6.- Find the area under the standard normal distribution: to the left of z=-1.55.

Answer:

(a) The expected value of the prize for one play of Instant Lotto is $3.50.

(b) The probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.

(c) The probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.

Step-by-step explanation:

(a)

The probability distribution of the monetary prizes that can be won at the game called Instant Lotto is:

X         P (X = x)

$10        0.05

$15        0.04

$30       0.03

$50       0.01

$1000   0.001

$0         0.869

___________

Total =   1.000

Compute the expected value of the prize for one play of Instant Lotto as follows:

[tex]E(X)=\sum x\cdot P (X=x)[/tex]

         [tex]=(10\times 0.05)+(15\times 0.04)+(30\times 0.03) \\+ (50\times 0.01)+(1000\times 0.001)+(0\times 0.869)\\=0.5+0.6+0.9+0.5+1+0\\=3.5[/tex]          

Thus, the expected value of the prize for one play of Instant Lotto is $3.50.

(b)

Let X = number of times a visitor wins some prize.

A visitor to the casino is given n = 20 free plays of Instant Lotto.

The probability that a visitor wins at any of the 20 free plays is, p = 1/20 = 0.05.

The event of a visitor winning at a random free play is independent of the others.

The random variable X follows Binomial distribution with parameters n = 20 and p = 0.05.

Compute the probability that the visitor wins some prize at least twice in the 20 free plays as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

              [tex]=1-[{20\choose 0}0.05^{0}(1-0.05)^{20-0}]-[{20\choose 1}0.05^{1}(1-0.05)^{20-1}]\\=1-0.3585-0.3774\\=0.2641[/tex]

Thus, the probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.

(c)

Let X = number of people who play Instant Lotto each day.

The random variable X is normally distributed with a mean, μ = 800 people and a standard deviation, μ = 310 people.

Compute the probability that a randomly selected day has at least 1000 people play Instant Lotto as follows:

Apply continuity correction:

P (X ≥ 1000) = P (X > 1000 + 0.50)

                    = P (X > 1000.50)

                    [tex]=P(\frac{X-\mu}{\sigma}>\frac{1000.50-800}{310})[/tex]

                    [tex]=P(Z>0.65)\\=1-P(Z<0.65)\\=1-0.74215\\=0.25785\\\approx0.2579[/tex]

Thus, the probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.

The type of triangle is,

⇒ A scalene triangle

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The angle measures in a triangle are 25°, 135°, and 20°.

Now, We have alL angles are different to each other.

Hence, By definition of a scalene triangle,

The type of triangle is,

⇒ A scalene triangle

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Answer:

Bruh i got correlation hw that i posted on here too and nobody helped lol.

Step-by-step explanation:

Answer:

The graphs of the equations intersect each other at two places.

The correct answer is the graphs of the equations intersect each other at two places.

A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solutions.

Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.

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Answer:

[tex]P(49.5<X<67.2)=P(\frac{49.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{67.2-\mu}{\sigma})=P(\frac{49.5-55.7}{5.2}<Z<\frac{67.2-55.7}{5.2})=P(-1.192<z<2.212)[/tex]

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)[/tex]

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)=0.987-0.117=0.870[/tex]

Step-by-step explanation:

We define X the random variable that represent the heights of a population for ten year old children, and for this case we know the distribution for X is given by:

[tex]X \sim N(55.7,5.2)[/tex]  

Where [tex]\mu=55.7[/tex] and [tex]\sigma=5.2[/tex]

We want to find this probability:

[tex]P(49.5<X<67.2)[/tex]

We can use the z score formula to solve this problem given by:

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

Using this formula we have:

[tex]P(49.5<X<67.2)=P(\frac{49.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{67.2-\mu}{\sigma})=P(\frac{49.5-55.7}{5.2}<Z<\frac{67.2-55.7}{5.2})=P(-1.192<z<2.212)[/tex]

And we can find this probability with this difference

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)[/tex]

We can use tables for the normal standard distribution, excel or a calculator and we got this

[tex]P(-1.192<z<2.212)=P(z<2.212)-P(z<-1.192)=0.987-0.117=0.870[/tex]

Answer:

7

Step-by-step explanation:

Final answer:

To factor a composite number into primes, divide it by its smallest divisor that is not 1, then continue dividing the quotient until all factors are prime. An example is the number 60, which factors into 2 x 2 x 3 x 5, or 2² x 3 x 5 when using exponents for the repeated factor of 2.

