A stray dog ate 21 of your muffins. That was 7/10 of all of them! With how many did you start with?

A) 30
B) 25
C) 28
D) 14.7​

Answer: B,C,D

Step-by-step explanation:

Since the only requirement is that the width needs to be at least 50 yds. B, C,D all work.

The area of quadrilateral OBEC is 16m - 8, which depends on the slope of line CD

To solve this problem, we can use the fact that the two lines intersect at point E(4,4).

We know that line AB has a slope of -2,

so its equation is y = -2x + b,

where b is the y-intercept.

Since it passes through point B(0,b), we can solve for b by substituting x = 0 and y = b:

b = -2(0) + b

b = b

So the equation of line AB is,

⇒ y = -2x + b.

We also know that it passes through point A(a,0), so we can substitute these coordinates into the equation to solve for a:

0 = -2a + b

b = 2a

Substituting b = 2a back into the equation for line AB, we get

y = -2x + 2a.

Now we need to find the equation of the second line CD.

We know that it passes through point C(8,0), so we can use point-slope form to find its equation:

y - 0 = m(x - 8)

where m is the slope of line CD.

To find the slope, we know that it passes through point D(0,d), so we can substitute these coordinates into the equation:

d - 0 = m(0 - 8)

d = -8m

Substituting d = -8m back into the equation for line CD, we get

y = -8/(-1/m)x = 8mx.

Now we can find the coordinates of point D by substituting x = 0:

D = (0, 8m)

To find the coordinates of point O, we need to find where lines AB and CD intersect.

Setting their equations equal to each other and solving for x, we get:

-2x + 2a = 8mx

x = 2a/(4m+1)

Substituting x back into either equation, we get:

y = -2(2a/(4m+1)) + 2a = -4am/(4m+1) + 2a

y = 8m(2a/(4m+1)) = 16am/(4m+1)

Either way, we now have the coordinates of point O(a, -4am/(4m+1)) or (2a/(4m+1), 0).

Finally, we can find the area of quadrilateral OBEC by subtracting the areas of triangles OEB and CED from the area of rectangle OCBD:

Area(OBEC) = Area(OCBD) - Area(OEB) - Area(CED)

                  = (8)(8m) - (1/2)(4)(4) - (1/2)(8-4)(8m-d)

                  = 64m - 8 - 16m + 4d

                  = 48m + 4d - 8

Substituting d = -8m, we get:

Area(OBEC) = 64m - 8 - 16m - 32m = 16m - 8

So, the area of quadrilateral OBEC is 16m - 8, which depends on the slope of line CD.

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Answer:

acute

Step-by-step explanation:

this is an acute triangle because all angles are less than 90 degrees

it is not obtuse because no angle is over 90 degrees

it is not equiangular because the angles are not equal to each other

and it is not right because there is no right angle

Acute

Triangles can be classified by the size of their angles.

Angle Classification

Angles can be classified into 3 sizes: acute, right, and obtuse.

Triangle Classification

Triangles are classified by their largest angle. If the largest angle is obtuse, then it is an obtuse triangle. If there is a right angle, then it is a right triangle. If the largest angle is an acute angle, then it is an acute triangle. Finally, there is one special classification that technical falls under acute angles. If all of the angles are equal (meaning they are all 60°), then it is an equiangular triangle.

The triangle in the picture has 3 angles that are all under 90°. The largest angle is 76°. Since this is an acute angle, it is an acute triangle.

Answer:

-1/2

Step-by-step explanation:

use a graphing calculator or use slope formula.

was -3/6 but I reduced it

The absolute value functions graphed are given as follows:

1. y = |x + 1|.

3. y = |x + 1| - 4.

4. y = 0.5(|x - 1| + 1)

An absolute value function of vertex (h,k) is defined by the following rule:

y = |x - h| + k.

For item 1, the vertex of the function is at point (-1,0), hence h = -1 and k = 0, and the rule is:

y = |x + 1|.

For item 3, the vertex of the function is at point (-1, -4), hence the coefficients are h = -1 and k = -4, and the rule is:

y = |x + 1| - 4.

