An isosceles triangle has slant height s and angle t opposite the base. Find a formula for the base length b in terms of the angle t and the slant height s.Find a formula for the enclosed area A in terms of t and s.

Answer:

Step-by-step explanation:

false

Yes, All the parabolas have the same domain.

What is Domain?

The set of all inputs of the function is called Domain of set.

Given that;

The statement is,

''All parabolas have the same domain.''

Now,

Since, The domain of the parabola will be (- ∞, ∞).

Hence,  All the parabolas have the same domain.

Thus,  All the parabolas have the same domain.

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Answer:

39% of 118.9=46.371

Step-by-step explanation:

Final answer:

To find out what 39% of a certain amount is equal to 118.9, we can set up an equation and solve for x. To solve "39% of what is 118.9?", we use the equation 0.39x = 118.9 and find that x, which represents the original number, is equal to 305.

Explanation:

To find 39% of a certain number that equals 118.9, we set up the equation where 0.39 (which is 39% as a decimal) times the unknown number (let's call it x) equals 118.9:

0.39x = 118.9

To find the value of x, we divide both sides of the equation by 0.39:

x = 118.9 / 0.39

x = 305

Therefore, 39% of 305 is equal to 118.9.

Answer:

x = log∨2 (17)

Explanation:

Calculate the difference

Move the constant to the right

Add the numbers

Then take the logarithm of both sides of the equation

Answer:

5

Step-by-step explanation:

Answer:

The value of the test statistic is [tex]t = -2.09[/tex]

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 6.6[/tex]

The alternate hypotesis is:

[tex]H_{1} \neq 6.6[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation(square roof of the variance) and n is the size of the sample.

In this problem, we have that:

[tex]X = 6.5, \mu = 6.6, \sigma = \sqrt{0.64} = 0.8, n = 280[/tex]

So

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \frac{6.5 - 6.6}{\frac{0.8}{\sqrt{280}}}[/tex]

[tex]t = -2.09[/tex]

The value of the test statistic is [tex]t = -2.09[/tex]

Answer:

402.12 meters

Step-by-step explanation:

to measure the circumference,

C = 2πr

2π(64) =

to run 1 full lap around the track would be 402.12 meters

i hope this helps!

:)

To find the distance of a full lap around a circular track, calculate the circumference using the formula C = 2π r. With a radius of 64 meters, the distance is approximately 402.12 meters.

To calculate the distance traveled on a full lap around a circular track, you need to find the circumference of the circle. The circumference of a circle is given by the formula C = 2π r, where π (Pi) is approximately 3.14159 and r is the radius of the circle.

Given that the radius of the track is 64 meters, we can substitute this value into the formula to find the circumference.

C = 2π(64 meters)

C = 128π meters

C = approx. 128 × 3.14159 meters

C = approx. 402.1232 meters

Therefore, if you ran one full lap around the circular track, you would travel approximately 402.12 meters.

Answer:

The probability that Susan's average score for the week is between 220 and 228 is 0.7594.

Step-by-step explanation:

Average score of Susan = u = 225

Standard deviation = [tex]\sigma[/tex] = 13

Score of Susan follow a Normal Distribution and we have the population standard deviation, as this standard deviation is of her scores of previous 14 years.

In a given week, Susan bowls 16 games. This means, our sample size is 16. So,

n = 16

We have to find the probability that her average score of the week is between 220 and 228. Since the distribution is normal and value of population standard deviation is known, we will use the concept of z-score and z-distribution to find the desired probability.

First we will convert the given numbers to their equivalent z-scores. The formula to calculate the z-scores is:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

x = 220 converted to z-score will be:

[tex]z=\frac{220-225}{\frac{13}{\sqrt{16}}}=-1.54[/tex]

x = 228 converted to z-score will be:

[tex]z=\frac{228-225}{\frac{13}{\sqrt{16}}}=0.92[/tex]

So, probability that Susan's score is between 220 and 228 is equivalent to probability of z score being in between - 1.54 and 0.92

i.e.

P (220 < X < 228) = P( -1.54 < z < 0.92)

From the z-table we can find the following values:

P( -1.54 < z < 0.92) = P(x < 0.92) - P(x<-1.54)

P( -1.54 < z < 0.92) = 0.8212 - 0.0618

P( -1.54 < z < 0.92) = 0.7594

Since, P (220 < X < 228) is equivalent to P( -1.54 < z < 0.92), we can conclude that the probability that Susan's average score for the week is between 220 and 228 is 0.7594.