Explanation:

The subject of the question is to select a composite number and break down its factors until all the factors are prime. As an example, let's choose the composite number 60. Here's how you can factor it into primes:

First, note that 60 is an even number, so it is divisible by 2. Start by dividing 60 by 2 to get 30.

Now, 30 is still even, so we can divide by 2 again to get 15.

15 is divisible by 3, so when we divide it by 3, we get 5, which is a prime number.

So, the prime factorization of 60 is 2 x 2 x 3 x 5, often written using exponents for any repeated factors as 22 x 3 x 5.

Through factorization, we have converted the composite number into a product of prime factors. Each factor multiplication is a step that requires one to find two numbers that multiply to the number we are factoring and continuing this process until we reach numbers that are prime.

Answer:

Check the explanation

Step-by-step explanation:

b ) [tex]P(s^2<p\sigma^2)=0.05[/tex]

or , [tex]P\left (\frac{(n-1)s^2}{\sigma^2}<(n-1)p \right )=0.05[/tex]

or , [tex]P\left (\chi^2_5<5p \right )=0.05=P(\chi^2_5< 1.145476 )[/tex]

or , 5p =1.145476

or , [tex]p =\frac{1.145476}{5}= 0.2290952[/tex]

Required percentage = 22.91

Answer:

25 miles per gallon x 7 gallons used=175 miles driven

175/7=25

NOTE: THIS IS AN EXAMPLE

The length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.

Pythagoras theorem states that, right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

A builder makes all the ramps with a base to height ratio of 12 to 1 to be wheelchair accessible.

Let p is the factor of ratio. Thus, the height and base is,

h = p

b = 12p

According to Pythagoras theorem,

unknown side (say l) is hypotenuse

l² = (12p)² + p²

[tex]l^2=144p+p^2[/tex]

[tex]l = \sqrt{144p+p^2}[/tex]

[tex]l = \sqrt{145} p[/tex]

A ramp needs to cover a height of 0.8 m. Height is equal to the factor p.

Thus, the value of p is,

p = h

p = 0.80

Thus, the length of the l is,

[tex]l = \sqrt{145} p[/tex]

[tex]l = \sqrt{145} {(0.8)}[/tex]

[tex]l=(12.041)(0.8)[/tex]

[tex]l=9.63m[/tex]

Hence, the length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.

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The correct question has in the image below

Answer: The final answer in proper fraction is 169/9

Step-by-step explanation:

Given the expression

-6 4/9-3 2/9-82/9

Firstly let us convert all mixed fraction to proper fraction to further simplify the expression

-58/9 - 29/9 - 82/9

We now have all terms in proper fraction, we can continue by finding the LCM which is 9

= (- 58-29-82)/9

= 169/9

Answer:

The expected number of tickets a customer will get is 4.75.

Step-by-step explanation:

The probability distribution of the number of ticket a wheel at a shopping center is arranged to give is as follows:

X           Probability (p)

2                  0.50

5                  0.25

10                  0.23

10                  0.02

The formula to compute the expected value of a random variable is:

[tex]E(X)=\sum x\cdot P (X=x)[/tex]

Compute the expected number of tickets a customer will get as follows:

[tex]E(X)=\sum x\cdot P (X=x)[/tex]

         [tex]=(2\times 0.50)+(5\times 0.25)+(10\times 0.23)+(10\times 0.02)\\=1+1.25+2.3+0.2\\=4.75[/tex]

Thus, the expected number of tickets a customer will get is 4.75.

