(-)*(-)*(-)
a. +
b. -
c. 0

pls help

The option are missing in the question. The options are :

A.  P = 2, a = 1

B.  \($P=\frac{1}{2} ; a =\frac{1}{3}$\)

C. \($P=\frac{1}{2} ; a =1$\)

D. P = 2, a = 3

Solution :

The given function is \($f(x)= Pa^x$\)

So for the function to be an exponential growth, a should be a positive number and should be larger than 1. If it less than 1 or a fraction, then it is a decay. If the value of a is negative, then it would be between positive and negative alternately.

When the four option being substituted in the function, we get

A). It is a constant function since \($2(1^x)=2$\)

B). Here, the value of a is a fraction which is less than 1, so it is a decay function. \($f(x)=\frac{1}{2}\left(\frac{1}{3}\right)^x$\)

C). It is a constant function since the value of a is 1.

D). Here a = 3. So substituting, as the value of x increases by 1, the value of the function, f(x) increases by 3 times.

  \($f(x)=2(3)^x$\)

Therefore, option (D). represents an exponential function.

Answer:

Its P = 1/5 ; a = 2

Step-by-step explanation:

I am doing the test; I got it right.

The probability value of (m, n) is (1, 2^1005).

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

(1/2) ⋅ (2^1004 + (-1)^1005)

Thus, the probability is: P = (1/2^1004) ⋅ (1/2) ⋅ (2^1004 + (-1)^1005) = 1/2 + 1/2^1005. Hence, (m, n) = (1, 2^1005).

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Complete question:

If m/n is the probability that the reciprocal of a randomly selected positive odd integer less than 2010 gives a terminating decimal, with m and n being relatively prime positive integers. what is probability value of m and n?

The probability value of (m, n) is (1, 2^1005).This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

Let n be a positive odd integer. We are asked to find the probability that its reciprocal gives a terminating decimal. This is equivalent to saying that the only prime factors of n are 2 and 5 because any other prime factor will yield a repeating decimal.

If n is less than 2010, then its only possible prime factors are 3, 7, 11, ..., 2009, since all primes greater than 2009 are greater than n. We want n to have no prime factors other than 2 and 5. There are 1005 odd integers less than 2010.

We want to count how many of these have no odd prime factors other than 3, 7, 11, ..., 2009. This is equivalent to counting how many subsets there are of {3, 7, 11, ..., 2009}. There are 1004 primes greater than 2 and less than 2010. Each of these primes is either in a subset or not in a subset. Thus, there are 2^1004 subsets of {3, 7, 11, ..., 2009}, including the empty set.

Thus, the probability is:

P = (number of subsets with no odd primes other than 3, 7, 11, ..., 2009) / 2^1004

We can count this number using the inclusion-exclusion principle. Let S be the set of odd integers less than 2010. Let Pi be the set of odd integers in S that are divisible by the prime pi, where pi is a prime greater than 2 and less than 2010. Let Pi,j be the set of odd integers in S that are divisible by both pi and pj, where i < j.

Then, the number of odd integers in S that have no prime factors other than 2 and 5 is:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...|

where the union is taken over all sets of primes with at least one element and less than or equal to 1005 elements.

By the inclusion-exclusion principle:

|S - ⋃ Pi + ⋃ Pi,j - ⋃ Pi,j,k + ...| = ∑ (-1)^k ⋅ (∑ |Pi1,i2,...,ik|)

where the outer summation is from k = 0 to 1005, and the inner summation is taken over all combinations of primes with k elements.

This simplifies to:

\((1/2) * (2^{1004} + (-1)^1005)\)

Thus, the probability is: P = \((1/2)^{1004}* (1/2) *(2^{1004} + (-1)^{1005}) = 1/2 + 1/2^{1005}.\)

Hence, (m, n) = (\(1, 2^{1005\)).

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Answer:

(x - 10)(x + 8)

Step-by-step explanation:

x² - 2x - 80

Consider the factors of the constant term (- 80) which sum to give the coefficient of the x- term (- 2)

The factors are - 10 and + 8 , since

- 10 × 8 = - 80 and - 10 + 8 = - 2 , then

x² - 2x - 80 = (x - 10)(x + 8)

The absolute minimum value of the function over the interval [-6, 6] is -18, which occurs at x = -6, and the absolute maximum value of the function over the interval [-6, 6] is 18, which occurs at x = 6.

To find the absolute maximum and minimum values of the function 3x [-6, 6],

we can find the critical points and evaluate the function at the critical points and the endpoints of the interval.

