Write a function in the form
y = mx + b.

The probability the card drawn is a face card is 3/13. The probability the card drawn is not a face card is 10/13. The odds in favor of drawing a face card is 3/10. The odds against drawing a face card are 10/3.

There are 52 cards in a standard deck, and 12 of them are face cards (jack, queen, and king). Therefore, the probability of drawing a face card is 12/52, or 3/13.

The probability of not drawing a face card is 1 minus the probability of drawing a face card. Since the probability of drawing a face card is 3/13, the probability of not drawing a face card is 1 - 3/13, which is 10/13.

The odds in favor of drawing a face card are 3:10, or 3/10. The odds against drawing a face card are 10:3, or 10/3.

In summary:

The probability the  card drawn is a face card: 3/13

The probability the card drawn is not a face card: 10/13

Odds in favor of drawing a face card: 3/10

Odds against drawing a face card: 10/3

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The polynomial that is the product of (4x−3)(x²+2x−6) is 4x³ + 5x² - 30x + 18

A polynomial simply refers to the expression that is composed of constant, variables, and exponents that are combined by mathematical operations.

The product of the polynomial will be:

= (4x −3)(x² + 2x − 6)

= 4x³ + 8x² - 24x - 3x² - 6x + 18

= 4x³ + 5x² - 30x + 18

The product is 4x³ + 5x² - 30x + 18.

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Answer:

1. 600 yd^3

2. 103,680 in^3

Step-by-step explanation:

1. To find volume we do l*w*h

(15)(8)(5)

120(5)

600 yards^3

2. We also find the volume for this

(36)(60)(48)

2160(48)

103680 in^3

Hopes this helps

Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 44 and 54 minutes is 0.8150= 81.5%.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean  and standard deviation  is given by:

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

The relative frequency of classical CDs with playing time X between 44 and 54 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 44, hence:

X = 54:

Z = 3

Z = 3 has a p-value of 0.9987.

X = 54:

Z = -1

Z = -1 has a p-value of 0.1584.

0.9987 - 0.1584 = 0.8150

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Answer: x=3

Step-by-step explanation:

6*6=36

36*6=216

6*6*6=216

6*6*6=[tex]6^{2}[/tex]

[tex]6^{x} =6^{3}[/tex]

x=3

Answer:

Step-by-step explanation:

we need to find a base for 216 that is equal to 6.

216 / 6  = 36

36 / 6 = 6,

So 6 * 6 = 36 and 36 * 6 = 216.

From this we know that 216 = 6^3

6^x = 6^3

x=3

The derivative of given function is D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814  

We have to find the directional derivative of the given function  

f(x,y,z) = yz+e^x at (x0,y0,z0)=(1,1,1) in the direction of the vector

d⃗ =(3,−5,5)  

Find the gradient of the function and evaluate it at the given point:  

To find the gradient of a function (which is a vector), differentiate the function with respect to each variable.  

∇f= (∂f/∂x,∂f/∂y,∂f/∂z)  

∂f/∂x = ∂( yz+e^x )/∂x  

The derivative of a sum/difference is the sum/difference of derivatives:  

∂f/∂x = ∂( yz)/∂x +∂(e^x )/∂x since the derivative of y and z with respect of x is zero.  

∂f/∂x = e^x The derivative of exponential is d(e^x)/dx=e^x.  

Similarly  

d(yz+e^x)/dy = z and d(yz+e^x)/dz = y  

∇(yz+e^x)(x0,y0,z0)=(e^x,z,y)  

Finally plug in the point we get the result  

∇(yz+e^x)|(x0,y0,z0)=(1,1,1)=(e,1,1)  

∇(yz+ex)|(x0,y0,z0)=(1,1,1)=(e,1,1)  

Now we Find the length of the vector: |d⃗ |=((3)^2+(−5)^2+(5)^2)^1/2 =(59)^1/2  

To normalize the vector, divide each component by length:  

d = ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)  

Finally, the directional derivative is the dot product of the gradient and the normalized vector:  

D(yz+e^x)d(1,1,1) = (e,1,1). ((3*((59)^1/2))/59 ,(−5*(59)^1/2)/59,(5*(59)^1/2)/59)  

D(yz+e^x)d(1,1,1) = (3*((59)^1/2)*e)/59≈1.06167045295814  

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The resulting conditional mean squared error of the LMS estimator, given N=3 is 0.0383746

In general, the conditional distribution of X given Y does not equal the conditional distribution of Y given X, i.e., pX|Y(x|y)≠pY|X(y|x). If X and Y are independent, discrete random variables, then the following are true: pX|Y(x|y)=pX(x)pY|X(y|x)=pY(y)

The full conditional for a given node (parameter) is simply the product of the probability model (likelihood or prior) for that node and its parent node (at least up to a constant of proportionality).