For item 4, the vertex of the function is at point (1,1), and the function is also vertically compressed by a factor of 0.5, as when x changes by 2, y changes by 1, hence the rule is:

y = 0.5(|x - 1| + 1)

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The percent change would be 36%

Percent increase and percent decrease are measures of percent change, which is the extent to which a variable gains or loses intensity, magnitude, extent, or value.

Given:

4 candy bars = 5$

1 candy bar = 5/4

1 candy bar = 1.25$

Now,

5 candy bars = 4$

1 candy bar =4/5

1 candy bar = 0.8$

% change = (0.8-1.25) / 1.25 *100

                  = 36%

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Answer:

8÷2=4×4×3.14=50.2

12÷2=6×6×3.14=113

113_50.2=62.8 m2

The statement "Just because there seems to be a linear relationship between an X and a Y, does not mean that Y is affected or influences by X" is false.

If there is a linear relationship between two variables X and Y, it means that changes in X are associated with changes in Y. This association can be positive, meaning that as X increases, Y also tends to increase, or negative, meaning that as X increases, Y tends to decrease.

However, it is important to note that a linear relationship does not necessarily imply causation. Just because two variables are linearly related, it does not necessarily mean that one variable is affecting or influencing the other. There could be other factors or variables that are affecting both X and Y, or the relationship could be spurious, meaning that the association is due to chance or some other factor that is not related to the variables in question.

Therefore, while a linear relationship is an important indicator of association between two variables, it does not necessarily imply causality or a direct influence between them. Additional research and analysis are often needed to establish the nature and direction of the relationship and to identify any possible underlying causes or factors.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

Year 1 - You earn interest on your Principal.

Year 2 - You earn interest on your (Principal + Interest of Year 1).

Year 3 - You earn interest on your (Principal + Interest of Year 1 + Interest of Year 2).

Compound interest is the basis of long-term growth of the stock market. It forms the basis of personal savings plans. Compound interest also affects inflation.

Types of Compound Interest

There are generally two types of compound interest used.

Periodic Compounding - Under this method, the interest rate is applied at intervals and generated. This interest is added to the principal. Periods here would mean annually, bi-annually, monthly, or weekly.

Continuous Compounding - This method uses a natural log-based formula and calculates interest at the smallest possible interval. This interest is added back to the principal. This can be equalled to the constant rate of growth for all natural growth. This figure was born out of physics. It uses Euler’s number which is a famous irrational number which is known to more than 1 trillion digits of accuracy. Euler’s number is denominated by the letter “E”.

Periodic Compound Interest Formula Overview

There are two formulas you can use to calculate compound interest, depending on what result you wish to find out. You can find out the following:

The total value of the deposit.

The total compound interest earned.

Value of the Deposit

Formulas can be a deterrent to many. If you aren’t savvy with math, your eyes turn away from these codes or just skip them altogether. But once it’s explained, it’s pretty simple to understand. To calculate the total value of your deposit, the formula is as follows:

P (1+ i/n)nt

P = Principal invested.

i = Nominal Rate of Interest.

n = Compounding Frequency or number of compounding periods in a year.

t = Time, meaning the length of time the interest is applicable, generally in years.

Simply put, you calculate the interest rate divided by the number of times in a year the compound interest is generated. For instance, if your bank compounds interest quarterly, there are 4 quarters in a year, so n = 4. This result must be multiplied to the power of the deposit period. For example, if your deposit is for 10 years, t = 10. This whole result should be multiplied by the principal you invested. The result generated will equal the total accumulated value of your deposit. You can find out how much your deposit is worth currently after accumulating interest.

Total Compound Interest Earned

To find out how much interest was earned, you can use the following formula for Compound Interest.

P[(1+ i/n))nt-1]

Compound Interest Equation and Calculation

To understand the compound interest equation further, we can break it down in simpler terms. If you decide to invest in a fixed deposit with compound interest, this is how you will earn interest every year.