To find the critical points, we need to set the derivative of the function equal to zero and solve for x:

\($$\frac{d}{dx}(3x) = 3 = 0$$\)

Since the derivative is constant and never equals zero, there are no critical points in the interval [-6, 6].

Therefore, the absolute maximum and minimum values occur at the endpoints of the interval.

We can evaluate the function at the endpoints:

\($$3(-6) = -18$$$$3(6) = 18$$\)

Therefore, the absolute minimum value of the function over the interval [-6, 6] is -18,

which occurs at x = -6, and the absolute maximum value of the function over the interval [-6, 6] is 18,

which occurs at x = 6.

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Answer:

D

Step-by-step explanation:

Recall the slope-intercept form of a line:

y = mx + b

slope -2/7 means m = -2/7

y = -2/7x + b

Intercept at (0, -1)

x = 0 and y = -1.

Hence, let's plug it back into the equation we made earlier (y = -2/7x + b)

(-1) = -2/7(0) + b

-1 = b

b must be -1

y = -2/7x -1

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality: x > -9

The missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x is step 6: The division property of inequality.

After step 4, which is -2x < 18, we need to divide both sides of the inequality by -2 to solve for x.

However, since we are dividing by a negative number, the direction of the inequality sign needs to be reversed.

Dividing both sides by -2:

-2x / -2 > 18 / -2

This simplifies to:

x > -9

Therefore, the correct answer is x > -9.

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Answer:

No please! Mr excuse me I am not your type bye

Based on the provided text, it appears to be a mixture of words that are jumbled or misspelled. It does not form a coherent sentence or phrase. Consequently, it is not possible to determine the intentions or meaning behind it.

Regarding the mention of "the author likely choose to vary the length of lines," it suggests a possibility of considering poetic structure or formatting. Varying the length of lines can be a deliberate stylistic choice by the author in poetry. Different line lengths can create visual and rhythmic effects, add emphasis, or convey certain emotions or ideas.

However, without further clarification or context, it is not possible to provide specific insights or interpretations about the intentions of the author or how line lengths may be relevant to the given text.

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The fraction that has been given illustrates that the person who ran further is Jane.

Your information isn't complete. Therefore, an overview of the fraction will given.

Let's assume that Lisa ran 1/2 of a mile and Jane ran 3/4 of a mile. In order to know who ran more, you can convert the fraction to percentage.

This will be:

Lisa = 1/2 × 100 = 50%

Jane = 3/4 × 100 = 75%

Therefore, Jane ran more.

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Answer:

c.3.95 gallons hopes this helps

Answer:

b

Step-by-step explanation:

Answer:

4.1 from my own work.

Step-by-step explanation:

Sin(80)=4/h

*h               *h

Sin(80)*h=4

/Sin(80)   /Sin(80

H=4/Sin(80)

H=4.061706448

H=4.1

The length of the hypotenuse of the right angle triangle is 4.1 inches

A right triangle has one of it sides as 90 degrees. Trigonometric ratios can be use to find the side of the right triangles.

using trigonometric ratio,

sin ∅ = opposite / hypotenuse

Therefore,

∅= 80°

opposite = 4

Therefore,

sin 80° = 4 / h

h = 4 / sin 80°

h = 4 / 0.98480775301

h = 4.06170666618

h = 4.1 inches

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Answer:

The angles in the smaller prism measure 90 degrees.

The perimeter of the rectangular bases changes by a factor of 2.

The area of the rectangular bases changes by a factor of 4.

Step-by-step explanation:

Two polygons are said to be similar if they have the same shape and angles. Also, the ratio of their corresponding sides are to be in the same proportion.

A) Since the two prism are similar, therefore they are to have the same angle measure. The bigger prism has angles with measure of 90°, hence the angles in the smaller prism will also measure 90.

B) Perimeter of bigger prism base = 2(2.2 + 0.8) = 6

Perimeter of smaller prism base = 2(1.1 + 0.4) = 3

Hence, The perimeter of the rectangular bases changes by a factor of 2 (6 / 3).