1) fY|N(y∣N=3)=84 y^6 (1-y)^3

2)0.0636363

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Answer:

There are 5 possible outcomes when the first spinner is spun, and 2 possible outcomes when the second spinner is spun. Therefore, the sample space of possible outcomes when both spinners are spun is 5 x 2 = <<5*2=10>>10.

The possible outcomes are:

1A

1B

2A

2B

3A

3B

4A

4B

5A

5B

Of these, 3A, 2A, 1A, and 4B have a number less than 3 or an A. Therefore, there are 4 possible outcomes that have a number less than 3 or an A.

Step-by-step explanation:

In the given circle with center O, DF is congruent to BC.

What is congruent?

When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.

Consider the given circle with center O.

We have to find DF is congruent to which line.

Let point E and A are the midpoints of chord DF and BC.

There is angle 90 degrees on both the points.

The chords DF and chord BC are on the same distance from the center of the circle which is 3.09.

So, the chords DF and BC are of same measure.

Therefore, the chord BC is congruent to DF.

Hence, in the given circle with center O, DF is congruent to BC.

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Answer:

1095

Step-by-step explanation:

Answer:

Step-by-step explanation:

3250 : 156 = y : 40

y = 3250 × 40 : 156

y = 833.(3)                                    3 repeating

--------------------------

check

3250 : 156 = 833.(3) : 40

20,83333333333333 = 20,83333333333333

the answer is good

When the expected value and variance are 3.5 and 15.25, the statistic probability distribution will be 5/10, 3/10, and 2/10.

Given that,

A box contains ten sealed envelopes labelled 1, 2, 3, and 10. Six of them are empty, two have $5 apiece, and the remaining two each contain a $10 bill. You obtain the most money in any chosen envelope when replacement is used; a sample of size 3 is selected (forming a random sample). The statistic of interest is m if the quantities in the selected envelopes are represented by x1, x2, and x3.

We know that,

The probability distribution will be

P(X=0) = 5/10

P(X=5) = 3/10

P(X=10) = 2/10

In probability theory, the expected value is a development of the weighted average. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the expected value.

The expected value is

E =0(5/10)+5(3/10)+10(2/10) = 3.5

The variance is

V = 0² x (5/10) + 5² ( 3/10 ) + 10² x (2/10) - 3.5² = 15.25

Therefore, the statistic probability distribution will be 5/10, 3/10, and 2/10 when the expected value and variance are 3.5 and 15.25.

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The probability of observing no positive reading if all suspects are telling the truth is d. 0.59. Probability theory is a branch of mathematics that is used to model and analyze random events.

Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

To solve this problem, we need to calculate the probability of observing no positive readings given that all suspects are telling the truth, which is equal to the probability that all 5 suspects receive a negative reading on the lie detector test. Since the lie detector will show a positive reading 10% of the time when a person is telling the truth, the probability that a suspect will receive a negative reading when telling the truth is 1 - 10% = 90%. Therefore, the probability that all 5 suspects will receive a negative reading when telling the truth is:

(90%)^5 = (0.9)^5 = 0.59049.

The correct answer is therefore (d) 0.59.

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Answer:

Mark's salary after 25 years is $52,499.39

Step-by-step explanation:

This situation can be modelled exponentially. We are given the starting amount, 32000, and the annual growth rate, 2%. This means that, for every year that passes, we'd have [tex][(32000)(1.02)][/tex] $ as the salary. As such, the model would be [tex]S(t) = 32000(1.02)^t[/tex]. We want to find Mark's salary 25 years from the starting point, t=25. Having developed a model for this situation, we can simply plug in 25 for t:

[tex]S(25) = 32000(1.02)^{(25)}[/tex]

[tex]S(25) = 52499.39[/tex]

Answer: Im sorry I cant help im just doing this for points

Step-by-step explanation:

The correct answer is [tex]H_0: p = 0.24 and H_1: p < 0.24[/tex].