Using the Central Limit Theorem and Z-scores, we calculate the probability that Susan's average weekly score will be between 220 and 228 from the standard normal distribution table.

This question revolves around the concept of standard deviation and probability in a normal distribution. Standard deviation measures the dispersion or variation of a set of values. In this case, her average score per week is a random variable, so Central Limit Theorem (CLT) applies because she plays a large number of games (16) every week. CLT states that the sum of a large number of independent and identically-distributed random variables has an approximately normal distribution.

We can calculate the mean (μ) and standard deviation (σ) of the weekly average:

To calculate the Z-scores for 220 and 228:

Finally, we need to find the probability P(Z₁ < Z < Z₂), which involves looking up these Z-scores in a Z-table or using statistical software or online resource that gives the values for a normal distribution.

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The toy rocket will take 2.5 seconds to reach its maximum height, which is 108 feet above the ground.

The question asks about the time it takes for a toy rocket to reach its maximum height and what that maximum height is, given the equation of its height h(t) = -16t2 + 80t + 8. This is a quadratic equation representing the height of the toy rocket as a function of time, which is a typical problem in physics or mathematics dealing with projectile motion. To solve for the time when the rocket reaches its maximum height, we need to find the vertex of the parabola shaped by the quadratic equation where the coefficient of t2 is negative indicating that the parabola opens downwards.

The formula to calculate the time to reach maximum height in a quadratic equation like this is t = -b/(2a), where a is the coefficient of t2 (-16) and b is the coefficient of t (80). Thus, t = -80/(2*(-16)) = 2.5 seconds. To find the maximum height, we plug this time into the height equation: h(2.5) = -16*(2.5)2 + 80*(2.5) + 8 = 108 feet.

Answer: 3,917 days

Step-by-step explanation:

Answer: the average speed of the runners increased since last year.

Step-by-step explanation:

The table is:

                   Mean     MAD

Last Year    16.2 s     1.2

This Year    14.7 s      1.9

Looking at this table we can see that this year, the mean time is smaller than the one from last year, so the runners are faster in average.

The mean absolute deviation is bigger, but the change in the mean is bigger.

difference of the mean   16.2 - 14.7 = 1.5

difference of the MAD  1.9 - 1.2 = 0.7

This means that the average speed of the runners increased since last year, and the fact that the MAD increased means that not all the runners increased their speed at the same rate, so now the speeds of the different runners are not as alike like last year.

Answer:

this guy above me is a genuies it correct

Step-by-step explanation:

Hey there!

All you have to COMBINE YOUR LIKE TERMS and you have your answer!

-2/3p + 1/5 - 1 + 5/6p

(-2/3p + 5/6p) + (1/5 - 1)

-2/3p + 5/6p = 1/6p

1/5 - 1 = -4/5

Answer: 1/6p + (- 4/5) ✅

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.

Step-by-step explanation:

Simple interest formula:

The simple interest formula is given by:

[tex]E = P*r*t[/tex]

In which E are the earnings, P is the principal(the initial amount of money), r is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex].

Compound interest formula:

The compound interest formula is given by:

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

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem:

[tex]P = 500, r = 0.08, t = 10[/tex]

So

Simple interest:

[tex]E = P*r*t = 500*0.08*10 = 400[/tex]

In total:

[tex]T = E + P = 500 + 400 = 900[/tex]

Using simple interest, you would withdraw an amount of $900.

Compound interest

We use n = 1

[tex]A = P(1 + \frac{r}{n})^{nt} = 500(1 + \frac{0.08}{1})^{10} = 1079.46[/tex]

You would withdraw $1079.86. Since you would withdraw more money with the compound interest, you would choose the bank which uses compund interest.

The correlation is 0.824. The equation of the regression line is Y = -12.6 + 0.722X. The estimated verbal score for a math score of 387 can be calculated by inputting 387 in place of X in the regression equation.

The subject of this question is regression analysis, which is a type of statistical modeling technique.

A) The correlation, as given in the question, is 0.824. This number tells us the degree to which the math and verbal scores vary together.