C) Surface area of bigger prism = 2(2.2*0.8 + 3.2*0.8 + 3.2*2.2) = 22.72

Surface area of smaller prism = 2(1.1*0.4 + 1.6*0.4 + 1.6*1.1) = 5.68

22.72 / 5.68 ≠ 8, hence the surface area does not change by a factor of 8

Option C is wrong

D) Volume of bigger prism = 3.2 * 2.2 * 0.8 = 5.632

Volume of smaller prism = 0.4 * 1.6 * 1.1 = 0.704

The volume of larger prism is not twice of the smaller prism (5.732 / 0.704 ≠ 2)

E) Area of bigger prism base = 2.2*0.8 = 1.76

Area of smaller prism base = 2.2*0.8 = 0.44

Since 1.76 / 0.44 = 4; The area of the rectangular bases changes by a factor of 4

Answer:

A

Step-by-step explanation:

The scale factor can be defined as the ratio of new dimension of an object after scaling to the original  dimension. The are of the new circle is 49 times the area of the original circle. The correct answer is option C.

Scaling factor is a conversion factor used to change the size of a figure without changing its shape. When the size of a figure is increased, it called scaled up and when it decreases it is called as scaled down.

Given that, Scale factor of circle = 7.

Since, the scale factor of a circle is the ratio of new radius to original radius.

The new radius of circle can be written as,

r' = 7r

Thus, the area of new circle is π × (r')^2= π × (49r^2).

Hence, the area of new circle is 49 times the original circle.

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To divide complex numbers, you multiply by the conjugate of the denominator:

    \(\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i}\)

We do this to turn the denominator into a real number.

\(\begin{aligned}\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i} &= \dfrac{-9+6i-18i+12i^2}{9-4i^2}\\[0.5em] &= \dfrac{-9-12i-12}{9+4}\\[0.5em] &= \dfrac{-21-12i}{13}\\[0.5em] &= -\dfrac{21}{13}-\dfrac{12}{13}i\end{aligned}\)

Answer:

\(-\dfrac{21}{13}-\dfrac{12}{13}i\)

Step-by-step explanation:

Given rational expression:

\(\dfrac{-3-6i}{3+2i}\)

Multiply the numerator and denominator by the complex conjugate of the denominator:

\(\implies \dfrac{-3-6i}{3+2i} \cdot \dfrac{3-2i}{3-2i}\)

Simplify:

\(\implies \dfrac{(-3-6i)(3-2i)}{(3+2i)(3-2i)}\)

\(\implies \dfrac{-9+6i-18i+12i^2}{9-4i^2}\)

\(\implies \dfrac{-9-12i+12i^2}{9-4i^2}\)

Apply the imaginary number rule \(i^2=-1\) :

\(\implies \dfrac{-9-12i+12(-1)}{9-4(-1)}\)

\(\implies \dfrac{-9-12i-12}{9+4}\)

\(\implies \dfrac{-21-12i}{13}\)

\(\textsf{Apply the fraction rule} \quad \dfrac{a-b}{c}=\dfrac{a}{c}-\dfrac{b}{c}:\)

\(\implies -\dfrac{21}{13}-\dfrac{12}{13}i\)

The number of voters that should be sampled for a confidence interval depends on the desired level of confidence and the margin of error.

A larger sample size generally leads to a smaller margin of error and a higher level of confidence in the accuracy of the results. However, the relationship between sample size and margin of error is not linear, meaning that doubling the sample size will not necessarily halve the margin of error.
To calculate the required sample size, a formula can be used that takes into account the margin of error, level of confidence, and population size.
the number of voters that should be sampled for a confidence interval depends on several factors and cannot be determined without more information.
To determine the required sample size, you can use the following formula:
n = (Z^2 * p * (1-p)) / E^2

Where:
- n is the sample size
- Z is the Z-score (usually 1.96 for a 95% confidence interval)
- p is the estimated proportion of the population (usually 0.5 for the worst-case scenario)
- E is the margin of error (in decimal form)

Hence, without the specific margin of error, we cannot provide the exact sample size needed.

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Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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Answer:

Step-by-step explanation:

One important statistic in baseball is a pitcher’s earned run average, or ERA. This number represents the average number of earned runs given up by the pitcher per nine innings. The following table lists the portion of the ERAs for pitchers playing for the New York Yankees and the Baltimore Orioles as of July 22, 2010; the complete data, labeled ERA , are available on the text website.

 New York

 Yankees ERA          Baltimore  Orioles ERA

 Sabathia 3.13        Guthrie                     4.58      

 Pettitte 2.88              Millwood                     5.77      

 Burnett 4.99              Matusz                      5.21      

 Hughes 3.99              Bergeson              6.51      

 Vazquez 4.68       Hernandez              4.29      

 Chamberlain 5.80        Berken 2.50      

 Gaudin 6.81             Hendrickson 5.23      

 Rivera 0.98           Albers 4.31      

 Robertson 4.86     Arrieta 4.87      

 Park 5.93        Simon 3.14      

 Mitre 2.88        Ohman 2.57      

 Logan 3.92        Tillman 7.92      

 Marte 4.08        Mata 7.79      

 Aceves 3.00        Meredith 5.40      

 Moseley 7.50        Uehara 2.92      

 Melancon 9.00        Castillo 10.13      

 Albaladejo 5.40        Johnson 6.52      

 Mickolio 7.36      

 Gonzalez 18.00      

a) Calculate the mean and the median ERAs for the New York Yankees. (Round your answers to 2 decimal places.)

