The frequency table shows the scores from rolling a dice.
Score
Frequency
1
9
2.
6
3
2.
4
5
5
2
6
1
Work out the median.
X
5

When organisms are crossed, there are only two possible phenotype outcomes, and they each have a 50/50 chance of emerging, which is known as a 1:1 phenotypic ratio.

In the given question we have to explian about 1:1 phenotypic ratio.

The phenotypic ratio is the relationship between the proportion of children that will exhibit a particular trait or a combination of features. This ratio is often obtained by performing a test cross, noting how frequently a characteristic or combination of traits will be manifested based on the genotype of the offspring, and using the information from that cross.

When organisms are crossed, there are only two possible phenotype outcomes, and they each have a 50/50 chance of emerging, which is known as a 1:1 phenotypic ratio.

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Answer: B(0,-6); C(-2,0)

Step-by-step explanation:

A was translated 4 units to the right (x) and 5 units down (y)

Do the same for the other points

B(-4+4, -1-5)                        C(-6+4, 5-5)

B(0, -6)                                C(-2, 0)

Answer: 1.2544

Step-by-step explanation:

2^-1 = 1/2

5^-1 = 1/5

1/2+1/5 = 7/10

(7/10)^2=49/100=0.49

(-5/8)^-2 = 64/25=2.56

(2^-1 +5^-1)^2 *(-5/8)^-2 = 0.49 * 2.56 = 1.2544

Answer:

Area=201.6^2

Step-by-step explanation:

Thus, angle q can either measure approximately 65.1 degrees or approximately 114.9 degrees.

To find all possible measures for angle q in triangle PQR, we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab cos(C)

where c is the length of the side opposite the angle we are trying to find (in this case, side q), and a and b are the lengths of the other two sides.

Plugging in the given values, we get:

85^2 = 45^2 + b^2 - 2(45)(b) cos(37°)

Simplifying and solving for b, we get:

b = 81.5 cm or b = 128.5 cm

However, we can only accept the solution b = 81.5 cm since the other value (b = 128.5 cm) would result in side b being longer than side c (which is not possible in a triangle).

So, the possible measures for angle q are:

q = 65.1° or q = 114.9°

Therefore, angle q can either measure approximately 65.1 degrees or approximately 114.9 degrees.

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Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

5.12 in. by 7.68 in.

Step-by-step explanation:

In similar triangles, the ratios of the lengths of corresponding sides are equal.

width of medium triangle = 4/5 width of large triangle

width of medium triangle = 4/5(8 in.) = 6.4 in.

length of medium triangle = 4/5 length of large triangle

length of medium triangle = 4/5(12 in.) = 9.6 in.

width of small triangle = 4/5 width of medium triangle

width of small triangle = 4/5(6.4 in.) = 5.12 in.

length of small triangle = 4/5 length of medium triangle

length of small triangle = 4/5(9.6 in.) = 7.68 in.

The correct response is C. 0.0036 Square degrees The field of vision of the Hubble Space Telescope is only 0.006 degrees, which is around 100 times less than that of the Micro Observatory telescopes. But it has a 100 times better angular resolution!

Skywatchers can readily view planets with just a modest or medium-sized telescope. How much of our solar system is visible will wow you! Additionally, you don't need a completely dark sky to see all of the planets in our solar system; a telescope can still make Venus, Mars, Jupiter, and Saturn easily visible even when viewed in a city. From $100 to well over $10,000, a telescope can be purchased. In 2022, you can anticipate that a good telescope for visual observing will start around $300 and a telescope capable of deep-sky astrophotography would start around $800. With a 25x telescope, even the tiniest telescope should be able to see Saturn's rings.

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Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST's) advanced camera has a field of view that is roughly square and about 0.06 degree on a side. Calculate the angular area of the HST's field of view in square degrees.

A. 0.006 Square degrees

B. 0.36 Square degrees

C. 0.0036 Square degrees

D. 0.06 Square degrees

The solutions of the equation are 0, pi/3, pi, 5pi/3 in the interval [0, 2pi).

