Choose the INCORRECT statement below.

The expected value of the number of points you get is 0.

To find the expected value of the number of points you get, we need to calculate the probability of getting each outcome (rolling a prime number or rolling a composite number) and multiply it by the corresponding points.

Here's how we can do that:

There are 10 possible outcomes when rolling the ten-sided die, each with an equal probability of 1/10.

Prime numbers on the die: 2, 3, 5, 7 (total 4 numbers)

Composite numbers on the die: 4, 6, 8, 9 (total 4 numbers)

For prime numbers (4 possible outcomes):

Probability of rolling a prime number = Number of prime numbers / Total possible outcomes = 4/10 = 2/5

Points gained for rolling a prime number = 1

For composite numbers (4 possible outcomes):

Probability of rolling a composite number = Number of composite numbers / Total possible outcomes = 4/10 = 2/5

Points lost for rolling a composite number = -1

Expected value = (Probability of prime number [tex]\times[/tex]Points gained) + (Probability of composite number [tex]\times[/tex] Points lost)

Expected value = (2/5 [tex]\times[/tex] 1) + (2/5 [tex]\times[/tex]   -1)

Expected value = 2/5 - 2/5

Expected value = 0

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In triangle ABC, the length of AC is 13 units

In triangle DEF, the length of DE is 24 units

By pythagoras theorem we find the missing length

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

In triangle ABC, we have to find length of AC

AC² = 5² + 12²

=25+144

=169

AC=13 units

In triangle DEF, we have to find length of DE

DF² =DE² + EF²

26²=DE² + 10²

676=DE² + 100

576=DE²

DE=24 units

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Answer:

x ≈ 50.7

Step-by-step explanation:

x/sin 90  =  23/sin(180-90-63) = 23/sin 27

x = (23 X sin 90) / sin 27

  ≈ 50.7

If those two angles = 180, then lines u and v are parallel.

90 + (x+102) = 180

192 + x = 180

x = 180-192

x = -12

So if x = -12, then lines u and v are parallel.

Answer:

x = -12

Step-by-step explanation:

90 + x + 102 = 180

192 + x = 180

x = -12

Therefore, in order for lines u and v to be parallel, the value of x must be -12

Answer:

We have parallel lines intersected by a transversal.

Corresponding angles are congruent:

5q + 3 = 3q + 11

2q = 8, so q = 4

Alternate interior angles are congruent:

3r - 4 = 6r - 19

3r = 15, so r = 5

Consecutive interior angles are supplementary:

4s + s + 90 = 180

5s = 90, so s = 18

Supplementary angles:

2t + 20 = 4t + 10

2t = 10, so t = 5

The final answer is So, to compute the probability, we need to find P(Z > 0.2) and subtract it from 1.

The random variable of interest in this scenario is the total time taken to download all 90 files and complete the installation of the software package.

This random variable is continuous since it represents a time duration, which can take on any value within a range. To compute the probability that the installation takes more than 28 minutes, we first need to calculate the mean and standard deviation of the total download time.

The mean download time for one file is given as 18 seconds, so the mean download time for 90 files is (18 seconds/file) * 90 files = 1620 seconds.

The standard deviation of the download time for one file is 10 seconds. Since the files are downloaded independently, the standard deviation of the total download time for 90 files can be calculated using the formula for the standard deviation of the sum of independent random variables:

Standard deviation of the total download time = square root(90) * 10 seconds =[tex]30 * 10[/tex] seconds = 300 seconds.

Now, to find the probability that the installation takes more than 28 minutes (which is equivalent to 28 minutes * 60 seconds = 1680 seconds), we need to standardize the value using the z-score formula:[tex]z = (x - μ) /[/tex]∅

where x is the desired time (1680 seconds), μ is the mean download time (1620 seconds), and σ is the standard deviation (300 seconds).

z = [tex]\frac{(1680 - 1620) }{300}[/tex]= [tex]\frac{60}{300}[/tex][tex]= 0.2[/tex]

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of 0.2. The probability that the installation takes more than 28 minutes is equal to 1 minus this probability, as we are interested in the probability of the installation taking more time.

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Answer:

275 miles

Step-by-step explanation:

110/2=55

(2*110)+55

=275

Answer:

275 miles

Step-by-step explanation:

110×2=220

110÷2=55

220+55=275

Therefore, there are 16,807,680 different combinations of pizzas that can be made if each pizza can have any number of toppings, including no toppings, but no two pizzas can have the same set of toppings and the same topping cannot be used more than once.