Period Deposit Balance

Investment P

Year 1 P + iP

Year 2 (P+ iP) + i(P+iP)

To collapse this formula, we can pull out factors of (1+i). Simply substitute iP with (1+i) to get the following:

Period Deposit Balance

The scale of the drawing is 1 inch represents 30 feet. This can be found by setting up a proportion:

18 inches (length of stage in drawing) / x (length of stage in real life) = 2 inches (length in drawing) / 45 feet (length in real life)

Simplifying this proportion gives:

x = 18 × 45 / 2 = 405

Therefore, the length of the stage in real life is 405 feet. To find the scale, we can set up another proportion:

1 inch (length in drawing) / x (length in real life) = 2 inches (length in drawing) / 60 feet (length in real life)

Simplifying this proportion gives:

x = 1 × 60 / 2 = 30

Therefore, the scale of the drawing is 1 inch represents 30 feet.

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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Out of 52 cards, there is only one Queen of Hearts. Hence, then, the probability = 47/52

5 cards can be chosen from a deck of 52 cards in ⁵²C₅

In order to avoid choosing a queen of hearts, we must choose 5 cards. There is only one queen of hearts in a deck of 52 cards. There are still 51 cards left, and 5 of them can be chosen in ⁵²C₅.

Therefore, the likelihood that a five-card poker hand does not include the queen of hearts is equal to ⁵¹C₅/⁵²C₅

47/52

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The full question

What is the probability that a five-card poker hand does not contain the queen of hearts?

Answer:17

Step-by-step explanation:

Accoding to the calculations , the correct answer is:

A) Depreciation charge 16,000; revaluation surplus £20,000

According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.

In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).

To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:

£400,000 / 25 = £16,000

Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.

Now, let's calculate the balance on the revaluation surplus as at that date.

The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).

Revaluation surplus = Fair value - Carrying amount

Revaluation surplus = £500,000 - £480,000

Revaluation surplus = £20,000

Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.

Based on the calculations above, the correct answer is:

A) Depreciation charge £16,000; revaluation surplus £20,000

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Answer:

10x+3y+2

Step-by-step explanation:

Answer:

4:5

Step-by-step explanation:

Binh's = 40

Davina's = 50

40:50 = 4:5

Answer:

the equation to finding slope is this:

y2-y1 / x2-x1

Where y2 is the y value of the second point, y1 is the y value of the first point, x2 is the value of the second x value, and x1 is the x value of the first point.

5-0 / -2-2

5/-4

-5/4 is the slope

Step-by-step explanation:

Answer:

\(m=\frac{-5}{4} \\\) which is the slope.

Step-by-step explanation:

Since we have two points on the line, we can easily calculate the slope.

Point 1 = (-2, 5)

Point 2 = (2, 0)

\(m=\frac{rise}{run}\\m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\m=\frac{0-5}{2-(-2)} \\m=\frac{-5}{4}\)

By using Python, you will come up with your own challenging algorithm for other students to trace.

If a certain is true, the if/else expression triggers a sequence of instructions to run. Another piece of code may be run if the condition is false.

The if/else statement is a component of Python's "Conditional" Statements, which are used to carry out various operations based on various circumstances.

These conditional statements are available in Python:

If you want a block of code to run only if a certain condition is true, use the if statement.

If the same expression is false, use instead that to provide a set of instructions that should be run.

If the first expression is false, can use else if sentence to establish a comprehensive criterion to test.

To choose which of the several program code should be performed, use the switch.

How to write the code?

num = 100

if num < 20:

print('Less than 20')

if num < 30:

print('Less than 30')

if num < 40:

print('Less than 40')

if num < 50:

print('Less than 50')

if num > 100 or num == 100:

print('More than or equal to 100')

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Three- Dimensional figures- Cube and Cylinder

Let a be the length of sides of cube and r and h be the radius and height of cylinder respectively.

Cube -  All sides are of same dimensions.

             Let a be the length of the dimensions

             The top, bottom and side view are squares each of length a units.

             The diagonal view is basically a three dimensional right angled   triangle.

Cylinder- h be the length/ height of cylinder and r be the radius of the cylinder.

The top view of cylinder is basically a circle of radius.

The side view is basically curved surface of the cylinder of length h.

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Answer:

1.11 is bigger

Step-by-step explanation:

Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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To find the value of the integral ∫[0 to 1] (f(x) - g(x)) dx, we can use the given information and properties of integrals. We are given that ∫[0 to 1] (f(x) - 2g(x)) dx = 6 and ∫[0 to 1] (2f(x) + 2g(x)) dx = 9. From these equations, we can derive the value of the desired integral.