B) The regression equation predicting verbal scores from math scores can be calculated as follows:

Regression line equation is Y = a + bX. 'a' is Y intercept, 'b' is the slope, 'X' is the value of the independent variable (in this case math scores), and 'Y' is the predicted value of the dependent variable (in this case, verbal scores). We calculate the slope 'b' using the formula b = r*(Sy/Sx), where r is the correlation coefficient, Sy is the standard deviation of Y (verbal scores) and Sx is the standard deviation of X (math scores).

Inserting our values in gets us: b = 0.824 * (168.9/191.4) = 0.722 (rounded to three decimal places). And a = My - b*Mx = 491.5 - 0.722*504.7 should give us our Y intercept. Plugging in your calculator should give you a roughly around -12.6.

The equation of the regression line would then be Y = -12.6 + 0.722X.

D) To predict the verbal score from a math score of 387, we substitute X = 387 into the regression equation: Y = -12.6 + 0.722 * 387, giving us a predicted verbal score when calculated.

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Answer:3 foot

Step-by-step explanation:

Answer:

[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]

Step-by-step explanation:

Since it is circular slick, it's volume can be modeled as,

[tex]V = \pi R^{2}h[/tex]

Where R is the radius in feet and h is the thickness of slick.

taking derivative of the above equation with respect to time yields,

[tex]\frac{dV}{dt} = \pi 2Rh \frac{dR}{dt}[/tex]

Where the rate of change of radius of the slick (dR/dt) is given,

[tex]\frac{dV}{dt} = \pi 2(400)(0.2)(0.31)[/tex]

[tex]\frac{dV}{dt} = 155.82[/tex] [tex]\frac{ft^{3}}{min}[/tex]

Therefore, the rate of change of volume is 155.82 cubic feet per minute.​

The value of dV/dt using pi almost equal to 3.14 gives; dV/dt = 155.82 ft³/min

dV/dt = 155.82 ft³/min

We are given;

Radius; R = 400 ft

Height; h = 0.2 ft

Rate of Increase of radius; dr/dt = 0.31 ft/min

Formula for Volume of a cylinder is;

V = πr²h

Differentiation of both sides of V and r with respect to t gives;

dV/dt = 2πrh(dr/dt)

Plugging in the relevant values gives;

dV/dt = 2π × 400 × 0.2 × 0.31

dV/dt = 155.82 ft³/min

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Answer:

  x = 1

Step-by-step explanation:

As you might guess, the zeros are symmetrical about the axis of symmetry. That is, the axis of symmetry is midway between the zeros, so will be their average value:

  x = (-2 +4)/2 = 1

The axis of symmetry is x = 1.

Answer:

The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.

Approximation at points (1.1,1.9) is 0.7

Step-by-step explanation:

Given:

Tangent plane to  a surface z=5x+2y-10 as the function at point (1,2)

To find :

f(x,y) at (1,2)

partial derivatives of function w.r.t. (x and y) and value of that function at given points.

Solution:(refer the attachment also)

Now we know that

the equation of tangent plane at given points to the surface is given by,

f(x1,y1,z1) and z=f(x,y)

z-z1=Fx(x1,y1)*(x-x1)+Fy(x1,y1)*(y-y1)

here Fx(x1,y1) and Fy(x1,y1) are the partial derivatives of x and y.

now

taking partial derivative w.r.t. x we get

Fx(x1`,y1)=[tex]\frac{d}{dx} (5x+2y-10)[/tex]

=5.

Then w.r.t y we get

Fy(x1,y1)=

[tex]\frac{d}{dy}(5x+2y-10)[/tex]

=2.

The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.

Using the Linearization or linear approximation we get

L(x,y)=f(x1,y1)+Fx(x,y)*(x-x1)+Fy(x,y)(y-y1)

=-1+5(x-1)+2(y-2)

=5x+2y-10

Approximation at F(1.1,1.9)

=5(1.1)+2(1.9)-10

=5.5+3.8-10

=0.7

Approximation at points (1.1,1.9) is 0.7

Final answer:

The partial derivatives of f(x, y) at (1, 2) are fx(1,2) = 5 and fy(1,2) = 2. The function value f(1,2) is 0. An approximation for f(1.1, 1.9) using the tangent plane is 0.5.

