. A small scale poultry farmer packs eggs for sale in boxes of 6, 12 or 18 eggs. What is the smallest number of eggs that can be packed?​

Answers

Answer 1

Answer:

6 = 2 × 3

12 = 2 × 2 × 3

18 = 2 × 3 × 3

LCM of 6, 12, and 18 = 2 × 2 × 3 × 3 = 36

The smallest number of eggs that can be packed is 36.


Related Questions

1000
Store Sales
Store A sells five times as many products as Store B and one third as many as Store C. If Store C sells 145,670
products, how many products does Store B sell?
9,711
48,557
87,402
242,783
728,350
Q Search
O
H
D
Submit

Answers

If Store C sells 145,670 products then Store B sells 9,711 products. Option A is the correct answer.

To determine the number of products Store B sells, we need to calculate it based on the information given in relation to Store C.

Given that Store C sells 145,670 products, and Store A sells one-third as many as Store C, we can find the number of products Store A sells:

Store A = (1/3) * Store C = (1/3) * 145,670 = 48,557

Now that we know Store A sells 48,557 products, and it sells five times as many products as Store B, we can calculate the number of products Store B sells:

Store B = (1/5) * Store A = (1/5) * 48,557 = 9,711

Therefore, Store B sells 9,711 products. Option A is the correct answer.

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Find the measure of the missing angles.
24°
122°
d
e
f

Answers

Therefore, the missing angle = (1080° - 947°) = 133°

Step-by-step explanation:

Given: Octagon

7 Interior Angles: 122°, 143°, 152°, 107°, 128°, 130° & 165°

Find: The measure of the missing angle:

Plan: Determine total sum of an octagons interior angles and subtract the total of the given angles

Sum of the Interior Angles of an Octagon:S = (n-2) 180°

S = (8 - 2)180° = 6 x 180° = 1080°

Sum of 7 Given Angles: S7IA = 947°

x/x-3+1/3=1 what values should be excluded

Answers

The value x = 3 should be excluded from the solution set because it would result in a division by zero in the equation.

How to determine the values that should be excluded

To determine the values that should be excluded in the equation x/(x - 3) + 1/3 = 1, we need to find the values of x that would make the equation undefined or result in a division by zero.

In this case, the expression x - 3 appears in the denominator, so we need to find the values of x that would make x - 3 equal to zero.

x - 3 = 0

x = 3

Therefore, the value x = 3 should be excluded from the solution set because it would result in a division by zero in the equation.

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Which function represents exponential growth?

f(x) = 3x
f(x) = x3
f(x) = x + 3
f(x) = 3x

Answers

The function that represents exponential growth is f(x) = 3x. Exponential growth is a type of growth in which the growth rate of a quantity increases over time, resulting in a continuously accelerating rate of growth.

In this function, the base of the exponent is 3, which means that the growth rate is tripling with each increase of x.

This is a characteristic of exponential growth.
Exponential growth can be seen in many real-world situations, such as population growth, compound interest, and the spread of diseases.

In each of these cases, the growth rate increases over time, leading to exponential growth.

The function f(x) = 3x is an example of exponential growth because it represents a situation in which the growth rate is increasing over time.
In summary, the function that represents exponential growth is f(x) = 3x.

Exponential growth is a type of growth in which the growth rate increases over time, leading to a continuously accelerating rate of growth.

This type of growth can be seen in many real-world situations and is characterized by a base exponent that is greater than one.

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I do not know these questions

Answers

Answer:

Step-by-step explanation:

1). 3/4

2). 5/2

3). 7/9

4). 12/5

5).5/6

please mark me brainliest

A company claims that its heaters last less than 5 years. Write the null and alternative hypotheses.

Answers

The goal would be to gather sufficient evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis.

The null hypothesis (H₀): The company's heaters have a mean lifespan of 5 years or more.

The alternative hypothesis (H₁): The company's heaters have a mean lifespan of less than 5 years.

In hypothesis testing, the null hypothesis represents the claim or assumption that is being tested. In this case, the null hypothesis assumes that the mean lifespan of the company's heaters is equal to or greater than 5 years. The alternative hypothesis, on the other hand, challenges this claim and suggests that the mean lifespan is less than 5 years.

To determine which hypothesis is supported by the evidence, statistical analysis would need to be conducted using appropriate data and methods. The goal would be to gather sufficient evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis.

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Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
19, 14, 9, ...

Answers

We represent it as -5. Thus, the common difference/ratio of the given sequence in the simplest form is -5.