Let's start by manipulating the second equation:

∫[0 to 1] (2f(x) + 2g(x)) dx = 9

2∫[0 to 1] (f(x) + g(x)) dx = 9

∫[0 to 1] (f(x) + g(x)) dx = 9/2

Now, let's subtract the first equation from the above equation:

∫[0 to 1] (f(x) + g(x)) dx - ∫[0 to 1] (f(x) - 2g(x)) dx = 9/2 - 6

∫[0 to 1] 3g(x) dx = -3/2

Since we want to find ∫[0 to 1] (f(x) - g(x)) dx, we can rewrite the equation as:

∫[0 to 1] (f(x) + g(x)) dx - 2∫[0 to 1] g(x) dx = -3/2

Substituting the value of ∫[0 to 1] (f(x) + g(x)) dx from the second equation, we get:

9/2 - 2∫[0 to 1] g(x) dx = -3/2

Simplifying the equation, we find:

∫[0 to 1] g(x) dx = 6

Therefore, the value of ∫[0 to 1] (f(x) - g(x)) dx is 6.

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Since the null hypothesis was not rejected, there is not enough evidence to conclude that under 46% of the residents favor construction of an adjoining bridge.

There are two decisions possible regarding the null hypothesis, as follows;

The hypothesis are given as follows:

The null hypothesis was not rejected, meaning that the conclusion regarding the mayor's claim is that there is not enough evidence from the sample of 190 voters to conclude that the percentage is below 46%.

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Answer: The length is 13cm and the width is 7cm

Step-by-step explanation:

For a rectangle of length L and width W, the area is:

A = W*L

In this case we have:

L = (2*x + 9) cm

W=(3*x + 1) cm

Then the area of the rectangle is:

A = (2*x + 9)*(3*x + 1) cm^2

A = (6*x^2 + 2*x + 27*x + 9) cm^2

A = (6*x^2 + 29*x + 9) cm^2

now we remove two squares with sides of x cm

The area of each one of these squares is (x cm)*(x cm)  = x^2 cm^2

Then the area of the figure will be:

area = (6*x^2 + 29*x + 9) cm^2 - (2*x^2 ) cm^2

area = (4*x^2 + 29*x + 9) cm^2

Now we know that the area of this shape is 83 cm^2, then we need to solve:

83 cm^2 = (4*x^2 + 29*x + 9) cm^2

0 =  (4*x^2 + 29*x + 9) cm^2 - 83 cm^2

0 = (4*x^2 + 29*x - 74) cm^2

Then we need to solve:

0 = 4*x^2 + 29*x - 74

Here we can use Bhaskara's equation, the solutions of this equation are given by:

\(x = \frac{-29 \pm \sqrt{29^2 - 4*4*(-74)} }{2*4} = \frac{-29 \pm 45}{8}\)

Then the two solutions are:

x = (-29 - 45)/8 = -9.25  (for how the length and width are defined, we can not have x as a negative number, then this solution can be discarded).

The other solution is:

x = (-29 + 45)/8 = 2

x = 2

Then the length and width of the rectangle are:

Length = (2*2 + 9)cm = 13 cm

Width = (3*2 + 1)cm = 7cm

Answer:

The probability of randomly picking a red candy is 1/20 and In percentage value 5%

Step-by-step explanation:

There are 5 blue candies, 6 red candies, and 9 yellow candies.

Now, Total

5 + 6 + 9 = 20 candies

Now, The probability of randomly picking a red candy is 1/20

Now, In percentage

1/20 × 100% = 5%

Thus, The probability of randomly picking a red candy is 1/20 and In percentage value 5%.

-TheUnknownScientist

Answer:

x ≈ 15

Step-by-step explanation:

using Pythagoras' identity in the right triangle

a² + b² = c²

with a = 8, b = x , c = 17

8² + x² = 17²

64 + x²  = 289 ( subtract 64 from both sides )

x² = 225 ( take square root of both sides )

\(\sqrt{x^2}\) = \(\sqrt{225}\)

x = 15