question 20


An archaeologist finds a barren land with a large number of fossils of Dinosaurs. The number N(t) of fossils that can be found per cubic meter after t years can be determined by solving the equation:

If 3 and 4 are the legs of a right triangle, the hypotenuse is 5.

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation

[tex]\sf a^2+b^2=c^2[/tex]

Given the question above, we need to find the hypotenuse if 3 and 4 are the legs of a right triangle.

So,

[tex]\sf a^2+b^2=c^2[/tex]

[tex]=\sf 9+16=25[/tex]

[tex]\sf \sqrt{25}=5[/tex]

Hence, the hypotenuse is 5 if 3 and 4 are the legs of a right triangle.

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The probability of randomly selecting a Spade or a face card given that it's black is approximately 0.8077 or 80.77%.

To calculate the probability of randomly selecting a Spade or a face card given that it's black, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Step 1: Determine the number of favorable outcomes.

In a standard deck of cards, there are 52 cards. Since we're looking for a Spade or a face card, let's calculate the number of favorable outcomes separately for each category.

Number of Spades:

In a deck, there are 13 spades (Ace of Spades, 2-10 of Spades, Jack of Spades, Queen of Spades, and King of Spades).

Number of Face Cards:

In each suit (Spades, Hearts, Diamonds, and Clubs), there are three face cards: Jack, Queen, and King. Since we're only interested in black cards, we need to consider the face cards of Spades and Clubs, which are black. Therefore, there are 2 black face cards in each suit, giving a total of 8 black face cards in the deck.

So the total number of favorable outcomes is 13 (spades) + 8 (black face cards) = 21.

Step 2: Determine the total number of possible outcomes.

In a standard deck of 52 cards, half are black cards (26 cards) since there are 26 black cards and 26 red cards.

Step 3: Calculate the probability.

The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability = 21 / 26

Simplifying the fraction, we get:

Probability = 0.8077 (rounded to four decimal places)

Therefore, the probability of randomly selecting a Spade or a face card given that it's black is approximately 0.8077 or 80.77%.

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The set of decimal numbers that is correctly ordered from least to greatest from left to right is option C: 308.463, 330.991, 328.463, 330.693.

To order the decimal numbers from least to greatest, we compare the numbers digit by digit, starting from the left.

Let's compare the numbers in each option:

A. 328.463, 308.463, 330.693, 330.991

The numbers are not in the correct order because 308.463 should come before 328.463.

B. 308.463, 330.991, 330.693, 328.463

The numbers are not in the correct order because 328.463 should come after 330.693.

C. 308.463, 330.991, 328.463, 330.693

The numbers are in the correct order from least to greatest.

D. 308.463, 328.463, 330.693, 330.991

The numbers are not in the correct order because 330.693 should come before 328.463.

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the square root of 598 is 24.4540385

Answer:

After Grace gave 2 cupcakes to Wonwoo, he had a total of 5 cupcakes. However, after he gave 1 cupcake to Grace, he was left with 4 cupcakes again. But then, things took a turn for the better when Lois and Seeun each gave him 4 cupcakes. This means that Wonwoo now has a total of 12 cupcakes!

Step-by-step explanation:

I believe this is right; please tell me if it is not.

Certainly! I'll be happy to solve and explain the given problem to you in a step-by-step manner.

In the given diagram, we have a triangle with two angles labeled as 4x° and (3x + 10)°. We need to solve for the value of x.

According to the properties of triangles, the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the following equation:

4x + (3x + 10) + 90 = 180

Let's simplify the equation:

4x + 3x + 10 + 90 = 180

7x + 100 = 180

Next, we'll isolate the variable term by subtracting 100 from both sides of the equation:

7x = 180 - 100

7x = 80

To solve for x, we'll divide both sides of the equation by 7:

x = 80 / 7

Now, let's calculate the value of x:

x ≈ 11.43

Therefore, the value of x is approximately 11.43.

Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.

Answer: the function's y-intercept, 64°F

Step-by-step explanation:

       Since "t" represents time, if we set t = 0 to find the initial temperature (0 minutes), we find the function's y-intercept.