To determine if a sequence is arithmetic or geometric, we have to find the differences (common differences) between the terms in the sequence.

The differences between the terms are calculated to determine if they are consistent for the arithmetic sequence or if they have a common ratio for the geometric sequence.

Therefore, the sequence below is arithmetic:19, 14, 9, ...To determine the common difference, we subtract each term from the previous term.19 – 14 = 5; 14 – 9 = 5Therefore, the common difference is 5. Hence, this is an arithmetic sequence with a common difference of 5.

Also, we can say that 14 - 19 = -5, 9 - 14 = -5, and so on. This is a common difference of 5 in the opposite direction. We can say that the difference is -5.

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Kevin tiene 2 veces la edad de Gabriela. Hace 12 años Kevin tenía 6
veces la edad de Gabriela.
¿Cuántos años tiene Kevin actualmente?

Answers

Answer:

30

Step-by-step explanation:

ahora:

edad de Kevin = k

edad de Gabriela = g

k = 2g

hace 12 años:

edad de kevin = k - 12

edad de gabriela = g - 12

k - 12 = 6(g - 12)

k = 2g

k - 12 = 6(g - 12)

2g - 12 = 6(g - 12)

2g - 12 = 6g - 72

4g = 60

g = 15

k = 2g = 2 × 15 = 30

Solving using the multiplication principle. Then graph.

5x<10

Answers

Answer:

x<2

Step-by-step explanation:

Solve for X

5x<10

1. Get X by itself by dividing both sides by 5

x<2

2. Graph the dotted asymptote on (0,2) and shade everything to the left since x<2

A town’s population increases at a constant rate. In 2010 the population was 57,000
By 2012 the population had increased to 80,000 If this trend continues, predict the population in 2016.

Answers

Answer:

126000

Step-by-step explanation:

if from 2010 to 2012 there was an increase of 23000 that means every two years 23000 people are added then add 23000 to 80000 for four years and you will get 126000.In other words if you get 23000 divide it by two to get the amount for one year then multiply it by 8

When building a house, the number of days required to build is inversely proportional to the number of workers. One house was built in 161 days by 4 workers. How many days would it take to build a similar house with 46 workers?​

Answers

It will take 14 days for 46 workers to build similar house.

How to find the number of days to build similar house?

When building a house, the number of days required to build is inversely proportional to the number of workers.

Therefore,

d α 1 / w

d = k / w

k = dw

where

k = constant of proportionalityd = number of daysw = number of workers

Therefore,

k = 161 × 4

k = 644

Let's find the number of days to build similar house with 46 workers.

Therefore,

d = 644 / 46

d = 14 days

Therefore, it will take 14 days.

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Saidhari bought a toaster oven for $105. This price was 1/4 off the list price.

Answers

Answer:

The list price would be $420.

3.5% of a number is 49 what is my original nnumber

Answers

Answer:

1400

Step-by-step explanation:

To preface, we should think about how percentages are taken from original numbers, and we may apply the operations oppositely.

First, let's set up an equation.

Let 3.5% equal to 49, where 3.5% is multiplied by x and x = the unknown factor.

3.5x = 49

Divide both sides by 3.5 to get x by itself.

3.5x/3.5 = 49/3.5

= x = 14.

Multiply the number by 100 and you will get your answer of 1400.

Check:

3.5% to decimal is... 3.5/100 = 0.035.

Multiply the quotient by the answer 1400 and you will obtain the given number of a percentage.

0.035 x 1400 = 49.

Select all the correct answers.

Which expressions are equivalent to the given expression?

Y^-8y^3x^0x^-2

Answers

Answer:

Step-by-step explanation:

4 then add 5 + 1 which would = 4

Planes A and B intersect.
n
m
W
k
1
Y
V
B
Z
P
ix
A

Answers

The point of intersection of line m and line n is: Line W

What is the point of intersection of the Lines?

The intersection of two lines is defined as the point where the two lines intersect or intersects.

Line segments m and n are assumed to intersect. That is, they must eventually intersect.

In this question we need to find the intersection of lines l and m.

And suppose lines  A and B intersect.

From the given figure, we can see that in plane A, lines m and n intersect at point W. The point W is therefore the intersection of the two lines m and n.  

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What is the effect on the graph of f(x) = x² when it is transformed to
h(x) = 3x²-7?
A. The graph of f(x) is horizontally compressed by a factor of 3 and
shifted 7 units to the right.
B. The graph of f(x) is vertically stretched by a factor of 3 and shifted
7 units down.
C. The graph of f(x) is vertically stretched by a factor of 3 and shifted
7 units to the right.
D. The graph of f(x) is horizontally stretched by a factor of 3 and
shifted 7 units down.

