What system of equations would you use to solve the problem below?
The owner of a bike shop sells tricycles (3 wheels) and bicycles (2 wheels),
keeping inventory by counting seats and wheels. One day she counts 35
seats and 80 wheels. How many of each type of cycle are there?

Answer:

The probability of healthcare expenses in the population being greater than $4,000 is 0.02275.

Step-by-step explanation:

We are given that yearly healthcare expenses for a family of four are normally distributed with a mean expense equal to $3,000 and a standard deviation equal to $500.

Let X = yearly healthcare expenses of a family

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{ X-\mu}{\sigma} }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean expense = $3,000

            [tex]\sigma[/tex] = standard deviation = $500

Now, the probability of healthcare expenses in the population being greater than $4,000 is given by = P(X > $4,000)

     P(X > $4,000) = P( [tex]\frac{ X-\mu}{\sigma} }[/tex] > [tex]\frac{4,000-3,000}{{500}{ } }[/tex] ) = P(Z > 2) = 1 - P(Z [tex]\leq[/tex] 2)

                                                                  = 1 - 0.97725 = 0.02275

The above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.

Answer:

[tex]1/\sqrt{2}[/tex]

Answer:

B

Step-by-step explanation:

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

[tex]Z = \frac{X - \mu}{s}[/tex]

X = 205

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{205 - 200}{5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413.

X = 195

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{195 - 200}{5}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{210 - 200}{5}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772.

X = 195

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{190 - 200}{5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

(a): The required probability is [tex]P(195 < \bar{x} < 205)=0.6826[/tex]

(b): The required probability is [tex]P(190 < \bar{x} < 200)=0.9544[/tex]

A numerical measurement that describes a value's relationship to the mean of a group of values.

Given that,

mean=200

Standard deviation=50

[tex]n=100[/tex]

[tex]\mu_{\bar{x}}=200[/tex]

[tex]\sigma{\bar{x}} =\frac{\sigma}{\sqrt{n} } \\=\frac{50}{\sqrt{100} }\\ =5[/tex]

Part(a):

within [tex]5=200\pm 5=195,205[/tex]

[tex]P(195 < \bar{x} < 205)=P(-1 < z < 1)\\=P(z < 1)-P(z < -1)\\=0.8413-0.1587\\=0.6826[/tex]

Part(b):

within [tex]10=200\pm 10=190,200[/tex]

[tex]P(190 < \bar{x} < 200)=P(-1 .98 < z < 1.98)\\=P(z < 2)-P(z < -2)\\=0.9772-0.0228\\=0.9544[/tex]

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Answer:

95% of the data falls between 0.64 and 3.92

Step-by-step explanation:

Using the Empirical Rule, 95% of the data will fall 2 standard deviations above and below the mean. Therefore, from the mean of 2.28, the lower change will be 2.28 - 2(0.82)= 0.64 and the upper change will be 2.28 + 2(0.82)= 3.92‬

Answer:

The mode would decrease by 3

Step-by-step explanation:

The mode right now is 6, as there are 4 6's. However, closely behind it is 3, with 3 3's. If we replaced a 6 with a 3, we would have 4 3's and 3 6's. Find the difference between 6 and 3 and you answer should be 3.

Answer:

126

Step-by-step explanation:

0.1x=12.6

126

Answer:

En álgebra, el teorema del factor es un teorema que vincula factores y ceros de un polinomio. Es un caso especial del teorema del resto polinómico.

Step-by-step explanation:

Answer:

$20 of credit left on the card

Step-by-step explanation:

If we say that the prepaid phone card has 25 minutes on it since Maya paid 25 dollars for it. We can multiply 25 times 4 which equals 1 dollar per 4 minutes. Then, we can divide 20 by 4 to get 5 which means that she used 5 dollars of call time. We can now subtract 25-5 and we get 20. This tells us that there is 20 dollars left on the card.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

b

Step-by-step explanation:

Answer:

- The center line is at 16.5 ounces.

- The standard deviation of the sample mean = 0.112 ounce.

- The UCL = 16.836 ounces.

- The LCL = 16.154 ounces.

Step-by-step explanation:

The Central limit theorem allows us to write for a random sample extracted from a normal population distribution with each variable independent of one another that

Mean of sampling distribution (μₓ) is approximately equal to the population mean (μ).