       To find the initial temperature, we will set t = 0. When we do this, we are finding the y-intercept which is the same as the constant value.

[tex]y=-\frac{1}{40}t^2+t+64[/tex]

[tex]y=-\frac{1}{40}(0)^2+(0)+64[/tex]

[tex]y=64[/tex]

   64°F

Answer:

Slope intercept form is y=3x-9

Graphing:

Step-by-step explanation:

If Graph g(x) the transformation of f(x)=x² then the graph of function g(x) is x²+4

To graph the transformation of the function f(x) = x² translated up 4 units, we need to add 4 to the function.

The new function, g(x), can be defined as g(x) = f(x) + 4.

Start with the graph of the original function f(x) = x²

Shift the graph vertically upward by 4 units.

To do this, for each point (x, y) on the graph of f(x), plot a new point (x, y + 4) on the graph of g(x).

This means that every y-coordinate is increased by 4 units.

g(x)= x²+4

Hence, the red line in the graph represents f(x) and blue line in graph represents the g(x)

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Answer:

Step-by-step explanation:

1) The number of combinations of the letters A, B, C, D, and E taken 4 at a time is 5.

The formula for the number of combinations is n!/(r!(n-r)!), where n is the total number of items, and r is the number of items to be selected. In this case, n = 5 and r = 4. Therefore, the number of combinations is 5!/(4!(5-4)!) = 5.

Theoretical probability is the likelihood or chance of an event occurring based on the ratio of the number of favorable outcomes to the total number of possible outcomes.

2) The theoretical probability of rolling a 2 on a die is 1/6.

There are six possible outcomes when rolling a die, and only one of those outcomes is a 2. Therefore, the probability of rolling a 2 is 1/6.

3) The theoretical probability of landing on blue when spinning the spinner is 1/5.

There are five possible outcomes when spinning the spinner, and only one of those outcomes is blue. Therefore, the probability of landing on blue is 1/5.

4) The ratio of wine lists to cookbooks in simplest form is 3/2.

To simplify the ratio, divide both the numerator and denominator by their greatest common factor, which in this case is 6. 18/6 = 3, and 12/6 = 2, so the ratio of wine lists to cookbooks in simplest form is 3/2.

5) The probability of drawing a red or yellow marble from the bag is 8/14 or 4/7.

There are a total of 14 marbles in the bag, 5 of which are red and 3 of which are yellow. Therefore, the probability of drawing a red or yellow marble is (5+3)/14 = 8/14 or 4/7.

6) The probability of drawing a number greater than 10 from a ball numbered 1-100 is 9/10.

There are 90 numbers greater than 10 in the set of numbers from 1 to 100, and there are 100 total numbers. Therefore, the probability of drawing a number greater than 10 is 90/100, which simplifies to 9/10.

7) The mean of the set of data {10, 15, 25, 50} is 25.

To find the mean, add up all of the numbers in the set and divide by the total number of numbers. (10+15+25+50)/4 = 100/4 = 25.

8) The median of the set of data {6, 23, 46, 3, 17} is 17.

To find the median, first put the numbers in order from smallest to largest: 3, 6, 17, 23, 46. Since there are an odd number of numbers in the set, the median is the middle number, which is 17.

9) The mode of the set of data {3, 7, 10, 18, 4, 5} is no mode.

The mode is the value that appears most frequently in the data set. In this case, none of the values appear more than once, so there is no mode.

10) In a stem-and-leaf plot, the leaf represents the ones place of the numbers in the data set.

The stem-and-leaf plot is a way to organize numerical data by placing the tens digit in the stem and the ones digit in the leaf.

11) Finding quartiles is like finding medians.

Quartiles divide a data set into

The interval notation of the number line is [-3, ∝) while that of the inequality is  called x >= 3

One can use interval notation to represent real numbers that are continuous by specifying the values that define their boundaries. Written intervals appear somewhat akin to ordered pairs.

The way to know the interval notation of the graph is:

Based on the number line in the question, one can see:

The rule that applies is that a closed line tells us that the number at that endpoint is one that is part of the solution set.