Answers

The effect on the graph of f(x) = x² when it is transformed to h(x) = 3x² - 7 is described by option B. The graph of f(x) is vertically stretched by a factor of 3 and shifted 7 units down.

The original function f(x) = x² represents a parabola with its vertex at the origin (0, 0). The graph opens upward and has a general U-shape.The transformation h(x) = 3x² - 7 indicates that the function has been multiplied by 3, resulting in a vertical stretch. This means that the points on the graph are now vertically spread out, making the U-shape more elongated.Additionally, the transformation includes subtracting 7 from the function, shifting the entire graph downward by 7 units. This means that each y-coordinate of the original function has been reduced by 7 units.The combination of the vertical stretch by a factor of 3 and the downward shift of 7 units results in a new graph h(x) that is vertically stretched and shifted downward. The overall shape of the graph remains a U-shaped parabola, but it is now wider and lower compared to the original graph.Therefore, option B accurately describes the effect of the transformation on the graph of f(x) = x² to h(x) = 3x² - 7.

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an american put futures option has a strike price of 0.55 and a time to maturity of 1 year. the current future price is 0.60. the volatility of the futures price is 25% and interest rate is 6% per annum. use a one-time step tree to value the option

Answers

The value of the American put futures option using a one-time step tree is $0.

To value the American put futures option using a one-time step tree, we can follow these steps:

Step 1: Calculate the risk-neutral probability of an up move (p) and a down move (1-p) based on the volatility and time step. Given that the volatility is 25% and the time to maturity is 1 year, we can calculate the time step as √(1 year) = 1.

Since this is a one-time step tree, there are two possible outcomes: an up move or a down move. We need to find the risk-neutral probabilities of these moves.

To calculate p, we use the formula:

p =[tex](e^(r * t) - d) / (u - d)[/tex]

Where:

r is the interest rate per annum (6% = 0.06),

t is the time step (1),

u is the up move factor (1 + volatility) = (1 + 0.25) = 1.25,

d is the down move factor (1 - volatility) = (1 - 0.25) = 0.75.

Substituting the values, we get:

p =[tex](e^([/tex]0.06 * 1) - 0.75) / (1.25 - 0.75)

p = (1.06183 - 0.75) / 0.5

p = 0.31183 / 0.5

p = 0.62366

Step 2: Calculate the option values at each possible outcome. Since this is a put option, the payoff at each node is the difference between the strike price and the future price at that node.

At the up move node:

Option value (up) = max(strike price - future price (up), 0)

                = max(0.55 - 0.60, 0)

                = max(-0.05, 0)

                = 0

At the down move node:

Option value (down) = max(strike price - future price (down), 0)

                  = max(0.55 - 0.55, 0)

                  = max(0, 0)

                  = 0

Step 3: Calculate the expected option value at the current node by taking the risk-neutral weighted average of the option values at the next nodes.

Expected option value = p * option value (up) + (1 - p) * option value (down)

                    = 0.62366 * 0 + (1 - 0.62366) * 0

                    = 0

Therefore, the value of the American put futures option using a one-time step tree is $0.

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Suppose u and v are functions of x that are differentiable at x=0 and that u(0)=-8, u'(0)=-4, v(0)=9, and v'(0)=5. Find the values of the following derivatives at x=0.

Answers

Answer:

(A) -76

(B) 4/81

(C) -1/16

(D) 3

Step-by-step explanation:

It is given that u and v are functions of x and are differentiable at x=0 and that u(0) = -8, u'(0) = -4, v(0) = 9, and v'(0) = 5. We are asked to find the following derivatives at x=0.

(A) - [tex]\dfrac{d}{dx}[uv][/tex]

(B) - [tex]\dfrac{d}{dx}\Big[\dfrac{u}{v} \Big][/tex]

(C) - [tex]\dfrac{d}{dx}\Big[\dfrac{v}{u} \Big][/tex]

(D) - [tex]\dfrac{d}{dx} [-5v-7u][/tex]

[tex]\hrulefill[/tex]

Part (A) - Using the product rule.

[tex]\dfrac{d}{dx}[uv]=uv'+vu'[/tex]

Substituting in our values:

[tex](-8)(5)+(9)(-4)\\\\\\\therefore \boxed{=-76}[/tex]

Part (B) - Using the quotient rule.