Mean is the average sum of the numbers. It is expressed as;

\(\overline x = \frac{\sum Xi}{N}\)

Xi are the individual data

N is the sample size

From the data, the sample size for New York Yankees is 19

\(\sum Xi = 3.13+2.88+4.99+3.99+4.68+5.8+6.81+0.98+4.86+5.93+2.88+3.92+4.08+3.00+7.50+9.00+5.40+7.36+18.00\\\\\sum Xi = 105.19\\\\\overline x = \frac{105.19}{19} \\\\\overline x = 5.54 (to \ 2dp)\)

Median value is the value at the middle after re-arranging.. On rearranging in ascending order;

0.98, 2.88, 2.88, 3.00, 3.13, 3.92, 3.99, 4.08, 4.68)4.86(4.99, 5.40, 5.8, 5.93, 6.81, 7.36, 7.5, 9.00 18.00

Hence the median value is 4.86

b) Calculate the mean and the median ERAs for the Baltimore Orioles. (Round your answers to 2 decimal places.)

\(\sum Xi =4.58+5.77+5.21+6.51+4.29+2.50+5.23+4.31+4.87+3.14+2.57+7.92+7.79+5.40+2.92+10.13+6.52\\\\\sum Xi = 89.66\\\\N = 17\\\\\overline x = \frac{89.66}{17} \\\overline x = 5.27 (to\ 2dp)\)

For the median value:

Re-arrange the value in ascending order

2.50, 2.57, 2.92, 3.14, 4.29, 4.31, 4.58, 4.87)5.21(5.23, 5.40, 5.77, 6.51, 6.52, 7.79, 7.92, 10.13

Hence the median value is 5.21

c.) Based solely on your calculations above, which team is likely to have the better winning record?

The team that is likely to have the better winning record is the team with the highest mean value.

Since New York Yankees has the highest mean value of 5.54, hence the are likely to have the better winning record.

Box plots are used to represent variation in a given dataset.

The statistic that is the same for both box plot is: The interquartile range

I've added the box plots of both pitchers as an attachment

See figure 2 of the attachment on how to read a box plot.

Using the figure 2 as a guide, we have the following statistics.

League A                                                          League B

\(Minimum = 1.1\)                                                 \(Minimum= 1.0\)

\(Q_1 = 3.0\)                                                              \(Q_1 = 3.0\)

\(Q_2 = 4.0\)                                                              \(Q_2 = 3.8\)

\(Q_3 = 5.0\)                                                              \(Q_3 = 5.0\)

\(Maximum = 7.5\)                                                 \(Maximum = 7.3\)

From the above readings, the statistics that have the same value for both leagues are:

\(Q_1 = 3.0\) ----- Lower quartile

\(Q_3 = 5.0\) ---- Upper quartile

The IQR of a dataset is:

\(IQR =Q_3 - Q_1\)

\(IQR =5.0 - 3.0\)

\(IQR =2.0\)

This means that, they have the same interquartile range.

Hence, both leagues have the same (b) interquartile range

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The thickness of each cookie is 0.318 cm.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

\(V = \pi r^2 h \: \rm unit^3\)

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

We are given that;

Diameter=5cm

Volume= 100cm3

Now,

To find the thickness of each cookie, you need to follow these steps:

Plug in the values into the formula for volume and solve for height:

Volume = π × radius^2 × height

100 = π × 2.5^2 × height

100 = 19.635 × height

height = 100 / 19.635

height = 5.093 cm

Divide the height by the number of cookies to get the thickness of each cookie:

Thickness = height / number of cookies

Thickness = 5.093 / 16

Thickness = 0.318 cm

Therefore, by the volume of cylinder answer will be 0.318 cm.

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The minimum is 29 cm and it represents the sensor's minimum height above the ground.

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

By critically observing the graph which models the sensor's height above the ground (in centimeters) shown in the image attached below, we can reasonably infer and logically deduce that it has a minimum height of 29 centimeters.