Explanation:

The question concerns the computation of partial derivatives and the evaluation of a function f(x, y) given its tangent plane at a specific point. Given the tangent plane to z=f(x,y) at the point (1, 2), which is z=5x+2y−10, we have:

fx(1,2) is the partial derivative of z with respect to x at the point (1,2), equivalent to the coefficient of x in the tangent plane equation, which is 5.

fy(1,2) is the partial derivative of z with respect to y at the point (1,2), equivalent to the coefficient of y in the tangent plane equation, which is 2.

To find f(1,2), we substitute x=1 and y=2 into the tangent plane equation to get z = 5(1) + 2(2) − 10 = 0.

The value f(1.1,1.9) can be approximated by using the tangent plane equation. By plugging x=1.1 and y=1.9 into the equation, we obtain z = 5(1.1) + 2(1.9) - 10 = 0.5, for an approximate value of f(1.1, 1.9).

Summary of Answers:

fx(1,2) = 5

fy(1,2) = 2

f(1,2) = 0

f(1.1,1.9) ≈ 0.5

Answer:

D

Step-by-step explanation:

200 men and 2,000 women

i dont know how but that was just the answer

The sampling distribution of ā-Ă will be approximately normal when both populations satisfy the conditions for np > 5 and nq > 5. The sample sizes must ensure these inequalities are met using the proportions 0.08 for men and 0.005 for women.

The sampling distribution of ā - Ă will be approximately normal when the sample sizes are large enough to satisfy the condition np > 5 and nq > 5 for both populations. Given that in the population of men, 8 percent carry the genetic trait (p1 = 0.08), and in the population of women, 0.5 percent carry the trait (p2 = 0.005), we need to find appropriate sample sizes for each population.

For the men's population:
n1p1 > 5 and n1(1 - p1) > 5.

For the women's population:
n2p2 > 5 and n2(1 - p2) > 5.

The sample sizes should be selected in a way that these inequalities are met for both populations to ensure that the sampling distribution of ā-Ă is approximately normal.

Answer: the null hypothesis states that there is no difference between the number of cavities of children who had used either Toothpaste brand X or Toothpaste brand Y for a year.

Step-by-step explanation:

The null hypothesis is the hypothesis that is assumed to be true. It is an expression that is the opposite of what the researcher predicts.

The alternative hypothesis is what the researcher expects or predicts. It is the statement that is believed to be true if the null hypothesis is rejected.

Looking at the given situation,

The difference was significant at the .05 level. This means that there was enough evidence to reject null hypothesis. Since the null hypothesis contradicts the alternative hypothesis, then the null hypothesis would state that there is no difference between the number of cavities of children who had used either Toothpaste brand X or Toothpaste brand Y for a year.

Answer:

D)6 units

Step-by-step explanation:

the answer is D because since side AB have the same y coordinate then you would have to either subtract or add the x. if one point on x is negative and the other is positive then you would add. but if they were both positive or both negative then you would subtract the x.

The height of the rectangle in inches is 6.5 inches.

The area of a rectangle  = lw

where

l = length

w = width

Therefore,

area = 45.5 in²

length = 7 inches

The height of the rectangle can be found below:

45.5 = 7h

divide both sides by 7

45.5 / 7 = h

h = 6.5 inches

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Based on the information given the height of the rectangle in inches is 6.5 inches.

Using this formula

Area of a rectangle  = Length× Width

Where:

Area = 45.5 in²

Length = 7 inches

Hence,

Let solve for Length

45.5 = 7h

Divide both sides by 7

h=45.5 / 7  

h = 6.5 inches

Inconclusion the height of the rectangle in inches is 6.5 inches.

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Answer:

[tex]28-2.064\frac{10}{\sqrt{25}}=23.872[/tex]    

[tex]28+2.064\frac{10}{\sqrt{25}}=32.128[/tex]    

So on this case the 95% confidence interval would be given by (23.9;32.1)  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X=28[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=25-1=24[/tex]

Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that [tex]t_{\alpha/2}=2.064[/tex]

Now we have everything in order to replace into formula (1):

[tex]28-2.064\frac{10}{\sqrt{25}}=23.872[/tex]    

[tex]28+2.064\frac{10}{\sqrt{25}}=32.128[/tex]    

So on this case the 95% confidence interval would be given by (23.9;32.1)    

The 95% confidence interval for the average age of the boutique's customers is from 24.1 to 31.9 years, calculated using the sample mean of 28 years, a standard deviation of 10 years, and a sample size of 25.

