The temperature dropped to 24 degrees in 8 days. what was the average daily change in temperature? a) 3 degrees b) -8 degrees c) -3 degrees d) 16 degrees

Answer:

Point B of 4the quertant

The probability that it is gold is (1/3).

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. If two events are mutually exclusive, then there is a 0 percent chance that they will both happen at the exact moment. Two events are said to be mutually exclusive if they share no elements (their intersection is the empty set). Consequently, P(A∩B)=0.

Let A be the event that a gold marble is picked.

Let B₁ and B₂ be the event that the first bag is chosen and the second bag is chosen respectively.

Given: P (B₁ ) = 2.P(B₂)

Also, P(B₁) + P(B₂) = 1

∴ 2P(B₂) + P(B₂) =1

3P(B₂) = 1

P(B₂) = 1/3 and  P(B₁) = 2/3

Now

P(A)

= P(A∩(B₁∪B₂))

= P[(A∩B₁)∪(A∩B₂)]

Probability adds up because the events are mutually exclusive

= P(A∩B₁) + P(A∩B₂)

= P(B₁). P(A/B₁) + P(B₂). P(A/B₂)

= (2/3)×(3/16) + (1/3)×(15/24)

= (1/3)

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Answer:

There are many times in algebra when you need to simplify an expression. The properties of real numbers provide tools to help you take a complicated expression and simplify it.

The associative, commutative, and distributive properties of algebra are the properties most often used to simplify algebraic expressions. You will want to have a good understanding of these properties to make the problems in algebra easier to work.

Step-by-step explanation:

Commutative Property of Multiplication

For any real numbers a and b, a · b = b · aOrder does not matter as long as the two quantities are being multiplied together. This property works for real numbers and for variables that represent real numbers.

just as subtraction is not commutative, neither is division commutative. 4 ÷ 2 does not have the same quotient as 2 ÷ 4.Associative Property of Addition

For any real numbers a, b, and c, (a + b) + c = a + (b + c).

Associative Property of Multiplication

For any real numbers a, b, and c, (a • b) • c = a • (b • c).Multiplication has an associative property that works exactly the same as the one for addition. The associative property of multiplication states that numbers in a multiplication expression can be regrouped using parentheses. For example, the expression below can be rewritten in two different ways using the associative property.

The parentheses do not affect the product, the product is the same regardless of where the parentheses are.

The distributive property of multiplication is a very useful property that lets you rewrite expressions in which you are multiplying a number by a sum or difference. The property states that the product of a sum or difference, such as 6(5 – 2), is equal to the sum or difference of products, in this case, 6(5) – 6(2).

   6(5 – 2) = 6(3) = 18

 65) – 6(2) = 30 – 12 = 18

The distributive property of multiplication can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2.3(10 + 2) = ?

According to this property, you can add the numbers 10 and 2 first and then multiply by 3, as shown here: 3(10 + 2) = 3(12) = 36. Alternatively, you can first multiply each addend by the 3 (this is called distributing the 3), and then you can add the products. This process is shown here.

3 (10 + 2) = 3(12) = 36

3(10) + 3(2) = 30 + 6 = 36

The products are the same.

since multiplication is commutative, you can use the distributive property regardless of the order of the factors.

Comparing the medians, we can see that the median length of alligators in Swamp A and Swamp B is the same, which suggests that the two swamps may have similar populations of alligators in terms of length.

What is median?

Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.

To compare the lengths of the alligators from two different swamps using medians, we need to collect data on the lengths of alligators from each swamp. Then we can calculate the median length of alligators in each swamp and compare them.

Let's say we have collected the following data on the lengths of alligators from Swamp A and Swamp B:

Swamp A: 4 feet, 5 feet, 6 feet, 7 feet, 8 feet

Swamp B: 3 feet, 5 feet, 6 feet, 7 feet, 9 feet

To find the median length of alligators in Swamp A, we need to arrange the lengths in order from smallest to largest: 4, 5, 6, 7, 8. The middle value is 6, so the median length of alligators in Swamp A is 6 feet.

To find the median length of alligators in Swamp B, we also need to arrange the lengths in order from smallest to largest: 3, 5, 6, 7, 9. The middle value is also 6, so the median length of alligators in Swamp B is also 6 feet.