In mathematical notation, the null hypothesis can be written as:

H_0: p = 0.24

where p is the proportion of uninsured motorists in Florida.

The alternative hypothesis can be written as:

H_1: p < 0.24

This means that we are testing the hypothesis that the proportion of uninsured motorists has decreased to a level that is less than 24%.

The null hypothesis is the default assumption, and we will only reject it if we have enough evidence to support the alternative hypothesis. In this case, we would need to collect data that suggests that the proportion of uninsured motorists has decreased to a level that is significantly less than 24%.

The correct answer is [tex]H_0: p = 0.24 and H_1: p < 0.24[/tex].

The other options are incorrect because they either do not specify the direction of the hypothesis test (i.e., whether we are testing whether the proportion of uninsured motorists has increased or decreased) or they are not supported by the given information.

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The critical values for a 99% confidence interval using the chi-square distribution with 10 degrees of freedom are 18.3278 and 28.3092.

The chi-square distribution is a continuous probability distribution that is used to determine the probability of a statistic being greater than or less than a certain value. The chi-square distribution with 10 degrees of freedom is used to calculate critical values for a 99% confidence interval.

To find the critical values, we need to use the chi-square distribution calculator. In the calculator, we should enter the degrees of freedom, which is 10 in this case, and the confidence level, which is 99% in this case. The calculator will then return the critical values for the 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

Step 1: Go to the chi-square distribution calculator.

Step 2: Enter the degrees of freedom, which is 10 in this case.

Step 3: Enter the confidence level, which is 99% in this case.

Step 4: Click the “Calculate” button.

Step 5: The calculator will return the critical values for a 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

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Answer:

C {(7, 2), (7, 0), (3,-2), (1,4)}

Step-by-step explanation:
In a function, x = 7 can't be at both 2 and 0 because it would not pass the vertical line test.

well, he has left only 6 oz.

now, if we take the 16(origin amount) to be the 100%, what is 6 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 16 & 100\\ 6& x \end{array} \implies \cfrac{16}{6}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 8 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 8x=300\implies x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]

Answer: The answer is -2.34

Step-by-step explanation: Get Good

To find out how much Mark still owes on his debt, we need to calculate the amount of interest that has accrued on the loan over the time that he has been paying it off. The interest on the loan is compounded semi-annually, so the amount of interest that accrues on the loan will be added to the principal every six months. Since Mark has been paying off his debt for 8 years and the interest is compounded semi-annually, he will have made 16 payments of $500.

To calculate the total amount of interest that has accrued on the loan, we need to know the original principal amount of the loan. Since we don't have that information, we won't be able to calculate the exact amount that Mark still owes on his debt. However, we can use the information that we have to make an educated guess.

If Mark has been making payments of $500 every six months for eight years, then he has paid a total of $500 x 16 = $<<50016=8000>>8000 in principal and interest payments. If the interest on the loan is 2% compounded semi-annually, then the total amount of interest that has accrued on the loan over the past eight years is $8000 x 2% = $<<80002*.01=160>>160. This means that the original principal amount of the loan was $8000 - $160 = $<<8000-160=7840>>7840.

Since Mark still has 8 years left to pay off the debt, and he is making payments of $500 every six months, he will need to make a total of 8 years x 2 payments per year = <<82=16>>16 more payments of $500 to pay off the debt. This means that he will have to pay a total of $500 x 16 = $<<50016=8000>>8000 in principal and interest over the next eight years.

Since the total amount of interest that has accrued on the loan over the past eight years was $160, the total amount of interest that will accrue on the loan over the next eight years is also $160. This means that the total amount of interest that Mark will have to pay over the next eight years is $160 x 2 = $<<160*2=320>>320.

Adding the amount of interest that Mark will have to pay over the next eight years to the amount of principal that he will have to pay, we find that the total amount that Mark will owe on the loan over the next eight years is $8000 + $320 = $<<8000+320=8320>>8320.

Therefore, if Mark has been paying off his debt for eight years and still has eight years left to pay, he still owes a total of $8320 on the loan.