μₓ = μ = 16.5 ounces

And the standard deviation of the sampling distribution is given as

σₓ = (σ/√N)

where σ = population standard deviation = 0.25 ounce

N = Sample size = 5

σₓ = (0.25/√5) = 0.1118033989 = 0.112 ounce

Now using the 3 sigma limit rule that 99.5% of the distribution lies within 3 standard deviations of the mean, the entire distribution lies within

(μₓ ± 3σₓ)

= 16.5 ± (3×0.112)

= 16.5 ± (0.336)

= (16.154, 16.836)

Hope this Helps!!!

Answer:

Step-by-step explanation:

Ray

Answer:

ray

Step-by-step explanation:

ray is a part of a line that has an endpoint in one side and extends indefinitely on the opposite side. hence, the answer is ray

hope this helps

Answer:

24

Step-by-step explanation:

Since you are given almost everything, you just simply divide by 5=>

120/5 = 24

Hope this helps

The radioactive compound has a half-life of around 3.09 hours.

The period of time needed for a radioactive substance's initial quantity to decay by half is known as its half-life. The half-life of a drug may be calculated as follows if the rate of decay is proportionate to the amount of the substance existing at time t:

Let t be the half-life of the substance, then after t hours, the amount of the substance present will be,

100 mg × [tex]\dfrac{1}{2}[/tex] = 50 mg.

At time 6 hours, the amount of the substance present is,

100 mg × (1 - 3%) = 97 mg.

Given that the amount of material available determines how quickly something degrades,

The half-life can be calculated as follows:

[tex]t = 6 \times \dfrac{50}{ 97} = 3.09 \ hours[/tex]

Therefore, the half-life of the radioactive substance is approximately 3.09 hours.

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Answer: x=45°

Step-by-step explanation:

Angles opposite from each other are equal. The angle 160 degrees in red on the bottom encompasses two angles: BEG and CEG. Angle BEG is on the opposite side as FEA which means it is equal to x.

Since angle FED on the other side is 115, you subtract 115 from 160 to get 45 degrees.

Answer: x=45°

The angle BEG, which is opposite to the angle FEA, is determined to be 45 degrees.

According to the information provided, in a figure with an angle of 160 degrees (red angle on the bottom), there are two angles labeled as BEG and CEG. It is stated that the angle BEG is opposite to the angle FEA, making them equal, so we can represent this angle as x.

Additionally, it is mentioned that the angle FED on the other side measures 115 degrees.

To find the value of x, we subtract 115 degrees from the angle of 160 degrees.
=160-115
= 45

Thus, the solution is x = 45°.

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Answer:

A

Step-by-step explanation:

The area of a kite is half of the product of the length of the diagonals, or in this case 16*12/2=96 square feet. Hope this helps!

Answer:

a. 96 ft^2

Step-by-step explanation:

You can cut the kite into 2 equal triangle halves vertically.

Then you can use the triangle area formula and multiply it by 2 since there are 2 triangles.

[tex]\frac{1}{2} *12*8*2=\\6*8*2=\\48*2=\\96ft^2[/tex]

The kite's area is a. 96 ft^2.

Answer: x = -5

Step-by-step explanation:

If you factor each denominator, you can find the LCM.

[tex]\dfrac{2}{x^2-x-12}=\dfrac{1}{x^2-16}\\\\\\\dfrac{2}{(x-4)(x+3)}=\dfrac{1}{(x-4)(x+4)}\\\\\\\text{The LCM is (x-4)(x+4)(x+3)}\\\\\\\dfrac{2}{(x-4)(x+3)}\bigg(\dfrac{x+4}{x+4}\bigg)=\dfrac{1}{(x-4)(x+4)}\bigg(\dfrac{x+3}{x+3}\bigg)\\\\\\\dfrac{2(x+4)}{(x-4)(x+4)(x+3)}=\dfrac{1(x+3)}{(x-4)(x+4)(x+3)}\\[/tex]

Now that the denominators are equal, we can clear the denominator and set the numerators equal to each other.

2(x + 4) = 1(x + 3)

2x + 8 = x + 3

x  + 8 =       3

x        =      -5

Answer:

[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]

Step-by-step explanation:

We are given the coordinates of points P(1,-6,7) and Q(-9,10,-5).

The values in the form of ([tex]x,y,z[/tex]) are:

[tex]x_1=1\\x_2=-9\\y_1=-6\\,y_2=10\\z_1=7\\z_2=-5[/tex]

[tex]$\vec{PQ}$[/tex] can be written as the difference of values of x, y and z axis of the two points i.e. change in axis.

[tex]\vec{PQ}=<x_2-x_1,y_2-y_1,z_2-z_1>[/tex]

[tex]\vec{PQ} = <(-9-1), 10-(-6),(-5-7)>\\\Rightarrow \vec{PQ} = <-10, 16,-12>[/tex]

The equation of line in vector form can be written as:

[tex]\vec{r} (t) = <1,-6,7> + t<-10,16,-12>[/tex]

The standard parametric equation can be written as:

[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]

Answer:

The second graph.