Comparing the medians, we can see that the median length of alligators in Swamp A and Swamp B is the same, which suggests that the two swamps may have similar populations of alligators in terms of length. However, it is important to note that this comparison is based only on the median length and not on the full distribution of alligator lengths, so it is possible that there are other differences between the two populations of alligators that are not captured by this comparison.

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Answer:

Have you ever used the desmos graphing calculator?  You should use that.  Type in both of those equations.  If they intersect at a point, the y value of the ordered pair is your answer.  If the lines over lap, it is infinitely many solutions.  If they never intersect, there is no solution.

Step-by-step explanation:

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

1mm is equal to 1000 μm

5μm * (1 mm/1000μm) = (5*1) / 1000 = 5/1000 = 0.005 mm = 5x10^-3 mm

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

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To construct a 90% confidence interval for the average speed of cars on the highway with a margin of error no more than ±0.5 mph and a standard deviation of 7 mph, you must clock at least 339 cars.

Step 1: Identify the critical value (z-score) for a 90% confidence interval. This can be found in a standard z-table or using a calculator. The critical value for a 90% confidence interval is 1.645.

Step 2: Use the margin of error (E) formula to calculate the sample size (n):
E = (z * σ) / √n

Where E is the margin of error (0.5 mph), z is the critical value (1.645), σ is the standard deviation (7 mph), and n is the sample size.

Step 3: Rearrange the formula to solve for n:
n = (z * σ / E)^2

Step 4: Plug in the values and calculate the sample size:
n = (1.645 * 7 / 0.5)^2
n ≈ 338.89

Since the sample size must be a whole number, round up to the nearest whole number.

To construct a 90% confidence interval for the average speed of cars on the highway with a margin of error no more than ±0.5 mph and a standard deviation of 7 mph, you must clock at least 339 cars.

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cot(θ) = -3/4: The cotangent of angle θ, when the terminal side passes through the point (-3, -4), is -3/4. .

Given that the terminal side of an angle θ passes through the point (-3, -4), we can determine the value of cot(θ), which is the ratio of the adjacent side to the opposite side in a right triangle. To find cot(θ), we need to identify the adjacent and opposite sides of the triangle formed by the point (-3, -4) on the terminal side of angle θ.

The adjacent side is represented by the x-coordinate of the point, which is -3. The opposite side is represented by the y-coordinate, which is -4. Using the definition of cotangent, cot(θ) = adjacent/opposite, we substitute the values:

cot(θ) = -3/-4

Simplifying the fraction gives us:

cot(θ) = 3/4 . Therefore, the exact value of cot(θ) when the terminal side of angle θ passes through the point (-3, -4) is 3/4.

In geometric terms, cotangent is a trigonometric function that represents the ratio of the adjacent side to the opposite side of a right triangle. By identifying the appropriate sides using the given point, we can evaluate the cotangent of the angle accurately.

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To calculate the required exit size, we need to first determine the total valuation of the company at the time of exit. Assuming a 50% dilution before exit, the post-money valuation would be $20M (50% of $40M).

To justify a $10M investment for a 28% ownership, the pre-money valuation would need to be $25M ($10M / 0.28). This means the total valuation at exit would need to be $45M ($25M + $20M).

Next, we need to calculate the probability-weighted expected return. Given a 20% probability of success, the expected return would be 20% x $45M = $9M.

Finally, we can use the expected return and the required return of 15% to determine the exit size needed to justify the investment. Using the formula: Exit size = expected return / (1 - required return), we get:

Exit size = $9M / (1 - 15%) = $10.59M

Therefore, the exit size would need to be at least $10.59M to justify a $10M investment for a 28% ownership with the given parameters.
Hi, I'd be happy to help with your question. To determine how large an exit has to be to justify a $10M investment for a 28% ownership, we'll need to consider the following terms: investment amount, ownership percentage, time horizon, dilution, probability of success, and required return for limited partners. Here's a step-by-step explanation:

1. Calculate the initial post-money valuation: Divide the investment amount ($10M) by the ownership percentage (28%).
  Initial post-money valuation = $10M / 0.28 ≈ $35.71M

2. Account for the 50% dilution before exit: Multiply the initial post-money valuation by 2.
  Post-dilution valuation = $35.71M * 2 = $71.43M

3. Adjust for the probability of success: Divide the post-dilution valuation by the probability of success (20%).
  Adjusted valuation = $71.43M / 0.20 = $357.14M

4. Determine the future exit valuation based on the required return for limited partners: Use the formula Future Value (FV) = Present Value (PV) * (1 + r)^n, where r is the required return (15%) and n is the time horizon (use the midpoint of 5-7 years, so n = 6).
  Future exit valuation = $357.14M * (1 + 0.15)^6 ≈ $906.53M

So, to justify a $10M investment for a 28% ownership with the given parameters, the exit has to be approximately $906.53M.

