So, the probability is P = 2/5.

Let's compute this:

P = 2/5

P = 0.4

Therefore, the probability that one of the minority candidates will be hired is 0.4, or 40%.

The question asks for the probability that the sample mean of income differs from the true mean by over 42 dollars for a sample size of 412. We use the Central Limit Theorem to approach this problem, calculating the standard error and Z-score to refer to the standard normal distribution to find the associated probability.

This question pertains to the field of statistics, more specifically, the Central Limit Theorem. The Central Limit Theorem says that if we take many samples from a population, the distribution of the sample means will approximate a normal distribution, regardless of the shape of the population distribution. We can use this theorem to calculate a probability related to the sample mean.

In this case, the population mean (μ) is a per capita income of 24,787 dollars and the population variance (σ²) is 169,744 dollars. We're asked to find the probability that the sample mean would differ from the true mean by more than 42 dollars if a sample of 412 persons is randomly selected.

The standard error of the sample mean is calculated by σ / sqrt(n), where σ is the standard deviation (sqrt(σ²)), and n is the sample size (412). After finding the standard error, we will calculate the Z-score of 42, which is the number of standard errors 42 is away from the mean. Calculating the Z-score is achieved by z = (X - μ) / SE, where X is the value of 42.

We can refer the calculated Z-score to the standard normal distribution to find the associated probability. However, since we are looking for the probability of a difference greater than 42, we want the probabilities in the tails of the distribution beyond our calculated Z-score, so it would be 1 minus this value.

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