To calculate a 95% confidence interval for the average age of all customers in the boutique, we will use the sample mean, standard deviation, and the size of the sample along with the z-score corresponding to a 95% confidence level.

The formula for a confidence interval when the population standard deviation is known is:

Confidence interval = {x} (Z  {Σ}/√{n}})

In this case, we have:

Sample mean ({x}): 28 years

Standard deviation (Σ): 10 years

Sample size (n): 25

Z-score for 95% confidence: 1.96 (from z-tables)

First, we calculate the margin of error:

The margin of error = Z{Σ}/{√{n}} = 1.96  {10}/{√{25}} = 1.96 × 2 = 3.92

Then, the confidence interval is:

Lower limit = {x} - Margin of error = 28 - 3.92 = 24.08

Upper limit = {x} + Margin of error = 28 + 3.92 = 31.92

Therefore, the 95% confidence interval for the average age of the boutique's customers is from 24.1 to 31.9 years.

Answer:

[tex]50\sqrt{2} feet[/tex]

Step-by-step explanation:

Given the vertices  (1, 5) and (11, 15) for the corners labeled with red stars, the diagonal of the square C will be the length of the line joining the two vertices.

Using the Distance Formula:

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex](x_1,y_1)=(1, 5) \:and\: (x_2,y_2)=(11, 15)[/tex]

[tex]Distance=\sqrt{(11-1)^2+(15-5)^2}\\=\sqrt{10^2+10^2}\\=\sqrt{200}\\=10\sqrt{2}[/tex]

Since 1 Square Unit = 25 Square Feet

1 Unit =5 feet

Therefore, the length of the diagonal

[tex]=5*10\sqrt{2} \\=50\sqrt{2} \:feet[/tex]

Answer:

50 with 2 squared

Step-by-step explanation:

Answer:

  in 6 years

Step-by-step explanation:

Using t=10 to represent today, we can write the exponential growth function as ...

  p(t) = 200(550/200)^(t/10)

Then we can set p(t) = 1000 and solve for t:

  1000 = 200(11/4)^(t/10) . . . . simplifying the growth factor

  1000/200 = (11/4)^(t/10) . . . . divide by 200

  log(5) = (t/10)log(11/4) . . . . . . take logs

  t = 10·log(5)/log(11/4) ≈ 15.91

That is, about 16 years from 10 years ago, the population will reach 1000.

The population will reach 1000 in about 6 years.

Answer: 55

Step-by-step explanation:

Answer:

42,43,46,46,49,52,52,55,56

Step-by-step explanation:

Answer:

The expression is undefined where the denominator equals  

0  , the argument of an even indexed radical is less than  

0  , or the argument of a logarithm is less than or equal to  0  .  k  =  −  2  ,  k  =  0  ,  k  =  2 ,  k = 6

Step-by-step explanation:

I'm not rocket scientist but I hope this helps in anyway, if not i'm so sorry i tried. :)

Answer:

Null hypothesis is rejected. There is no or little evidence to support the claim made by Mars.In

Step-by-step explanation:

Solution:-

- A claim is made by Mars.In that the M&M candies in a packet are distributed by color percentage given below.

- A random sample of N = 460 M&M's was taken and the frequencies of different colors were observed as given below.

- We are to test a claim made by the Mars.In regarding the color distribution of M&Ms at significance level α = 0.05.

- Compute the expected frequency of distribution for color as per Mars.In claim. Use the following formula for expected outcome:

                          Expected = N*pi

Where, pi : The percentages for each color.

- The table for expected and observed frequencies for each color is tabulated below.