Answer:

[tex]a. \ H_o:p=0.45, \ \ \ \ H_a:p\neq 0.45\\\\b.\ \hat p=0.2209\\\\c. \ Yes\ (-4.2706<-1.96)[/tex]

Step-by-step explanation:

a. The professor's claim is that 45% first-timers fail his test. The null hypothesis is therefore stated as:

[tex]H_o:p=0.45[/tex]

-The alternative hypothesis is that more or less people fail the test as opposed to the professor's exact claim, hence:

[tex]H_a:p\neq 0.45[/tex]

b. To compute the P-value we use the z-value for a 95% confidence level:

[tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]

#The proportion of failures in the sample of 86 is 19:

[tex]\hat p=\frac{19}{86}\\\\=0.2209[/tex]

The z-value is calculated as:

[tex]z=\frac{\hat p-p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}[/tex]

[tex]=\frac{0.2209-0.45}{\sqrt{\frac{0.45(1-0.45)}{86}}}\\\\\\=-4.2706[/tex]

-4.2706 is less than the stated confidence level for the given 45% proportion and greatly differs from it.

- Reject the null hypothesis as there is enough evidence to reject the claim.

-Hence,Yes, Professor Brown can conclude that percentage  of failures differs from 45%.

Answer:

=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)

0.001324586

Step-by-step explanation:

The success probability is p = 70% = 0.70

The number of trials are n = 25

The Excel formula for the binomial distribution is given by

BINOMDIST(Number_s, Trial_s, Probability_s, Cumulative)

Where

Numbers = 5 and 10

Trials = 25

Probability = 70%

Cumulative = FALSE

The probability of between 5 and 10 customers is then

=BINOMDIST(10,25,70%,FALSE) -BINOMDIST(5,25,70%,FALSE)

0.001324586

Note: FALSE option provides the probability of exactly 10 and 5 where TRUE option gives cumulative results (0 to 5 or 0 to 10) that would be wrong in this case.

Using the binomial distribution, it is found that the Excel statement that will find the probability of between 5 and 10 customers is:

BINON.DIST.RANGE(25, 0.75, 5, 10)

For each customer, there are only two possible outcomes, either they purchase a pair of running shoes, or they do not. Customers' purchases are independent, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Using Excel, the probability of the number of successes being between a and b, inclusive, is given by:

BINOM.DIST.RANGE(n, p, a, b)

In this problem:

Then, the Excel statement is:

BINON.DIST.RANGE(25, 0.75, 5, 10)

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Answer:

a) - The population consists of all of Danielle's colleagues that could have been one of the randomly surveyed 50.

- The sample is Danielle's 50 colleagues that she ramdomly sampled.

b) From the statistical test performed, there is significant evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.

c) Check Explanation

Step-by-step explanation:

The full complete, correct question is attached to the solution of this question.

a) The population is normally the extended distribution where every selected random sample is extracted from. So, for this question, the population will be all of Danielle's colleagues.

The sample is the subset distribution obtained from the population. In the question, it is stated explicitly that Danielle randomly picked 50 of her colleagues to participate in the survey. Hence, the sample is Danielle's 50 colleagues that she ramdomly sampled.

b) The appropriate statistical inference for this question is to carry out the t-test hypothesis test.

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, Danielle wants to prove that she is overpaying for her auto insurance compared to her colleagues.

So, the null hypothesis is that there is no significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.

That is, Danielle isn't overpaying for her auto insurance compared to her colleagues or better stated that her colleagues are paying more than or just about the same for auto insurance compared to her.

While, the alternative hypothesis is that there is significant evidence to conclude that Danielle is overpaying for her auto insurance compared to her colleagues.

Let μ be the mean Danielle's colleagues' auto insurance fees.