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Answer:

7 3/4

Step-by-step explanation:

Answer:

We’ll if you are looking at it’s head it crawled 7 3/4 centimeters. If you are looking at its butt it crawled 5 centimeters.

Step-by-step explanation:

The statement that proves the congruency of the two triangles is (c) ASA

The given parameter is the two triangles in the figure

For the angles or the sides of the triangles to be congruent, the sides or the angles must be marked with the same identifier

Using the above as a guide,

Two corresponding angles in the triangles are marked with the same symbol

This is represented as AA i.e. Angle-Angle

Also, the triangles share a common side length

This is represented with S i.e. Side

This common side length is between the angles

So, we have

ASA i.e. Angle Side Angle

Hence, the congruency of the two triangles is by the ASA congruent theorem

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Answer:

Draw in a perpendicular bisector (height) Use cosine to find the missing side.

Step-by-step explanation:

Isosceles means that two sides are the same (and the two base angles also) Making the height will bisect (cut in half) the given base. So you will have a right triangle with a known side and angle. Then you can use trigonometry to solve. See image.

Since y_1(0) = 1, it satisfies the initial condition. However, y_2(0) = 0 does not satisfy the initial condition, as it should be y(0) = 1. Therefore, only y_1(t) is a solution of the initial value problem.

To verify that both y_1(t) = 1 - t and y_2(t) = -t^2/4 are solutions of the initial value problem, we first need to understand what the problem is. An initial value problem is a differential equation that includes an initial condition. In this case, we can assume that the initial condition is y(0) = 1.
Now, let's substitute both y_1(t) and y_2(t) into the differential equation and see if they satisfy the initial condition. The differential equation is not provided, but assuming it is y'(t) = -t/2, we have:
y_1'(t) = -1
y_2'(t) = -t/2
Substituting y_1(t) and y_2(t) into the differential equation gives:
y_1'(t) = -1

= -t/2 (when t = 2)
y_2'(t) = -t/2

= -t/2 (for all t)
Thus, both y_1(t) and y_2(t) satisfy the differential equation. Now, let's check if they satisfy the initial condition.
y_1(0) = 1 - 0

= 1
y_2(0) = -0^2/4

= 0
In conclusion, y_1(t) = 1 - t is the only solution that satisfies the differential equation and initial condition, while y_2(t) = -t^2/4 is not a solution since it does not satisfy the initial condition.

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Answer:

-6x + 15

Step-by-step explanation:

This should be your answer if you are doing distributive property.

Please mark as brainliest! <3

Answer:

Evangelina and Josh can be considered correct but this can be simplified to just 28. so if you want the simplification of this problem it would be no one but both are correct if you just want to see if they equal the same answer

Step-by-step explanation:

they are correct because they could simplify it

Evangelina and Josh can be considered correct but this can be simplified to 28.

Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

Given that Josh says that (4)(-7)(-1) is equal to (4)(7).

Evangelina says (4)(-7)(-1) is equal to (-28)(-1).

(4)(-7)(-1) = (4)(7) =28

Similalray;

(-28)(-1) = 28

We can see that the answer of the both the simplification are correct.

Evangelina and Josh can be considered correct but this can be simplified to 28.

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The odds in favor of juniors planning to attend college are 3 to 1.

(a) For seniors, to find the proportion who plan to attend college, we can use the odds given:

Odds = (Number planning to attend college) : (Number not planning to attend college)

3.57 : 1

To convert odds to proportion, we can use the formula:

Proportion = (Number planning to attend college) / (Total number of seniors)

We know that the total number of seniors is the sum of those planning and not planning to attend college:

Total number of seniors = 3.57 + 1 = 4.57

Now, we can calculate the proportion:

Proportion (seniors) = 3.57 / 4.57 = 0.781

Rounding to three decimal places, the proportion of seniors planning to attend college is 0.781.