There are 2^5 = 32 possible combinations of toppings for a single pizza, since each topping can either be included or not. However, since no two pizzas can have the same set of toppings, once a combination is used for one pizza, it cannot be used again.

Therefore, for the first pizza, there are 32 possible combinations of toppings. For the second pizza, there are only 31 possible combinations left, since the combination used for the first pizza cannot be used again. For the third pizza, there are 30 possible combinations left, and so on.

So the total number of different combinations of pizzas that can be made is:

32 x 31 x 30 x 29 x 28 = 16,807,680

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Answer:

Step-by-step explanation:

You want the measures of the angles marked x° and y° in the given diagram.

The measure of an inscribed angle is half the measure of the arc it intercepts. This means any inscribed angles that intercept the same arc will have the same measure.

The inscribed angles with vertices J and K both intercept arc FH, so both have the marked measure of 56°.

  x = 56

The angle where the chords cross (y°) will be half the sum of the arcs those chords intercept. Here, those are arcs FH and JK.

Given that half the arc measure is the measure of the intercepting inscribed angle, we can simply sum the inscribed angles to get y°:

  y° = 56° +19° = 75°

  y = 75

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To prove that lim x → 0 x^4 cos(2/x)=0, we need to show that for any ε > 0, there exists a δ > 0 such that |x^4 cos(2/x)| < ε whenever 0 < |x| < δ.

First, we note that -1 <= cos(2/x) <= 1 for all x. Therefore, we have:

x^4 <= x^4 cos(2/x) <= x^4 for all x

Taking the limit as x approaches 0 of both sides, we get:

lim x â 0 x^4 <= lim x â 0 x^4 cos(2/x) <= lim x â 0 x^4

Using the fact that lim x â 0 x^4 = 0, we can conclude that:

0 <= lim x â 0 x^4 cos(2/x) <= 0

Thus, by the squeeze theorem, we have:

lim x â 0 x^4 cos(2/x) = 0

Therefore, we have shown that lim x â 0 x^4 cos(2/x) = 0.

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Answer:

4044.32

Explanation:

6506.08 (total) - 2461.76 (top)=

4044.32 (lateral+top)

Formulae:

total = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)

top= T= πr2

8000 pounds is equal to 4 tons.

A pound is a unit of weight that is approximately equal to 16 ounces, while a ton is a unit of weight equal to 2000 pounds.

Therefore, to convert pounds to tons, you divide the weight in pounds by 2000.

8000 pounds is the weight that we want to convert to tons.

Dividing 8000 by 2000 gives us 4

which means that 8000 pounds is equal to 4 tons.

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It's not entirely clear what is meant by "5 Apples in 6 rows," so I will provide a general answer that could apply to a few different interpretations of the question.

If Johnny has 5 apples and places them in 6 rows, the answer to how many apples he will have left depends on how many apples are in each row and what Johnny does with them. For example, if he eats one apple from each row, he will be left with 5 - 6 = -1 apples, which doesn't make sense. If instead he rearranges the apples into one row, he will still have 5 apples. If he gives away 2 apples, he will have 3 apples left.

In summary, the number of apples Johnny will have left depends on the details of the scenario, including how many apples are in each row and what Johnny does with them.

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Since we don't have the initial population size N(0), we'll represent it as a variable. The logistic equation for this population will be: N(t) = 2506 / (1 + (2506 - N0) / (N0 * e^(-0.018 * t))). This equation describes the population growth over time based on the given r value and carrying capacity.