Using the identity sin 2t = 2sin t cos t, we can rewrite the equation as:

sin t - 2sin t cos t = 0

Factoring out sin t, we get:

sin t (1 - 2cos t) = 0

This equation is satisfied when either sin t = 0 or cos t = 1/2.

When sin t = 0, the solutions in the interval [0, 2π) are t = 0 and t = π.

When cos t = 1/2, the solutions in the interval [0, 2π) are t = π/3 and t = 5π/3.

Therefore, the solutions in the interval [0, 2π) are t = 0, t = π, t = π/3, and t = 5π/3.

So, the solutions are: 0, pi/3, pi, 5pi/3.

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The given sequence;–3.2, 4.8, –7.2, 10.8, is a geometric progression common ratio of -1.5.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

The given sequence ;

–3.2, 4.8, –7.2, 10.8, …

The common ratio

= -4.8/ 3.2

= - 1.5

The terms having a common ratio of -1.5 best describe the relationship between the successive terms in the sequence of the terms.

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Answer:

739 x 4

2926 ft³ is your answer

Answer:

Step-by-step explanation:

radius=18/2=9 ft

\(V=\frac{4}{3} \pi r^3\\=\frac{4}{3} \pi (9)^3\\\approx \frac{4}{3} \times 3\times 729\\\approx 4 \times 729\\\approx 2916 ~ft^3\)

Answer:

X / 4 + 22

Step-by-step explanation:

22 more means we add 22. Then, we take x as our variable, in this case, it is "a number". We divide x by 4, and then we add 22. x / 4 + 22.

The value of x is obtained as follows:

128º.

The measure of angle A is given as follows:

m < A = 132º.

For a parallelogram, the opposite angles are congruent, meaning that they have the same measure, hence the value of x is obtained as follows:

5x - 508 = x + 4.

4x = 512

x = 512/4

x = 128.

Then the measure of angle A is given as follows:

m < A = 5(128) - 508

m < A = 132º.

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Answer:

See below

Step-by-step explanation:

IN a right triangle , remember  S-O-H-C-A-H-T-O-A   <===memorize this!

sin z = O/H = opposite side/hypotenuse = 16/20

cos z = A/H = adjacent / hy[potenuse = 12/20

tan z  = O/A = 16/12

Answer:

First one is 41

Second one is 87

Step-by-step explanation:

Make the shaded part as a trapezoid which is (3+6)*10/2 you just have to get rid of 2*2. So you get 41 as the answer.

The unshaded part will be 16*8 then subtracts the shaded part which is 41.  Then you get the answer 87.

9514 1404 393

Answer:

  see below

Step-by-step explanation:

The cost for purchase of 0 tokens is $60. This "initial value" is the y-intercept of the function.

The cost for each token is $1.00/10 = 1/10 (dollar), so the slope of the function is 1/10.

The slope-intercept form of the function can be written ...

  y = mx + b . . . . . for slope m and y-intercept b

  y = 1/10x + 60

__

The minimum value of this function is 60, so the range is y ≥ 60.

The function is defined for all real numbers, but only makes sense for all non-negative integers. So, we cannot claim the domain is all real numbers.

Answer:

(B, C, E)

Step-by-step explanation:

Let's evaluate each answer choice:

"The slope of the function is $1.00"

Wrong. The slope is how much one game token costs. It costs $1 per 10 tokens, not 1 token. To find the cost of 1 game token, you would divide 1 by 10, giving you a value of 1/10.

"The y-intercept of the function is $60"

Correct. The initial fee is $60, and this initial fee doesn't change, so it's the y-intercept.

"The function can be represented by the equation y = 1/10x + 60"

Correct. We just mentioned before that the slope is 1/10 and the y-intercept is 60.

"The domain is all real numbers"

Wrong. "All real numbers" also includes negative numbers. However, x represents the number of tokens bought, and you can't buy a negative amount of tokens.