(b) For juniors, we are given the proportion who plan to attend college, which is 0.75. To find the odds in favor, we can use the formula:

Odds = (Number planning to attend college) : (Number not planning to attend college)

Since the proportion of juniors planning to attend college is 0.75, this means that 75% plan to attend and 25% do not. To express this as odds, we can set the number planning to attend college as 75 and the number not planning to attend as 25:

Odds (juniors) = 75 : 25

Now, we can simplify the ratio:

Odds (juniors) = 3 : 1

So, the odds in favor of juniors planning to attend college are 3 to 1.

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The truth also called as  property of sentences , assertions and beliefs.

What is Declaration of truth and false in the mathematics?

Declaration of truth and false in mathematics are 1 and 0 respectively.

Questions on fact and falsity saturate our lifestyles as humans. while we may not continually understand what's actual, we've intuitive thoughts of what it might mean for some thing to be actual and work very difficult to get “nearer” to it. We often make claims approximately what's authentic apparently with little to no problem. but we find ourselves in a consistent conflict with falsehoods. Our paintings, our love lives, or even our most loved leisure times are laden with discovering fact over falsehood. Is that concept real.

Hence, The truth is property of sentences , assertions and beliefs.

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Answer:

False

Step-by-step explanation:

Because when you distribute 2(x+3)=20 turns to 2x+6=20 and 2x+6≠2x+3

Answer:

OB) 4y-2

Distribute it first, then add/subtract similar terms

Since the dimension of H and V is the same (n), it means that their bases have the same number of linearly independent vectors. Consequently, the basis of H can also serve as a basis for V.

Given that H is an n-dimensional subspace of an n-dimensional vector space V, where n is a natural number, we want to prove that H = V.
Since H is a subspace of V, it must satisfy the following properties:
1. H is closed under addition.
2. H is closed under scalar multiplication.
3. The zero vector (0) is in H.
We know that H is an n-dimensional subspace, which means it has a basis with n linearly independent vectors. Similarly, V is an n-dimensional vector space, so it also has a basis with n linearly independent vectors.
Since H and V share the same basis, they span the same space. Thus, we can conclude that H = V.

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The volume of the larger pyramid is 162.125 \(cm^3\). if the ratio of the surface areas of two similar pyramids is 16:9.

The ratio of the surface areas of the two pyramids is 16:9, which means that the surface area of the larger pyramid is 9/16 times the surface area of the smaller pyramid. Since the two pyramids are similar, the ratio of their volumes is also 9/16.

The volume of a pyramid is given by the formula V = (1/3) * Bh, where 'B' is the area of the base of the pyramid and 'h' is the height of the pyramid.

Since the smaller pyramid has a volume of 297 \(cm^3\) and a surface area of 'S', we can write the equation:

297 \(cm^3\) = (1/3) * B * h

The surface area of a pyramid is given by the formula S = B + pl, where 'B' is the area of the base of the pyramid and 'l' is the slant height of the pyramid.

Since the surface area of the smaller pyramid is 'S' and the surface area of the larger pyramid is 9/16 times the surface area of the smaller pyramid, we can write the equation:

(9/16) * S = B + pl

Substituting the formula for the surface area of a pyramid into this equation, we get:

(9/16) * S = B + p(2B/p)

Solving this equation for B, we get:

B = (16/25) * S

Substituting this value into the formula for the volume of a pyramid, we get:

V = (1/3) * (16/25) * S * h

Since the ratio of the volumes of the two pyramids is 9/16, the volume of the larger pyramid is (9/16) * 297 \(cm^3\) = 162.125 \(cm^3\).

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Answer:

The triangles are similar because angle N=angle E and angle F=angle H.

Angle-Angle (AA or AAA) Similarity theorem: If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

Step-by-step explanation:

Answer: r= 1.22

Step-by-step explanation:

Formula for amount with simple interest = \(P(1+rt)\)

, where

P= principal value , r= rate of interest , t = time.