     Colors            Percentage                 Expected                 Observed

     Brown                  20%                   460*0.2 = 92                     90

     Yellow                  20%                   460*0.2 = 92                     94

        Red                   30%                    460*0.3 = 138                    99

     Orange                10%                    460*0.1 =  46                      64

      Green                 10%                    460*0.1 =  46                      51

       Blue                   10%                    460*0.1 =  46                      62

- To test the claim for color distribution of M&Ms using X^2 - test. We will state the Null and Alternate hypothesis as follows:

Null Hypothesis: The distribution is colors is as its claimed by the company

Alternate Hypothesis: The distribution is colors is not its claimed by the company

- We will first determine the X^2 statistics value using the following relation:

    [tex]X^2-test = Sum [ \frac{(Oi- Ei)^2}{Ei} ]\\\\X^2-test = \frac{(90- 92)^2}{92} + \frac{(94- 92)^2}{92} + \frac{(99- 138)^2}{138} + \frac{(64- 46)^2}{46} + \frac{(51- 46)^2}{46} + \frac{(62- 46)^2}{46} \\\\X^2-test = \frac{4}{92} + \frac{4}{92} + \frac{1521}{138} + \frac{324}{46} + \frac{25}{46} + \frac{256}{46} \\\\X^2-test = 0.04347 + 0.04347 + 11.0217 + 7.04348 + 0.54348 + 5.56522\\\\X^2-test = 24.2608[/tex]  

- The rejection region is defined by the significance level ( α ) = 0.05 and degree of freedom. The bound ( critical value ), X^2-critical is determined using the look-up table:

             degree of freedom = number of observation category - 1 = 6 - 1 = 5

             P ( X < X^2 - critical ) = 0.025

             X^2 - critical = 12.8        

- All the test values of X^2 > X^2-critical lie in the rejection region.

             24.2608 > 12.8

             X^-test > X^2-critical

Hence, Null hypothesis is rejected.

Conclusion: As per Chi-square test the claim made by the Mars.In has little or no evidence to be true; hence, the color distribution of M&M is not what is claimed.

Answer:

Check the explanation

Step-by-step explanation:

let the money on bet is X.

probability of winning =18/38=9/19

probability of losing =(1-9/19)=10/19

expected outcome =[tex]\tiny \sum[/tex]probability *return   =(

Expected value of return after one bet is =(9/19*x)-(10/19*x)=-1x/19

it is negative which is obvious cause casinos are there to earn money.

a) Our best strategy in this case as probability of winning is near by 50 %, we should place a bet of 1 $ each,and when we lose one bet consecutively we should bet twice the amount..

Cause two consecutive losses on black has less probability.

c) In case we have to reach 30 $ we have to use the same strategy as above.

Explaining the best gambling strategy using expected value in roulette scenarios.

Expected value is a key concept when determining the best strategy in gambling scenarios like this. In the given situation, if you want to play until you reach $20 starting with $10, the best strategy is to bet the maximum amount on each spin. This way, your expected value increases, giving you a higher chance of reaching $20.

On the other hand, if you aim to reach $30 starting with $10, it's better to bet smaller amounts on each spin to minimize the risk of going broke quickly. By betting conservatively, you increase your chances of eventually reaching $30.

The sample points in the event A ∪ B are 1, 2, 3, 4, 5, 6, 8, and 10, which is determined by the union.

To identify the sample points in event A ∪ B (the union of events A and B), we need to determine the numbers that satisfy either event A or event B or both.

Event A: The number is even.

Sample points in event A are: {2, 4, 6, 8, 10}.

Event B: The number is less than 7.

Sample points in event B are: {1, 2, 3, 4, 5, 6}.

To find the sample points in the union of events A and B (A ∪ B), we combine the sample points from both events without duplication.

Thus, the sample points in A ∪ B are: {1, 2, 3, 4, 5, 6, 8, 10}.

Learn more about set theory here:

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The sample points in the event A ∪ B, which include numbers that are either even or less than 7, are {1, 2, 3, 4, 5, 6, 8, 10}.

To find the sample points in the event A ∪ B, where event A: {The number is even} and event B: {The number is less than 7}, we first identify the numbers between 1 and 10 that satisfy each event. For event A, the even numbers between 1 and 10 are 2, 4, 6, 8, and 10. For event B, the numbers less than 7 are 1, 2, 3, 4, 5, and 6.

The union of two events, A ∪ B, includes all sample points that are in event A, event B, or in both A and B. Therefore, the union of A ∪ B includes the even numbers (2, 4, 6, 8, 10) and the numbers less than 7 (1, 2, 3, 4, 5, 6), without listing any number more than once.

Thus, the sample points in the event A ∪ B are {1, 2, 3, 4, 5, 6, 8, 10}.

Answer:16

Step-by-step explanation:

The lcm of 4 and 16 is 16.

16

the lcm of 4 and 16 is 16