"The range is {y| y >= 60}"

Correct. The range represents the total cost of a yearly membership. When you get the membership, you're ALWAYS going to have to pay $60, no matter how many tokens you buy after that.

Hope this helps (●'◡'●)

The correct answer is OD. Although the word "then" appears in the statement, it is not used as a logical connective. So the statement is not compound.

The statement "If Laura sells her quota, then Marie will be happy" is a single declarative sentence. It consists of a conditional clause ("If Laura sells her quota") and a consequent clause ("then Marie will be happy"). However, these two clauses are not independent statements that can stand alone. Instead, they are connected in a cause-and-effect relationship. The word "then" in this context is not functioning as a logical connective, but rather as an indicator of the consequent clause.

A compound statement is formed by combining two or more independent statements using logical connectives such as "and," "or," or "if...then." In the given statement, there is no logical connective joining two independent statements.

Therefore, the statement is not compound.

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Answer: He can use 3 x 5 = 15 and 15 + 3.

Step-by-step explanation:

Since a small car is $3, and the large car is 5x the price of the small car, he can use the equation 3 x 5 = 15, because the small car is $3, and the large car is 5x the price. You can use 15 + 3 = 18, because the small car is $3, so you also have to add that.

Here to help!

The equation is x + 5x = 18 , where x is the cost of small toy car and the total cost of the two cars = $ 18

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total cost of the two cars be A

Now , the equation will be

Let the cost of the small toy car be = x

The cost of small toy car = $ 3

The cost of the large car = 5 x cost of small toy car

Substituting the values in the equation , we get

The cost of the large car = 5 x 3

The cost of the large car = $ 15

So , the cost of two cars = x + 5x

Substituting the values in the equation , we get

The total cost of the two cars A = 15 + 3

The total cost of the two cars A = $ 18

Therefore , the value of A is $ 18

Hence , the equation is A = x + 5x

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The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.

Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.

The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.

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Answer:

volume of prism = lbh

Step-by-step explanation:

Volume of a cuboid = (length × breadth × height) cubic units. = (l × b × h)

lbh

Don't know for sure whether this is what the question wanted but oh well

Answer:

C. x = 3

Step-by-step explanation:

8x - 8 = 2x + 10

get the x on it's own

8x - 8 + 8 = 8x

2x + 10 + 8 = 2x + 18

8x = 2x + 18

8x - 2x = 6x

2x + 18 - 2x = 18

6x = 18

now divide each side by 6

6x / 6 = x

18 / 6 = 3

x = 3

X=3

Explanation

8x-8=2x+10

6x=18

x=3

Answer:

e is 111°

Step-by-step explanation:

\({ \tt{ \angle a = \angle b = 69 \degree}} \: \\ { \sf{(alternate \: angles)}} \\ \\ { \tt{b + c = 180 \degree}} \: \\ { \sf{(corresponding)}} \\ { \tt{69 + c = 180}} \\ { \tt{c =111 \degree }} \\ \\ { \tt{ \angle c = \angle d = 111 \degree}} \\ \\ { \tt{ \angle d = \angle e = 111 \degree}}\)

Answer:

111 degrees

Step-by-step explanation:

angle a and b are equal due to alternate interior angles  and since b is 69 degrees as well we can subtract it from 180 to get 111 degrees which is the measure of angle c and angle c and e are equal due to corresponding angles so the measure of angle e is 111 degrees.

Answer:

f(x) = -11

Step-by-step explanation:

you should end up with -9-2, a negative minus a negative brings you further into the negatives, meaning the answer is -11

So we know that if you multiply a negative number by a positive number, you get a negative number. We also know that if you multiply a negative number by a negative number you get a positive number! (Two negatives cancel each other out!)

So going down the list:

(-3)(-6) = positive (two negatives!)

(-3)(6) = negative (one negative, one positive!)

-(-3)(6) = positive (this is because you multiple left to right. because the negative is technically a -1 multiplying the -3, your -3 turns into a +3!)

(2)(3)(-6) = negative

(-2)(-3)(-6) = negative (remember, you multiply in the order of left to right! So multiplying the -2 and -3 gives you a positive. However, the -6 makes that positive number negative!)