In conclusion, the sensor's minimum height above the ground cannot exceed 29 centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

B would equal 9

Step-by-step explanation:

take 3/2 you get 1.5

multiple what b is now x 1.5

6*1.5 = 9

Find ratio

\(\\ \sf\longmaosto \dfrac{x}{B}=\dfrac{2}{6}\)

\(\\ \sf\longmaosto \dfrac{x}{B}=\dfrac{1}{3}\)

Put x=3

\(\\ \sf\longmaosto \dfrac{3}{B}=\dfrac{1}{3}\)

\(\\ \sf\longmaosto B=3(3)\)

\(\\ \sf\longmaosto B=9\)

The rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.

Given mechanic first worked 20 hours and mechanic second worked 15 hours and they charged $1650. The sum of rates of first mechanic and second mechanic is $95 per hour.

let the rate charged by first mechanic be x .

let the rate charged by second mechanic be y.

According to question

x +y=95-----------1

20x+15y=1650----------2

Multiply equation 1 by 20 and subtract equation 2 from 1.

20x+20y-20x-15y=1900-1650

5y=250

y=50

put the value of y=50 in 1 to get the value of x.

x +y=95

x+50=95

x=95-50

x=45

Hence the rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.

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Question is incomplete as it should be as under:

Two mechanics worked on a car, the first mechanic worked 20 hrs. and the second mechanic worked 15 hours together. They charged a total of $ 1650.  What is the rate charged per hour for each mechanic if the sum of the two rates per hour was $95 per hour?

The system of equations associated with the augmented matrix [6 3 6 -2 -4 -9] is 6x + 3y + 6z = -2 and -4x - 9y + z = -9. The system of equations associated with the augmented matrix [3 2 1 11; 2 1 3 15; 0 2 -1 -2] is 3x + 2y + z = 11, 2x + y + 3z = 15 and -2x + 4y - z = -2.

For the first augmented matrix, the system of equations would be

6x + 3y + 6z = -2

-4x - 9y + z = 1

The coefficients of x, y, and z can be found in the first three columns of the matrix, and the constants are in the last column. The system of equations can be written by using these coefficients and constants.

For the second augmented matrix, the system of equations would be

3x + 2y + z = 11

2x + y + 3z = 15

-2x + 4y - z = -2

Again, the coefficients of x, y, and z can be found in the first three columns, and the constants are in the last column. The system of equations can be written using these coefficients and constants.

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--The given question is incomplete, the complete question is given

"Write the system of equations associated with each augmented matrix. Do not solve. 6 3 6 -2 -4 -9 1) a) 6x 3y  [ 3 2 1 11 [2 1 3 15. 02 42 -1 -2 3 15 "--

Answer:

Step-by-step explanation:

1. If the circumference is 72, our equation will be d=72/π.

2. 72/π is approximately 22.92.

3. The diameter is approximately 22.92.

The true statement about the counterexample is;

''The counter example must satisfy the hypothesis of the conditional                       statement.''

The option (2) is correct.

Here;

To prove a conditional statement false we use a counterexample.

We have to write the true statement about the counterexample.

What is Counterexample?

A counterexample is an example in which the hypothesis is true, but the conclusion is false.

Now,

Since, A counterexample is used to prove a conditional statement to be false.

So, To prove a statement to be false, only one counterexample is sufficient.

And, When using a counterexample to prove a conditional statement false.

Then, The counterexample must satisfy the hypothesis of the conditional statement.

Therefore, The true statement about the counterexample is;

''The counterexample must satisfy the hypothesis of the conditional                       statement.''

Hence, The option (2) is correct.

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The probability that the result is either 3 and 4 or 5 and a prime number is 33%

Given,

There are probably certain hints that you need to watch out for. You must ADD their individual probabilities when it instructs you to determine the probability of event 1 "or" event 2. You must MULTIPLY their separate probabilities when it instructs you to determine the likelihood of events 1 and 2.

Here,

Two dice are available.

You are need to calculate the likelihood of receiving a face of 3, 4, or 5.

Since there are a total of 6 faces on a dice, the probability of each face is 1/6.

When two dice are used, the result is either 2/12 or still 1/6.

Therefore, 1/6 + 1/6 + 1/6 = 1/2 is the overall likelihood of getting either 3, 4, or 5.

You must still multiply this by the overall likelihood of finding one of the prime numbers, which are 1, 2, 3, and 5.

Thus, 1/6 + 1/6 + 1/6 + 1/6 = 2/3

Then,

The probability is 1/2 × 2/3 = 1/3 or 33%

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