So this tells us that the interval notation of the number line is [-3, ∝). When depicted as an inequality, One can have x >= 3

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The proportion that can be used to determine Jason's height based on the relationship between the lengths of their shadows is J/8 = H/10.

Given that Joshua is 5 ft tall and casts an 8-ft shadow.

He is standing next to Jason, who casts a 10 shadow.

We have to find a proportion that could be used to determine Jason's height

Let's denote Joshua's height as J and Jason's height as H.

We can set up the proportion by taking the height by shadow

J/8 = H/10

Hence, J/8 = H/10 is the proportion can be used to determine Jason's height based on the relationship between the lengths of their shadows.

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Answer:

The perimeter of this rectangle is 10 cm.

Answer: The time it takes for a sum of money to amount to a certain amount at a certain interest rate can be calculated using the following formula:

Time = (100 x (Amount - Principal)) / (Principal x Rate)

In this case, the principal is Rs. 2000, the amount is Rs. 2240, and the rate is 4%. Therefore, the time is:

Time = (100 x (2240 - 2000)) / (2000 x 4) = 3 years

Therefore, it will take 3 years for Rs. 2000 to amount to Rs. 2240 at 4% simple interest.

Step-by-step explanation:

To find the z-score for a population value of 21, we can use the formula:

z = (x - μ) / σ

where:

x = population value

μ = mean of the population

σ = standard deviation of the population

In this case, x = 21, μ = 12, and σ = 4.

Substituting the values into the formula:

z = (21 - 12) / 4

z = 9 / 4

z = 2.25

Therefore, the z-score for a population value of 21 is 2.25.

Note:
I hoped this helped in any kind of way.

Savings play a crucial role in wealth creation and financial security while savings alone may not determine an individual's overall wealth

Wealth and savings are closely related concepts and often go hand in hand.

Savings refer to the portion of income or resources that individuals or households set aside for future use or to meet financial goals.

It represents the act of not spending all of one's income and instead preserving a portion for later use.

Wealth, on the other hand, refers to the total accumulated assets, possessions, and financial resources that an individual or household possesses.

It encompasses not only the current income and savings but also the value of investments, properties, and other assets.

Savings contribute to the accumulation of wealth over time.

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The number of possible combinations of 10 men chosen from 26 men in the juror pool is, 44128260

Since, A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

We have to given that;

Total person = 26

Number of choose person = 10

Hence, The number of possible combinations of 10 men chosen from 26 men in the juror pool is,

⇒ ²⁶ C ₁₀

⇒ 26! / 10! 16!

⇒ 44128260

Thus, The number of possible combinations of 10 men chosen from 26 men in the juror pool is, 44128260

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Given statement solution :-  Party A received the most votes with a total of 47, compared to Party B's total of 38 votes.

Let's calculate the number of votes each party received based on the given information.

Assuming there is a population of 100 people (this is an arbitrary number chosen for ease of calculation), we can determine the number of votes for each party.

Percentage of people who said they would vote for Party A = 33%

Number of people who said they would vote for Party A = 33/100 * 100 = 33

Percentage of people who said they would vote for Party B = 10%

Number of people who said they would vote for Party B = 10/100 * 100 = 10

Percentage of people who said they would not vote = 15%

Number of people who said they would not vote = 15/100 * 100 = 15

Now, let's calculate the votes from the rest of the population (those who didn't state their voting preference).

Percentage of people who voted for Party A from the rest of the population = 1/3

Number of people who voted for Party A from the rest of the population = (1/3) * (100 - (33 + 10 + 15)) = (1/3) * 42 = 14

Percentage of people who voted for Party B from the rest of the population = 2/3

Number of people who voted for Party B from the rest of the population = (2/3) * (100 - (33 + 10 + 15)) = (2/3) * 42 = 28

Now, let's calculate the total votes for each party:

Total votes for Party A = votes from those who stated their preference + votes from the rest of the population

= 33 + 14 = 47

Total votes for Party B = votes from those who stated their preference + votes from the rest of the population

= 10 + 28 = 38

Therefore, Party A received the most votes with a total of 47, compared to Party B's total of 38 votes.