(2)(-3)(-6) = positive

I hope this helps!

Historical scientists deal with falsification by rigorously analyzing evidence, using peer review and scholarly discourse, and revising hypotheses based on new discoveries and interpretations.



Historical scientists deal with falsification by employing rigorous methodologies and critical analysis of evidence. They strive to gather as much relevant data as possible to test hypotheses and theories. This is done through meticulous research, including the examination of primary sources, archaeological artifacts, historical records, and other forms of evidence. Historical scientists also engage in peer review and scholarly discourse to subject their findings to scrutiny and criticism.

The mechanism used by historical scientists to falsify hypotheses involves a combination of evidence-based reasoning and the application of established principles of historical analysis. They aim to construct coherent and logical explanations that are supported by the available evidence. If a hypothesis fails to withstand scrutiny or is contradicted by new evidence, it is considered falsified or in need of revision. Historical scientists constantly reassess and refine their hypotheses based on new discoveries, reinterpretation of existing evidence, and advancements in research techniques. This iterative process helps to refine our understanding of the past and ensures that historical knowledge remains dynamic and subject to revision.

Therefore, Historical scientists deal with falsification by rigorously analyzing evidence, using peer review and scholarly discourse, and revising hypotheses based on new discoveries and interpretations.

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Main Answer:The circumstances under which the shape of the sampling distribution of pn is approximately normal.

Supporting Question and Answer:

What is the Central Limit Theorem and how does it relate to the shape of the sampling distribution of pn?

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean (or sum) approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. This theorem is applicable to the sampling distribution of pn (proportion) because the proportion can be considered as the sample mean of a binary variable (success or failure). As the sample size increases, the Central Limit Theorem ensures that the sampling distribution of pn becomes more approximately normal, making it a useful approximation for making inferences about the population proportion.

Body of the Solution:The shape of the sampling distribution of pn (proportion) is approximately normal under certain circumstances. These circumstances are related to the properties of the population being sampled and the sample size. Here are the key factors:

1.Large sample size: The sampling distribution of pn tends to become more approximately normal as the sample size increases. This is known as the Central Limit Theorem. As the sample size grows larger, the distribution of sample proportions approaches a normal distribution regardless of the shape of the population distribution.

2.Random sampling: The sample should be selected randomly from the population to ensure that each member of the population has an equal chance of being included in the sample. Random sampling helps to ensure that the sample is representative of the population.

3.Independence assumption: The sampled observations should be independent of each other. This means that the selection of one observation should not influence the selection or behavior of other observations. Independence is crucial to ensure that the sampling distribution accurately reflects the population distribution.

4.Adequate population size: If the population size is sufficiently large,

relative to the sample size, the shape of the sampling distribution of pn is approximately normal. In practice, if the population is at least 10 times larger than the sample size, this condition is considered to be met.

5.Binomial distribution approximation: The shape of the sampling distribution of pn is also approximately normal when the underlying population distribution follows a binomial distribution. The binomial distribution is characterized by a fixed number of trials and two possible outcomes (success or failure) for each trial.

Final Answer: These circumstances increase the likelihood of the sampling distribution of pn being approximately normal, it does not guarantee it in all cases. In practice, checking the normality of the sampling distribution can be done using statistical tests or graphical methods, such as a histogram or a normal probability plot.  

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The circumstances under which the shape of the sampling distribution of pn is approximately normal.

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean (or sum) approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution. This theorem is applicable to the sampling distribution of pn (proportion) because the proportion can be considered as the sample mean of a binary variable (success or failure). As the sample size increases, the Central Limit Theorem ensures that the sampling distribution of pn becomes more approximately normal, making it a useful approximation for making inferences about the population proportion.

The shape of the sampling distribution of pn (proportion) is approximately normal under certain circumstances. These circumstances are related to the properties of the population being sampled and the sample size. Here are the key factors:

1.Large sample size: The sampling distribution of pn tends to become more approximately normal as the sample size increases. This is known as the Central Limit Theorem. As the sample size grows larger, the distribution of sample proportions approaches a normal distribution regardless of the shape of the population distribution.