Mathematically,

The null hypothesis is represented as

H₀: μ ≥ 476

The alternative hypothesis is given as

Hₐ: μ < 476

To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ₀)/σₓ

x = sample mean = $447

μ₀ = Danielle's auto insurance bill that we're comparing the sample against = $476

σₓ = standard error = [σ/√n]

σ = Sample standard deviation = $75

n = Sample size = 30 (30 colleagues got back to Danielle)

σₓ = [75/√30] = $13.693

t = (447 - 476) ÷ 13.693

t = -2.117 = -2.12

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 30 - 1 = 29

Significance level = 0.05 (Most hypothesis tests are carried out at this level of significance)

The hypothesis test uses a one-tailed condition because we're testing only in one direction. (Checking whether Danielle is overpaying or that the mean is of her colleagues' auto insurance fees is less than Danielle's)

p-value (for t = -2.12, at 0.05 significance level, df = 29, with a one tailed condition) = 0.021342

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.021342

0.021342 < 0.10

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that Danielle is truly overpaying for her auto insurance compared to her colleagues.

c) The two type of errors associated with this test include the Type I and Type II errors.

In Hypothesis testing, A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.

A type II error involves failing to reject the null hypothesis when in reality it should have been rejected. It entails not rejecting the null hypothesis and making conclusions based on the null hypothesis, when in reality, the alternative hypothesis should have been accepted together with its conclusion.

For this question, a type I error entails obtaining from the statistical test that Danielle is overpaying when she isn't overpaying for her auto insurance compared to her colleagues in reality.

A type II error would be obtaining from the statistical test that Danielle isn't overpaying when she is truly overpaying for her auto insurance compared to her colleagues, in reality.

Hope this Helps!!!

The comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.

Step 1:

The comparison of the slopes of the two lines can be made by calculating the slope of each line. Let's calculate the slopes:

For Car 1:

The coordinates are (2, 50) and (4, 100).

Using the slope formula [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex]:

[tex]\[ m = \frac{100 - 50}{4 - 2} = \frac{50}{2} = 25 \][/tex]

For Car 2:

The coordinates are (2, 40) and (4, 80).

Using the slope formula:

[tex]\[ m = \frac{80 - 40}{4 - 2} = \frac{40}{2} = 20 \][/tex]

Step 2:

Comparing the slopes:

- The slope of the line for Car 1 is 25.

- The slope of the line for Car 2 is 20.

Therefore, the comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.

Answer:

Point Estimate for different between population means = - 0.99

Step-by-step explanation:

We are given data of two samples and we have to find the best point estimate of the true difference between two population means. Remember that in absence of data about population the best estimator is the sample data. So, we will find the means of both sample data and find the difference of that means. This difference between the means of sample data will be the best point estimate for the true difference between the population means.

Formula to calculate the mean is:

[tex]Mean=\frac{\text{Sum of Values}}{\text{Number of Values}}[/tex]

Mean of Sample 1:

[tex]Mean=\frac{1414}{11}=128.55[/tex]

Mean of Sample 2:

[tex]Mean=\frac{1684}{13}=129.54[/tex]

Therefore the best point estimate for difference between two population means would be = Mean of Sample 1 - Mean of Sample 2

= 128.55 - 129.54

= - 0.99

Final answer:

The point estimate for the true difference between the given population means is -1.028.

Explanation:

The point estimate for the true difference between the given population means can be found by subtracting one sample mean from the other. Let's calculate it:

Sample 1: 129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127
Sample 2: 131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131

Sample mean of Sample 1 = (129+127+129+129+128+130+127+129+128+131+127)/11 = 128.818

Sample mean of Sample 2 = (131+126+132+129+128+131+131+130+128+129+126+132+131)/13 = 129.846

Point estimate for the difference = Sample mean of Sample 1 - Sample mean of Sample 2 = 128.818 - 129.846 = -1.028

Answer:

a =8

Step-by-step explanation:

-5(a + 3) = -55

Distribute

-5a -15 = -55

Add 15 to each side

-5a-15+15 = -55+15

-5a = -40

Divide each side by -5

-5a/-5 = -40/-5

a = 8

The total cost of two packets of fig rolls, with the second one at half price, is £1.62. The calculation involves the normal price of one packet plus half of that price for the second one.