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Answer:

Yes, x/5 is a linear equation. A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable x is 1, so it is a linear equation.

The graph of x/5 is a straight line with a slope of 1 and a y-intercept of 0.

Answer:

----------------------

If the middle number is x, the other numbers are x - 1 and x + 1.

They sum to 3x and it is equal to 51:

The numbers are 16, 17 and 18.

The total surface area of the figure is twice this amount, or 192π square inches.

Given that the height of each individual cone is 8 inches, we can use the Pythagorean theorem (a²  + b²  = c² ) to calculate the radius. The hypotenuse of the right triangle formed by the cone is the slant height, which is 10 inches, and one side is the height, which is 8 inches. So:

10²  - 8²  = r²

100 - 64 = r²

r²  = 36

r = √36 = 6 inches.

Substituting these values into the surface area formula, we get:

A = π * 6 * (6 + √(8² + 6² ))

= π * 6 * (6 + √(64 + 36))

= π * 6 * (6 + √100) = π * 6 * (6 + 10)

= π * 6 * 16 = 96π square inches.

Since we have two cones, the total surface area of the figure is twice this amount, or 192π square inches.

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The rewritten  statement : "It is not the case that there exists an x for which P(x) and Q(x) are true, and for all y, if R(y) is true, then P(y) is true."

The symbolic logic statement: ¬(∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y)).

The statement can be translated as: "There does not exist an x such that P(x) and Q(x) hold true, and for all y, if R(y) is true, then P(y) is true."

Potential ambiguities in this statement can arise from the unclear precedence of logical operators, specifically the negation operator "¬" in relation to the existential quantifier "∃".

To eliminate ambiguities while maintaining the original meaning, we can add parentheses to make the precedence explicit: (¬(∃x)(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y)).

This ensures that the negation applies only to the existential quantifier, not to the entire conjunction.

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The relative position of a score and provide a standardized way to compare scores from different distributions with varying means and Standard deviations.

The z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where:

- z is the z-score,

- x is the value we want to find the z-score for (330 in this case),

- μ is the mean of the distribution (195 in this case),

- σ is the standard deviation of the distribution (50 in this case).

Substituting the values into the formula:

z = (330 - 195) / 50

Calculating this expression:

z = 135 / 50

Simplifying:

z = 2.7

Therefore, the z-score of a person who scored 330 on the exam is 2.7.

A z-score represents the number of standard deviations a particular value is from the mean of a normal distribution. In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean of 195. This means that their score is relatively high compared to the average performance on the exam.

Z-scores are useful for comparing and understanding individual scores within a distribution. They allow us to determine the relative position of a score and provide a standardized way to compare scores from different distributions with varying means and standard deviations.

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Answer:

22148 pounds

Step-by-step explanation:

radius = half of diameter = 5.

Volume of hemisphere = (2/3) X π X r ³

= (2/3) X π X (5) ³ = (250/3)π

density = mass/volume, mass = density X volume

= 84.6 X (250/3)π

= 7050π

= 22148 pounds (to nearest full pound)

There are 72 different meals that you can get for $3.98

We know that for $3.98 you can get a salad, a main course, and a dessert at the cafeteria.

The total number of different meals that you can get, is equal to the product between the number of options for each one of the selections, such that the selections (and correspondent options) are:

Then the total number of different meals is:

M = 3*4*6

M = 72

That is the number of different meals.

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The measure of angle 1 in the given figure is 56 degrees.

From the image of the angle:

Measure of angle ABD = 62 degrees

Measure of angle 2 = 6 degrees

Measure of angle 1 = ?

From the diagram, angle 1 and angle 2 makes up angle ABD.

To solve for the missing angle ( angle 1 ), sum up both angle 1 and 2 and equate to angle ABD.

Hence:

Angle 1 + Angle 2 = Angle ABD

Plug in the values and simplify:

m∠1 + 6 = 62

Subtract 6 from both sides

m∠1 + 6 - 6 = 62 - 6

m∠1 = 62 - 6

m∠1 = 56 degrees

Therefore, angle 1 measures 56 degrees.

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