[tex]\dfrac{d}{dx}\Big[\dfrac{u}{v} \Big]=\dfrac{vu'-uv'}{v^2}[/tex]

Evaluating at x=0:

[tex]\dfrac{(9)(-4)-(-8)(5)}{(9)^2}\\\\\\\therefore \boxed{=\frac{4}{81} }[/tex]

Part (C) - Using the quotient rule.

[tex]\dfrac{d}{dx}\Big[\dfrac{v}{u} \Big]=\dfrac{uv'-vu'}{u^2}[/tex]

Evaluating at x=0:

[tex]\dfrac{(-8)(5)-(9)(-4)}{(-8)^2}\\\\\\\therefore \boxed{=\frac{-1}{16} }[/tex]

Part (D) - Deriving the function.

[tex]\dfrac{d}{dx} [-5v-7u]=-5v'-7u'[/tex]

Substituting in our values:

[tex]-5(5)-7(-4)\\\\\\\therefore \boxed{=3}[/tex]

Thus, all parts have been solved.

Evaluate:
10
8(2)n-1
n=1
S = [?]
Remember: for a geometric series, S = (1 – r")
1-r
Enter

Answers

Evaluating when [tex]\( n = 1 \)[/tex], the value of S is: S = 1

How to determine the value of S

Evaluate:

[tex]\[ S = 108(2)^{n-1} \][/tex]

When n = 1.

Remember: For a geometric series, the sum can be calculated using the formula:

[tex]\[ S = 108(2)^{n-1} \][/tex]

In this case, we have r = 2, since each term is multiplied by 2 to get the next term.

Substituting the values into the formula, we get:

[tex]\[ S = \frac{{(1 - 2^n)}}{{1 - 2}} \][/tex]

Simplifying further:

[tex]\[ S = \frac{{1 - 2^n}}{{-1}} \][/tex]

Since the denominator is -1, multiplying the numerator and denominator by -1, we get:

[tex]\[ S = 2^n - 1 \][/tex]

Therefore, when [tex]\( n = 1 \)[/tex], the value of S is:

S = [tex]2^1[/tex]- 1 = 2 - 1 = 1

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Drag the tiles to the correct boxes to complete the pairs.
Match each polynomial function with one of its factors.
f(x) = x3 − 3x2 − 13x + 15
f(x) = x4 + 3x3 − 8x2 + 5x − 25
f(x) = x3 − 2x2 − x + 2
f(x) = -x3 + 13x − 12
x − 2
arrowRight
x + 3
arrowRight
x + 4
arrowRight
x + 5
arrowRight
Reset Next

Answers

The correct matches for the polynomial are:

x - 3 (matches) f(x) = x³ − 3x² − 13x + 15

x - 2 (matches) f(x) = x⁴ + 3x³ − 8x² + 5x − 25

x - 1 (matches) f(x) = x³ − 2x² − x + 2

x + 3 (matches) f(x) = -x³ + 13x − 12

What is a polynomial?

A polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, combined using addition, subtraction, and multiplication. The variables in a polynomial are raised to non-negative integer exponents.

f(x) = x³ − 3x² − 13x + 15:

Factor: x - 3

f(x) = x⁴ + 3x³ − 8x² + 5x − 25:

Factor: x - 2

f(x) = x³ − 2x²− x + 2:

Factor: x - 1

f(x) = -x³ + 13x − 12:

Factor: x + 3

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for y=6/5x-2, which value represents the slope of a line parralel to the equation 5/6 6/5 -1/2 1/2

Answers

Answer:

The slope of a line parallel to the equation y = (6/5)x - 2 is 6/5.

Step-by-step explanation:

In general, when two lines are parallel, they have the same slope. Therefore, any line that is parallel to the given equation will have a slope of 6/5.

Find the set A U U.
U=(a, b, c, d, e, f, g, h)
A={c, d, g, h)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. AUU={__} (Use a comma to separate answers as needed.)
OB. AUU =Ø

Answers

The set A U U is:

A U U = {a, b, c, d, e, f, g, h}

How to find the set A U U?

A set is a collection or grouping of distinct objects, which are called elements or members of the set. These objects can be anything: numbers, letters, shapes, or even other sets.