The question involves calculating the total cost of fig rolls when a shop offers a deal where if you buy one packet, you get the second packet at half the price.

To find the total cost of two packets under this offer, we first take the normal price of one packet (£1.08) and add it to half of that price (which is £1.08 / 2 = £0.54). The total cost for two packets is therefore £1.08 (first packet) + £0.54 (second packet at half price), which equals £1.62.

For 3 packets of fig rolls and 6 packets of crisps, the total price is £8.42 considering the offers of buy one, get 2nd half price and three for the price of two, respectively.

For the fig rolls:

Normal price for 1 packet = £1.08

Buy one, get 2nd half price.

So, for 3 packets of fig rolls, we'd pay for 2 and get the third at half price.

Total cost for 3 packets of fig rolls = Cost of 2 packets + Half price of 1 packet

[tex]= 2 \times £1.08 + \frac{1}{2} \times £1.08[/tex]

= £2.16 + £0.54

= £2.70

For the crisps:

Normal price for 1 packet = £1.43

Three for the price of two.

So, for 6 packets of crisps, we'd pay for 4 and get 2 free.

Total cost for 6 packets of crisps = Cost of 4 packets

[tex]\(= 4 \times £ 1.43\)[/tex]

= £5.72

Therefore, the total price for 3 packets of fig rolls and 6 packets of crisps would be:

Total = Cost of 3 fig roll packets + Cost of 6 crisps packets

= £2.70 + £5.72

= £8.42

Complete Question:

The number in question is found by setting up the equation (x + 13) / -7 = -4, and solving for 'x'. Following order of operations and sign rules, we determine that the number is 15.

The question asks us to find a number when given that the quotient of that number increased by 13 and -7 is -4. To solve this, we set up an equation and follow the multiplication and division rules for signs and the order of operations.

Let the unknown number be 'x'. According to the problem, (x + 13) / -7 = -4. Multiplying both sides by -7 to eliminate the denominator, we get x + 13 = (-7)(-4). Applying the rule that the product of two negative numbers is positive, we simplify the right side to get x + 13 = 28. Now, we subtract 13 from both sides to isolate 'x': x = 28 - 13, which gives us x = 15.

The number in question is therefore 15.

Answer:

7

Step-by-step explanation:

67ururiierururf8fucicififfifig

Answer:

The height that cuts off the top 5% is 74.83 inches.

Step-by-step explanation:

We are given that in the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches.

Let X = heights of respondents

So, X ~ N([tex]\mu=69.9,\sigma^{2} =3^{2}[/tex])

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

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

where, [tex]\mu[/tex] = mean height = 69.9 inches

            [tex]\sigma[/tex] = standard deviation = 3.0 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, we have to find the height that cuts off the top 5%, that means;

           P(X > [tex]x[/tex]) = 0.05   {where [tex]x[/tex] is the height that cuts off top 5%}

           P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{ x -69.9}{3}[/tex] ) = 0.05

           P(Z > [tex]\frac{ x -69.9}{3}[/tex] ) = 0.05

Now, in the z table the critical value of X that gives the area of top 5% is given as 1.6449.

So,         [tex]\frac{ x -69.9}{3} = 1.6449[/tex]

              [tex]x -69.9= 1.6449 \times 3[/tex]

                 [tex]x[/tex] = 69.9 + 4.9347 = 74.83

Hence, the height that cuts off the top 5% is 74.83 inches.

Answer:

The y-intercept is y = 2

Step-by-step explanation:

A linear function has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept, which is the value of y when x = 0.

We are given these three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to build a system, to find values for m and b.