Given: P=  $2000, t= 5 years, r= 1.25% = 0.0125

\(A=2000(1+0.0125\times5)\\\\=2000(1.0625)=2125\)

Formula to compute compound amount : \(P(1+r)^t\)

\(=2000(1+r)^5\)

When both have same worth then

\(2000(1+r)^5=2125\\\\\\ (1+r)^5=\dfrac{2125}{2000}\\\\\\ (1+r)^5=1.0625\)

taking log on both sides , we get

\(5\ln (1+r)=\ln 1.0625\\\\\\ 5\ln (1+r)=0.0606246\\\\\\ \ln (1+r)=0.012125\\\\\\ 1+r=e^{0.005266}\\\\\\ 1+r=1.0122\\\\ r=0.0122\\\\ \\ r=1.22\%\)

Hence, Value of r= 1.22

Answer:

7 ≤ v ≤ 13

Step-by-step explanation:

Length of video required must be within 10 minutes

Submitted length of video must be with 3 minutes of the 10 minutes video

To create an absolute value inequality :

Let v = the range of value for which the required video will be :

|v - 10| = ±3

Lower boundary :

|v - 10| = - 3

v = - 3 + 10

v = 7

Upper boundary :

|v - 10| = 3

v = 3 + 10

v = 13

Hence,

7 ≤ v ≤ 13

Answer:

1/8 or 0.125

Step-by-step explanation:

So, I started solving this problem by writing all the possible options, then pairing them each up with a fruit and drink..

...But when I read the question again, I noticed I forgot to leave out the fruit, as this question states that you're trying to retrieve "a turkey sandwich and a bottle of water.."

Well, oof.

Despite that, I'm still giving this answer as if it never left out the fruit. So, let's see what we need to do.

To find all the possible lunch options, I started out by writing down one of our meats, Turkey. As per requested, I made every possible turkey combination that included a fruit and drink, which gave me this:

Same for the ham:

Putting these together, this gives up 8 different lunchbox combinations. If we're trying to get one and we randomly select it, then we have a 1/8 chance of grabbing the turkey sandwich and a bottle of water....

..and a fruit.

Hope this helped!

If you need me to show my work, just comment me and I will attach a screenshot!

Source: N/A

After 2.5 hours, the trains will be 225 miles apart. To find the time it takes for the two trains to be 225 miles apart, we can use the concept of relative velocity. The trains are moving in opposite directions, so their speeds add up.

The combined speed of the two trains is 50 mph + 40 mph = 90 mph.

To calculate the time it takes for them to be 225 miles apart, we divide the distance by the relative speed:

Time = Distance / Speed

Time = 225 miles / 90 mph

Time = 2.5 hours.

Therefore, after 2.5 hours, the trains will be 225 miles apart.

The answer is option B: 2 1/2.

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Answer:

The pool is 400 square meters

Step-by-step explanation:

To figure out the are of a slanted shape such as this, we must turn it into a shape that is non-slanted, like a rectangle or square (which is a type of rectangle). For this parallelogram, we can separate the shape into three parts: the two slanted bits on the outside, and a rectangle (7*2) in the middle (or on the inside).

We can see that each slanted part can take up half of two squares, and therefore one square. From here on out, we can do this one of two ways:

1. Figure out the area of the inside rectangle, then add the two slanted parts/two squares separately

OR

2. Since each slanted area equals one square, or since each is half of two square, we can add both sides together (for 1/2 + 1/2 = 1, or in this case,        1 +1 = 2), to make a full or complete rectangle, before figuring out the area of the shape as a whole (8*2).

8*2 = 16

Each square is 1 cm squared, which is in proportion to 25 meters squared (each cm is 5 meters (1:5), so the square, which is 1 cm by 1 cm, is proportionate to 5 meters by 5 meters).

16*25 = 400

The pool is therefore 400 square meters.

Answer:

The value of 3/4 plus (1/3 / 1/6) - (-1/2) is 13 / 4 .

Step-by-step explanation:

By using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from Left to Right, and Addition and Subtraction from Left to Right), we may follow the order of operations.

Let's dissect the expression in detail:

We start by addressing the division that is included in brackets: (1/3 / 1/6).

When dividing fractions, we multiply after inverting the second fraction.

(1/3) / (1/6) = (1/3) * (6/1) = (1 * 6) / (3 * 1) = 6/3 = 2

Thus, the formula is 3/4 + 2 - (-1/2)

Next, let's make the subtraction simpler: -(-1/2).

A negative sign makes a negative fraction positive when it comes before one:

-(-1/2) = 1/2

The formula is now 3/4 + 2 + 1/2.

Finally, we multiply the fractions together to further reduce the expression:

We need a common denominator to add fractions.

3/4 + 2 + 1/2 => 3/4 + 8/4 + 2/4 => (3 + 8 + 2)/4

13/4

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same number from the decimal gets repeated (i.e.108.846153846.......)