The logistic model is used to describe population growth that is limited by a carrying capacity. In this case, the carrying capacity is given as 2506. The value of r, which represents the maximum growth rate of the population, is given as 0.018.
The logistic equation is given by:
dN/dt = rN(1-N/K)
where N is the population size, t is time, r is the intrinsic growth rate, and K is the carrying capacity.
Given that the carrying capacity is 2506 and the initial population size is n(0), we can rewrite the equation as:
dN/dt = 0.018N(1-N/2506)
This equation describes how the population size changes over time based on the initial population size and the carrying capacity. The equation predicts that as the population approaches the carrying capacity, the growth rate slows down until it eventually levels off.
In summary, the logistic equation satisfied by the population with an initial size of n(0) is dN/dt = 0.018N(1-N/2506), and it can be used to predict how the population size changes over time. This equation shows that population growth is not always unlimited and can be influenced by environmental factors such as carrying capacity.
Based on the information provided, we can construct a logistic equation for the given population growth model. The logistic model is represented by the equation:
N(t) = K / (1 + (K - N0) / (N0 * e^(-r * t)))
Where:
- N(t) is the population size at time t
- K is the environmental carrying capacity (in this case, 2506)
- N0 is the initial population size (N(0))
- r is the intrinsic growth rate (0.018)
- e is the base of the natural logarithm (approximately 2.718)
- t is the time
Since we don't have the initial population size N(0), we'll represent it as a variable. The logistic equation for this population will be:
N(t) = 2506 / (1 + (2506 - N0) / (N0 * e^(-0.018 * t)))
This equation describes the population growth over time based on the given r value and carrying capacity.

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The average rate of change of the function over the interval 3 ≤ x ≤ 7 is 3/2 or 1.5.

To find the average rate of change of a function over an interval, we can use the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a and

b are the endpoints of the interval and f(x) is the function.

Using the values from the table, we have:

a = 3, b = 7

f(a) = 2, f(b) = 8

Therefore, the average rate of change of the function over the interval 3 ≤ x ≤ 7 is:

average rate of change = (f(b) - f(a)) / (b - a) = (8 - 2) / (7 - 3) = 6/4 = 3/2

So the average rate of change of the function over the interval 3 ≤ x ≤ 7 is 3/2 or 1.5.

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In the diagram, if ΔABC= ΔDEF, then angle A is congruent to angle D.

Option C.

Similar triangles are triangles that have the same shape, but not necessarily the same size. In other words, their corresponding angles are equal, and their corresponding sides are proportional in length.

Two triangles are considered similar if they satisfy one of the following conditions:

ABC ≅ DEF

∠A ≅ ∠ D

Thus, two triangles are similar if their corresponding angles are congruent, and their corresponding sides are in proportion, so angle A of triangle ABC is congruent to angle D of triangle DEF.

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The range of the data on the 4th of July parade is greater than the range of the data in the New Years's Day parade.

A dataset's range, which reflects the gap among its greatest and lowest values, is measured statistically.

By deducting lowest value from the greatest value, it is computed. If range of total data is wider in Fourth of July parade than it is in the New Year's Day parade, then highest and lowest figures in Fourth of July parade will be further apart than highest and lowest values in New Year's Day parade.

For example, if highest value in 4th of July parade is 100 and lowest value is 10, then total range is 100 - 20 = 80.

If the highest value in the New Year's Day parade is 60 and the lowest value is 20, then the range is 60 - 20 = 40.

Thus, here range of the data in 4th of July parade is greater than range of the data in the New Year's Day parade.

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These two equations have the same slope, slope = 5.

They have different intercepts (the origin (0,0) and (0, -4)).

These lines are parallel.

The proof that shows that sides SP is congruent to side TR is explained below.

First, using the given information, we have to establish that both triangles are congruent to each other, then state that the two sides are congruent since corresponding parts of congruent triangles are congruent.

Therefore, the correct proof is:

Statement                                 Reason                                            

1. QP ≅ QR; SQ ≅ TQ              1. Given

2. <SQP ≅ <TQR                     2. Vertical Angle Theorem

3. ΔSQP ≅ ΔTQR                    3. SAS congruence theorem

4. SP ≅ TR                               4. Corresponding parts of congruent              

                                                      triangles are congruent.

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C, figure C

hope this helps, and have a good day! :)

To evaluate the given integral, we need to plug in the limits of integration, which are 0 and 4, into the antiderivative of the integrand.

The antiderivative of 4/5 t^3 - 3/4 t^2 + 2/5 t is:

(4/5) * (t^4/4) - (3/4) * (t^3/3) + (2/5) * (t^2/2) + C

where C is the constant of integration.

Now, plugging in the limits of integration:

[(4/5) * (4^4/4) - (3/4) * (4^3/3) + (2/5) * (4^2/2)] - [(4/5) * (0^4/4) - (3/4) * (0^3/3) + (2/5) * (0^2/2)]

Simplifying this expression, we get:

(256/5 - 64 + 16/5) - (0 - 0 + 0)

= 240/5

= 48

Therefore, the value of the given integral is 48.