Answer:

a. (0,1)

b. slope is -2

y-1=-2x

Step-by-step explanation:

Answer:$85.5

Step-by-step explanation:

So divide 66.50 by 7 and that will get you 9.5 then multiply that by 9 which is then 85.5

The result for all expressions are

a) r(t) = 6.5t radians

b) C(t) = 20cos(6.5*t) feet

c) H(t) = 36 - C(t)

The situation is depicted in the picture attached considering the center of the wheel as the center of the coordinates system.

Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply:

6.5 radians __________ 1 minute

r(t) radians ____________  t minutes

and obviously, r(t) = 6.5t radians

The height C(t) above the center after t minutes is given by

C(t) = 20cos(r(t)) ===>  C(t) = 20cos(6.5*t) feet

When C(t) < 0 means that derek wheel is below the center of the wheel.

Since the center of the Ferris wheel is 36 feet above the ground, the height H(t) above the ground after t minutes is given by

H(t) = 36 - C(t)

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Answer:

2n + 5 ≤ 7  The first choice

Step-by-step explanation:

2n + 5 ≤ 7  Subtract 5 from both sides.

2n + 5 - 5 ≤ 7 - 5

2n ≤ 2  Divide both sides by 2

[tex]\frac{2n}{2}[/tex] ≤ [tex]\frac{2}{2}[/tex]

n [tex]\leq[/tex] 1

Answer:

2x +5 ≤ 7

I hope my answer helps you.

Answer:

The correct answer is 15 potatoes.

Step-by-step explanation:

To solve this problem, we can determine the unit rate and use proportions. We know that Sarai needs 6 potatoes for 16 latkes. We want to know how many potatoes she will need to make 40 latkes. Let's call this unknown value x. We can set up the following equation:

6 potatoes/16 latkes = x potatoes/40 latkes

To solve this equation, we can first simplify the left side to find the unit rate.

3 potatoes/8 latkes = x potatoes/40 latkes

To solve, we can recognize that 40 latkes is 5 times the amount shown in the unit rate (8 latkes), which means that we need 5 times the amount of potatoes.

3 potatoes * 5 = 15 potatoes

Therefore, the correct answer is 15 potatoes. Note that you could have also just solved the equation for x to find your answer as well.

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There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.

Given that a recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent.

Let p1 be the proportion of local seniors and p2 national seniors.

H₀ : p₁ =  p₂

Hₐ : p₁ > p₂

(right tailed test at 5% significance level)

Group I II  

Success 69 60 129

Total 100 100 200

p 0.69 0.6 0.645

q 0.31 0.4 0.355

se 0.046249324 0.048989795 0.033836002

p diff 0.09  

Std error 0.03384  

Z 2.659574468 0  

p 0.00391  

we find that p value is 0.00391 < 0.05

Hence we reject null hypothesis. There is evidence to claim that the proportion of drug and alcohol use is higher locally than nationally.

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The solution for the given equation is am = -15.

The given equation is -2(am + 4) = 22

On simplifying the given equation for its solution, we get

-2(am + 4) = 22

⇒ -2am - 8 = 22

⇒ -2am = 22 + 8

⇒ -2am = 30

∴ am = -30/2 = -15

So, the solution for the given equation is -15.

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Answer:

Step-by-step explanation:

Using the properties of confidence interval and probability we can conclude from the observations that the process is not a statistical control process.

(a) The process is not a statistical process .

b) The control & chart is not in control because there some false alarm at 8-15. There are some special causes in the clata (may be in manufacturing) exist.

(c) (i) Given that Target length = 37 USL + LSL = 37 USL+2SL= 74

and Tolerance = 0.01 USL LSL = 0.01

After Solving equation 1 & 2 we get VSL = 37.005, LSL = 36.995

cp =2 × 0.01 6/0.05 × 2.059 = 0.01 ×0.1457 = 0.0686

(ii) Cp = min (Cpu, CP).

Cpu = 37.005-37 0.073 = 0.06849

CPL = 0.06859

Срк = 2 × 0.06849 = 0.024

The application of statistical methods to monitor and regulate the quality of a manufacturing process is known as SPC (statistical process control) or SQC (statistical quality control).

This increases the efficiency of the process, resulting in more specification-conforming goods with less waste (rework or scrap). SPC can be used to any process that can measure the output of a "compliant product" (a product that fulfils standards).

The primary tools of SPC are run charts, control charts, a focus on continuous improvement, and experiment design. Manufacturing lines are one example of a process that employs SPC.

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