We have:

A= {c, d, g, h}

U= {a, b, c, d, e, f, g, h}

A U U is the set of all elements (letters) that appear in both A and U. Thus, we can say:

A U U = {a, b, c, d, e, f, g, h}

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Solve the proportion for X.
5/2.5=
X/2
1
4
5.5
6.25​

Answers

To solve the proportion 5/2.5 = X/2, we can cross-multiply:

5 * 2 = 2.5 * X

10 = 2.5X

Divide both sides by 2.5:

10/2.5 = X

4 = X

Therefore, X is equal to 4.

4. Researchers weighed a sample of river otters and a sample of sea otters. These dot plots show the results (rounded to the nearest pound).



a) Identify the shape of each dot plot. (2 points: 1 point for each dot plot)






b) Which dot plot has a larger center? What does this mean in terms of the otters? (2 points: 1 point for each question)








c) Identify any outliers. What do you think the outliers represent? (2 points: 1 point for identifying, 1 for explanation)








d) Which dot plot has a larger spread? (1 point)






e) How do the outliers affect the spread of the dot plot? (1 point)

Answers

Outliers can be useful in detecting whether a sample is representative of the population or not, but they should be treated with caution as they may skew the results.

a) The shape of each dot plot can be described as follows: The dot plot of river otters is symmetrical. The dot plot of sea otters is skewed to the right.

b) The dot plot of river otters has a larger center compared to sea otters. This means that the average weight of river otters is larger than that of sea otters. Therefore, in terms of otters, river otters are heavier on average compared to sea otters.

c) There are no outliers in the dot plot of river otters. However, there is one outlier in the dot plot of sea otters. The outlier represents the weight of a sea otter that is much larger or smaller than the rest of the sea otters in the sample. This may be due to various reasons such as measurement error, or simply because the otter is much larger or smaller than the rest of the sea otters.

d) The dot plot of sea otters has a larger spread compared to the dot plot of river otters. This means that the weights of sea otters vary more widely compared to the weights of river otters.

e) Outliers can affect the spread of the dot plot by increasing it or decreasing it. In this case, since there is only one outlier in the dot plot of sea otters, it does not have a significant effect on the spread of the dot plot. However, if there were more outliers, they would increase the spread of the dot plot.

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What is the solution? 3x + 5 = 3x - 5

Answers

3x+5=3x-5
3x+5-5=3x-5-5
3x-3x=3x-10-3x
0=10
No solution

Answer:

0

Step-by-step explanation:

Certainly! Let's solve the equation step by step:

1. Write down the equation:

3x + 5 = 3x - 5

2. Attempt to isolate x by subtracting 3x from both sides:

3x - 3x + 5 = 3x - 3x - 5

3. Simplify the equation:

5 = -5

At this point, we see that the equation 5 = -5 is not true. This means there is no solution for x in the given equation, as the two sides of the equation cannot be equal.

Before doing the actual calculation, let's round 11.5 feet to the nearest foot. Since 11.5 is exactly halfway between 11 and 12, it is technically equal distance from both. But, according to the Rounding Rules," if the number being looked at (in this case the 5) is 5 or above (so, if it's a 5, 6, 7, 8 or 9), give it a shove! If it it a shove! If it is 4 or below (4, 3, 2, 1 or 0), let it go (meaning that it stays the same)! How much carpet is needed?​

Answers

The  12 feet of carpet is needed.

To round 11.5 feet to the nearest foot, we look at the decimal part, which is 0.5. According to the Rounding Rules, if the number being looked at is 5 or above, we round up by giving it a shove! Since 0.5 is exactly 5, we round up to the next whole number, which is 12 feet.

So, after rounding 11.5 feet to the nearest foot, we get 12 feet.

To determine how much carpet is needed, we use the rounded measurement, which is 12 feet.

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What is the value of c?
a)4 units
b)5 units
c)6 units
d)7 units

Answers

The value of c in the triangle is (b) 5 units

Finding the value of c in the triangle

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

The right triangle

The length c is the hypotenuse of one of the triangles and can be calculated using the following Pythagoras theorem

c² = sum of squares of the legs

Using the above as a guide, we have the following:

c² = 3² + 4²

Evaluate

c² = 25

Take the square roots

c = 5

Hence, the hypotenuse of the right triangle is 5

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What is the average of the points A, B and C with weights 1, 1 and 2 respectively?

Answers

Step-by-step explanation:

Weighted Average = (A * 1 + B * 1 + C * 2) / (1 + 1 + 2)

Since the weights are 1, 1, and 2 respectively, we can simplify the equation further:

Weighted Average = (A + B + 2C) / 4

Therefore, the average of the points A, B, and C with weights 1, 1, and 2 respectively is (A + B + 2C) / 4.