2.Random sampling: The sample should be selected randomly from the population to ensure that each member of the population has an equal chance of being included in the sample. Random sampling helps to ensure that the sample is representative of the population.

3.Independence assumption: The sampled observations should be independent of each other. This means that the selection of one observation should not influence the selection or behavior of other observations. Independence is crucial to ensure that the sampling distribution accurately reflects the population distribution.

4.Adequate population size: If the population size is sufficiently large,

relative to the sample size, the shape of the sampling distribution of pn is approximately normal. In practice, if the population is at least 10 times larger than the sample size, this condition is considered to be met.

5.Binomial distribution approximation: The shape of the sampling distribution of pn is also approximately normal when the underlying population distribution follows a binomial distribution. The binomial distribution is characterized by a fixed number of trials and two possible outcomes (success or failure) for each trial.

These circumstances increase the likelihood of the sampling distribution of pn being approximately normal, it does not guarantee it in all cases. In practice, checking the normality of the sampling distribution can be done using statistical tests or graphical methods, such as a histogram or a normal probability plot.  

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If demand or annual usage increases by 10 percent, the Economic Order Quantity (EOQ) will increase. The EOQ model is used in inventory management to determine the optimal order quantity that minimizes total inventory costs.

The Economic Order Quantity (EOQ) is a model used in inventory management to determine the optimal order quantity that minimizes total inventory costs. It takes into account factors such as demand, holding costs, and ordering costs. When demand or annual usage increases by 10 percent, it means that more units are being consumed or sold within a given time period.

With an increase in demand, the EOQ will also increase. This is because the EOQ formula takes into consideration the trade-off between holding costs and ordering costs. Holding costs are the costs associated with holding inventory, such as warehousing and insurance, while ordering costs are the costs incurred when placing an order, such as administrative and transportation costs.

When demand increases, more units need to be ordered to meet the higher demand. This results in an increase in ordering costs, as more frequent orders will need to be placed. Consequently, the EOQ will increase to find the new optimal order quantity that balances the increased ordering costs with the holding costs.

In summary, if demand or annual usage increases by 10 percent, the EOQ will increase due to the need to order more frequently to meet the higher demand, resulting in increased ordering costs. This adjustment ensures that the inventory management system remains efficient and cost-effective.

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Answer:

1/6 serving

Step-by-step explanation:

1 SERVING = 3/2 OUNCES

        x        = 1/4 OUNCES

CROSS MULTIPLY.

1 * 1/4 ( serving * ounces) = x * 3/2 (ounces)

REARRANGE, THEN DIVIDE BOTH SIDES BY 3/2 OUNCES TO MAKE x THE SUBJECT.

x * 3/2 (ounces) = 1 * 1/4 ( serving * ounces)

[x * 3/2 (ounces)] / 3/2 OUNCES = [1 * 1/4 ( serving * ounces)] / 3/2 OUNCES

x = (1/4) / (3/2) SERVING

x = 1/4 * 2/3 (serving)

x = 1/2 * 1/3 (serving)

x = 1/6 serving

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It will take 120 minutes for smaller hose to fill the complete swimming pool on its own.

Let us represent the complete swimming pool as 1. Now, total time required to fill the swimming pool is 40 hours. So, amount of swimming pool filled in 1 minute = 1/40

Similarly, amount fo swimming pool filled by larger hose in 1 minute = 1/60

Now for the smaller hose, the amount of swimming pool filled in 1 minute = 1/40 - 1/60

The amount of swimming pool filled in 1 minute = (60 - 40)/2400

The amount of swimming pool filled in 1 minute = 20/2400

The amount of swimming pool filled in 1 minute = 1/120

Total time taken to fill swimming pool = 1 ÷ (1/120)

Total time taken to fill swimming pool = 120 minutes

Thus, 120 minutes are required.

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