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To evaluate the integral ∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt, we can use the power rule of integration.

Applying the power rule, we can integrate each term of the polynomial separately:

∫ (4/5t^3) dt = (4/5) * (1/4) * t^4 + C1 = t^4/5 + C1

∫ (-3/4t^2) dt = (-3/4) * (1/3) * t^3 + C2 = -t^3/4 + C2

∫ (2/5t) dt = (2/5) * (1/2) * t^2 + C3 = t^2/5 + C3

Adding the constants of integration, we can write the complete integral:

∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt = (t^4/5 + C1) - (t^3/4 + C2) + (t^2/5 + C3)

To evaluate the definite integral between the limits 0 and 4, we substitute the upper limit (4) and lower limit (0) into the expression:

[(4^4/5 + C1) - (4^3/4 + C2) + (4^2/5 + C3)] - [(0^4/5 + C1) - (0^3/4 + C2) + (0^2/5 + C3)]

Simplifying the expression further, we get:

[(1024/5 + C1) - (0 + C2) + (16/5 + C3)] - [(0 + C1) - (0 + C2) + (0 + C3)]

Since the constants of integration cancel out, we are left with:

[(1024/5) - (0) + (16/5)] - [(0) - (0) + (0)]

= 1024/5 + 16/5

= 1040/5

= 208

Therefore, the value of the integral ∫[0, 4] (4/5t^3 - 3/4t^2 + 2/5t) dt is 208.

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Step-by-step explanation:

if you gave us the whole information, then we have 4 cards with the values : 4, 5, 6 and 7.

the probabilty to pick the card with the value 4 is the same as the probabilty to pick a card with value less than 5.

in both cases there is only one card for the desired outcome : 4.

therefore, P(4 or less than 5) = P(4)

a probability is always the ratio

desired cases / totally possible cases

so, in our case the probabilty to pick one specific card out of a total of 4 cards is

1/4

and so, the probability to pick 4 is

P(4) = 1/4.

The volume and the surface area is 85.33π in³ and 16π in² respectively.

Given that a sphere of diameter 8 in, we will find it surface area and volume,

Surface area of a sphere = 4π × radius²

= 4π × (8/2)² [∵ diameter = 2 × radius]

= 16π in²

Volume of a sphere = 4π/3 × radius³

= 4π/3 × 4³

= 256π/3

= 85.33π in³

Hence the volume and the surface area is 85.33π in³ and 16π in² respectively.

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Answer:

The slope of this line is 1/4.

The correct answer is D.

we can answer it as follow

The red one show the GCF factor form it is -7 then you you ommit negative of numinator by negative of denominator . then you multiply both side by 4/7

the you simplify and solve a .

The online version, because the downloaded version usually requires better equipment than the online version.

The online version of the graphic design software is likely the better option for the student using a weak computer. This is because the online version typically runs on the software provider's servers, rather than on the user's computer.

Therefore, the online version does not require as much processing power or memory from the user's computer, making it more accessible to those with weaker or older machines.

Additionally, the online version may also have the advantage of automatic updates, so the student can always have the latest version of the software without needing to manually download and install updates.

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Answer:

$16.48

Step-by-step explanation:

If 6% is sales tax, that means that the total cost of the doll is 106% of the original cost. (basically 100% is the originall doll, and you add 6% of the tax). If you convert 106% from percentage form to decimal form (which you do by dividing by 100), 106% is the same as 1.06 times the original cost of the doll.

Thus you do 1.06 x 15.55 = 16.483 which rounds down to $16.48

Answer:

(1/2)(15)(7 + 15) = (1/2)(22)(15) = 165 m^2

Answer:

165m²

Step-by-step explanation:

First you make it into a triangle and rectangle.  The rectangle would be 15x7.  The triangle would be 1/2x15x8.

15x7=105

1/2x15x8=60

105+60=165 meters squared

The equation of the parabola graphed below is given as follows:

x = -1/49(y - 2)² - 1.

The parabola in the context of this problem is in horizontal form, hence the equation is given as follows:

x = a(y - k)² + h.

In which the parameters are given as follows:

The coordinates of the vertex are given as follows:

(-1, 2).

Hence:

x = a(y - 2)² - 1.

When x = -2, y = -5, hence the leading coefficient a is obtained as follows:

-2 = a(49) - 1

a = -1/49.

Hence the equation is:

x = -1/49(y - 2)² - 1.

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