(-28, -54)

This means that when [tex]x = -28, y = -54[/tex]

So

[tex]y = mx + b[/tex]

[tex]-54 = -28m + b[/tex]

[tex]28m = b + 54[/tex]

[tex]m = \frac{b + 54}{28}[/tex]

(-21, -40)

This means that when [tex]x = -21, y = -40[/tex]

So

[tex]y = mx + b[/tex]

[tex]-40 = -21m + b[/tex]

[tex]-40 = -21\frac{b + 54}{28} + b[/tex]

[tex]-40 = \frac{-21b - 1134 + 28b}{28}[/tex]

[tex]7b - 1134 = -40*28[/tex]

[tex]7b = 14[/tex]

[tex]b = \frac{14}{7}[/tex]

[tex]b = 2[/tex]

The y-intercept is y = 2

Answer:

y = (0,2)

Step-by-step explanation:

Answer:

(5 x 15) + (3 x 15) = 120

Step-by-step explanation:

5 x 15 = 75

3 x 15 = 45

75 + 45 = 120

Hope this helps :)

Answer:

5 * 15 = 75

3 * 15 = 45

45 + 75 = 120

Step-by-step explanation:

When you have a equation like that, you need to multiply. It is a faster way to solve the problem.

You had 15 five times.

15+15+15+15+15= 75 It equals the same thing because it is the same as 5 * 15

Same for the three fifteens.

15+15+15= 45.

The sum of the whole equation is 120 because you add 75 and 45.

Hope this helps, have a good day/night. Stay safe and healthy!

Answer:

840cm³

Step-by-step explanation:

devide them into 2 shapes.

a×b×h

a×b×h

V=720cm³+120cm³=840cm³

Answer:

840 cm^3

Step-by-step explanation:

L x W x H = V

Split the prism into 2 different prisms.

6 is constant throughout the figure, so all we have to do is find the L and H of the two prisms and multiply them by 6.

15 x 8 = 120

The height of the higher prism can be determined by subtracting the bottom height from the total height.

12 - 8 = 4

5 x 4 = 20

Add the two side areas together.

20 + 120 = 140

Multiply by the width, 6.

140 x 6 = 840

The probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is 12/95.

The probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is the product of the probability of choosing a purple jelly bean and the probability of choosing a blue jelly bean given that a purple jelly bean was already chosen.

The probability of choosing a purple jelly bean is 8/20 = 2/5.

The probability of choosing a blue jelly bean given that a purple jelly bean was already chosen is 6/19. This is because there are only 6 blue jelly beans left after the purple jelly bean is eaten, and there are a total of 19 jelly beans left.

Therefore, the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is 2/5 * 6/19 = 12/95.

Another way to solve this problem is to use the following formula:

P(A and B) = P(A) * P(B | A)

Where:

P(A) is the probability of event A happening

P(B | A) is the probability of event B happening given that event A already happened

In this case, event A is choosing a purple jelly bean and event B is choosing a blue jelly bean.

Therefore, the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean is:

P(purple jelly bean) * P(blue jelly bean | purple jelly bean) = 2/5 * 6/19

= 12/95.

To learn more about probability here:

https://brainly.com/question/32117953

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Answer:

(D) 180 degrees

Step-by-step explanation:

There are 12 hours on the clock.

For each 1 hour, the hour hand rotates = [tex]360^0 \div 12=30^0[/tex]

From 8 o'clock in the morning to 2 o'clock in the afternoon= 6 Hours

Therefore:

Number of degrees rotated by the hour hand = [tex]6 X 30^0 =180^0[/tex]

Answer:

  17 points

Step-by-step explanation:

20% × 85 = 0.20 × 85 = 17

Jayla scored 17 points.

Answer:

It should go exponents, multiplication and division, then addition and subtraction

Step-by-step explanation:

By using PEMDAS, for order of operations, it's easier to remember which set comes first. (parentheses, exponents, multiplication, division, addition, subtraction)

Answer:

4/6 > 3/10

Step-by-step explanation:

4/6 < 3/10

First get a common denominator of 30

4/6 *5/5   < 3/10 *3/3

20/30 < 9/30

This is false since 20 > 9