Step-by-step explanation:

0-9: 6 numbers

10-19: 2 numbers

20-29: 1 number

30-39: 3 numbers

40-49: 1 number

50-59: 2 numbers

60-69: 0 numbers

70-79: 5 numbers

80-89: 3 numbers

90-99: 1 number

Answer:

[tex]25[/tex]

Step-by-step explanation:

[tex](4 + 6 \times 3) + 3[/tex]

[tex]=(4 + 18) + 3[/tex]

[tex]=(22) + 3[/tex]

[tex]=22+3[/tex]

[tex]=25[/tex]

Answer:25

Step-by-step explanation:

Pemdas

(4+6*3)+3

(Parentheses and Multiplication first)

4+18

22+3

Then addition

22+3=25

Answer:

1 - 4x

Step-by-step explanation:

First, do multiplication

4 times x is 4x

Then subtract 4x from 1

1 - 4x

Answer:

(1) Given

(2) Definition of midpoint

(3) Transitivity

(4) PWP (Parts Whole Postulate)

Answer:

a)  y₂ (x) = e ⁵ˣ  

Complementary function

               [tex]y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }[/tex]

b) particular integral

[tex]P.I = y_{p} = \frac{-4}{25}[/tex]

Step-by-step explanation:

step(i):-

Given differential equation y''-25y= 4

operator form

             ⇒    D²y - 25 y =4

            ⇒     (D² - 25) y =4

       This is the form of f(D)y = ∝(x)

where f(m) = D² - 25     and ∝(x) =4

The auxiliary equation A(m) =0

                         ⇒ m² - 25 =0

                          m² - 5²  =0

                      ⇒ (m+5)(m-5) =0

                     ⇒ m =-5 , 5

Complementary function

               [tex]y_{C} = C_{1} {e^{-5x} } + C_{2} {e^{5x} }[/tex]

This is form of

             [tex]y_{C} = C_{1} y_{1} (x) + C_{2} y_{2} (x)[/tex]

where y₁ (x) = e⁻⁵ˣ   and  y₂ (x) = e ⁵ˣ  

Step(ii):-

Particular integral:-

[tex]P.I = y_{p} = \frac{1}{f(D)} \alpha (x)[/tex]

[tex]P.I = y_{p} = \frac{1}{D^{2} -25} 4[/tex]

      =  [tex]= \frac{1}{D^{2} -25} 4e^{0x}[/tex]

put D = 0

The particular integral

[tex]y_{p} = \frac{1}{ -25} 4[/tex]

[tex]P.I = y_{p} = \frac{-4}{25}[/tex]

Conclusion:-

General solution of given differential equation

[tex]y = y_{C} +y_{P}[/tex]

[tex]y = C_{1} {e^{-5x} } + C_{2} {e^{5x} } -\frac{4}{25}[/tex]

Answer:

x=1

Step-by-step explanation:

sqrt(x+3) = sqrt(5x-1)

Square each side

x+3 = 5x-1

Subtract x from each side

3 = 4x-1

Add 1 to each side

4 =4x

Divide by 4

x=1

Answer:

x= 1

Step-by-step explanation:

[tex]\sqrt{x+3}=\sqrt{5x-1}[/tex]

Square both sides.

x + 3 = 5x - 1

Subtract 3 and 5x on both sides.

x - 5x = -1 - 3

-4x = -4

Divide -4 into both sides.

-4x/-4 = -4/-4

x = 1

Complete question is;

In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.

Answer:

P(has diabetes | positive) = 0.442

Step-by-step explanation:

Probability of having diabetes and being positive is;

P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)

We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.

Thus;

P(positive & has diabetes) = 0.08 × 0.95 = 0.076

P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)

P(negative & has diabetes) = 0.004

P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)

We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease

Thus;

P(positive & no diabetes) = 0.92 × 0.1 = 0.092

P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)

P(negative &no diabetes) = 0.828

Probability that a person selected having diabetes actually has the disease is;

P(has diabetes | positive) =P(positive & has diabetes) / P(positive)

P(positive) = 0.08 + P(positive & no diabetes)

P(positive) = 0.08 + 0.092 = 0.172

P(has diabetes | positive) = 0.076/0.172 = 0.442

Using formula:

[tex]P(\text{diabetes diagnosis})\\[/tex]:

[tex]=\text{P(having diabetes and have been diagnosed with it)}\\ + \text{P(not have diabetes and yet be diagnosed with diabetes)}[/tex]

[tex]=0.08 \times 0.95+(1-0.08) \times 0.10 \\\\=0.08 \times 0.95+0.92 \times 0.10 \\\\=0.076+0.092\\\\=0.168[/tex]

[tex]\text{P(have been diagnosed with diabetes)}[/tex]:

[tex]=\frac{\text{P(have diabetic and been diagnosed as having insulin)}}{\text{P(diabetes diagnosis)}}[/tex]

[tex]=\frac{0.08\times 0.95}{0.168} \\\\=\frac{0.076}{0.168} \\\\=0.452\\[/tex]

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Answer:

a prism is a three dimensional shape with the same width all the way through.

Step-by-step explanation:

Step-by-step explanation:

i think this will help.

Answer:

49.95+/-0.5543

= ( 49.3957, 50.5043) pounds

the 95% confidence interval (a,b) = ( 49.3957, 50.5043) pounds

And to 2 decimal points;

the 95% confidence interval (a,b) = ( 49.40, 50.50) pounds

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 49.95 pounds

Standard deviation r = 1.9999 pounds

Number of samples n = 50

Confidence interval = 95%

z value(at 95% confidence) = 1.96

Substituting the values we have;

49.95+/-1.96(1.9999/√50)

49.95+/-1.96(0.282828570338)

49.95+/-0.554343997864

49.95+/-0.5543

= ( 49.3957, 50.5043) pounds

Therefore, the 95% confidence interval (a,b) = ( 49.3957, 50.5043) pounds

Answer:

Option 1.

Step-by-step explanation:

[tex]y=2x+1[/tex]

[tex]x=2y+1[/tex]

[tex]x-1=2y[/tex]

[tex]\frac{x-1}{2} = \frac{2y}{2}[/tex]

[tex]\frac{x-1}{2} = y[/tex]

[tex]\frac{1}{2}x -\frac{1}{2} = y[/tex]

Answer:

  see the attachment

Step-by-step explanation:

You can find the inverse by swapping the variables and solving for y.

  y = f(x) . . . . . original function

  x = f(y) . . . . . variables swapped

  x = 2y +1

  x -1 = 2y . . . subtract 1

  (x-1)/2 = y . . . divide by 2

  y = (1/2)x -1/2 . . . expand

If the inverse function is named h(x), then it is ...

  h(x) = x/2 -1/2

Using the Central Limit Theorem, it is found that the measures are given by:

a) 2,500,000.

b) 88,388.35.

c) 2,500,000.

By the Central Limit Theorem, the sampling distribution of sample means of size n for a population of mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] has the same mean as the population, but with standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

Hence, we have that for options a and c, the mean is of 2,500,000 users, while for option b, the standard deviation is given by:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{625000}{\sqrt{50}} = 88,388.35.[/tex]

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Answer: height = 13.24 m

Step-by-step explanation:

Draw a picture (see image below), then set up the proportions to find the length of QB.  Then input QB into either of the equations to find h.

Given: PQ = 10

          ∠TPB = 23°

          ∠TQB = 32°

[tex]\tan P=\dfrac{opposite}{adjacent}\qquad \qquad \tan Q=\dfrac{opposite}{adjacent}\\\\\\\tan 23^o=\dfrac{h}{10+x}\qquad \qquad \tan 32^o=\dfrac{h}{x}\\\\\\\underline{\text{Solve each equation for h:}}\\\tan 23^o(10+x)=h\qquad \qquad \tan 32^o(x)=h\\\\\\\underline{\text{Set the equations equal to each other and solve for x:}}\\\tan23^o(10+x)=\tan32^o(x)\\0.4245(10+x)=0.6249x\\4.245+0.4245x=0.6249x\\4.245=0.2004x\\21.18=x[/tex]

[tex]\underline{\text{In put x = 21.18 into either equation and solve for h:}}\\h=\tan 32^o(x)\\h=0.6249(2.118)\\\large\boxed{h=13.24}[/tex]

Answer:

P(X=2) = 0.302

Step-by-step explanation:

With the conditions mentioned in the question, we can model this variable as a binomial random variable, with parameters n=9 and p=0.2.

The probability of having k defective items in the sample of nine chips is:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{9}{k} 0.2^{k} 0.8^{9-k}\\\\\\[/tex]

Then, the probability of having 2 defective chips in the sample is:

[tex]P(x=2) = \dbinom{9}{2} p^{2}(1-p)^{7}=36*0.04*0.2097=0.302\\\\\\[/tex]