Final answer:

The average of the points A, B, and C with respective weights of 1, 1, and 2 can be calculated using the weighted average formula: (1*a + 1*b + 2*c) / (1+1+2). The values of points A, B, and C are represented as a, b, and c.

Explanation:

The question asks for the average of points A, B, and C, which are weighted 1, 1, and 2 respectively. To calculate a weighted average, we multiply each value by its respective weight and then sum these products. We then divide this sum by the sum of the weights. So, let's assume the values of points A, B, and C be a, b, and c respectively. Using the formula for weighted average we get Average = (1*a + 1*b + 2*c) / (1+1+2)This formula will give us the average of the points A, B, and C with the specified weights.

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Please answer the builders one URGENT thank you

Answers

a) The total number of days to finish by the builders is: 112 days

b) The speed per 1 hour is: 19 km/hr

How to Solve Algebraic Expressions?

An algebraic expression is the idea of ​​representing numbers in letters or alphabets without specifying the actual values. In Algebra Basics, we learned how to use letters such as x, y, and z to represent unknown values. These characters are called variables here. Algebraic expressions can use a combination of variables and constants. Any value that comes before the variable and is multiplied is a factor.

a) The builders complete 3/8 of a project in 42 days.

If the total number of days to finish is x, then we can say by proportion that:

(3/8)x = 42

x = (42 * 8)/3

x = 112 days

b) The rate of speed is 38 km per 2 hours.

Thus speed per hour = 38/2 = 19 km/hr

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A bag of sweets contains only red sweets and yellow sweets. Thre are twice as many red as yellow. What fraction of the sweets are red?

Answers

Answer:

2/3

Step-by-step explanation:

Other Questions
Find the parametric equation for the line where the planes \[ 2 y+3 z=-1 \text { and }-7 x-6 y+10 z=22 \] intersect. \[ \overrightarrow{r(t)}=0 \] Which is Which?Compare two vocal works by listening to these songs entitled, "Gretchen am Spinnrade" by F. Schubert, and "Mutya ng Pasig" by Nicanor Abelardo. Write their characteristics Suppose the probability of success in a Bernoulli trail is 0.6. Let X be the number of trials until a success occurs. (a) What are the values that X takes? (b) What is the probability that the first success occurs on the 5th trial? (c) What is the probability that the 4th success occurs on the 8th trial? Which one of the following statement is NOT true given the following R code and result for analyzing Alibaba's stock? getSymbols('BABA',src='yahoo',from='2020-01-01',to='2021-04-01') BABA_Adj=BABASBABA.Adjusted adfTest(BABA Adj,lags=10, type=c("c")) STATISTIC: Dickey-Fuller: -1.3371 P VALUE: 0.5602 O A. BABA's stock price is mean reverting O B. 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Briefly explain how geologists distinguish between an intrusive igneous rock and an extrusive igneous rock. Describe in your explanation the physical characteristics used to determine the difference between intrusive and extrusive. 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Find , the projection of onto w. 2. Find the vector such that is perpendicular to and = +. Please show your work in your written work, you do not need to show work the below. Edit Format Table [0, 0,-1] be vectors in R. 12pt Paragraph BI UA 2 T~||| : V Write a shell script and it will return the area of anequilateral triangle. The script will ask for a number toread from input as the length of sides, then it willdisplay the output "The area of the equilateral trianglewith side length xx is: xxx" (remain 3 digits afterdecimal point). As we known the area of an equilateraltriangle should be V3a?/4, where a is the side length It is given that F(w) = eu(-w) + e "u(w). a) Find f(t). b) Find the 12 energy associated with f(t) via time-domain integration. c) Repeat (b) using frequency-domain integration. d) Find the value of w if f(t) has 90% of the energy in the frequency band 0 w 0. 1. What is being described here: "How a country views thecontribution of skills towards its economic and social life,finding expression in the policies and practices of the state, itsagents and i if a sole proprietor is found negligent of an action, then that person could face multiple choice a gain in business assets. stock options. danger of dispute settlement. unlimited liability. limited liability. A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 12 cm. (Note the answer is a positive number). mincm 3Hint: The volume of a sphere of radius r is V= 34r 3 A historian chooses a specific type of claim depending on his At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve, as requested. 3x 2ycosy=4, normal at (1,) A. y=2x+3 B. y= 21x 21+ c. y= 1x+ 1+ D. y= 1x 1+ Andrew will select 6 different integers from the set of positive integers from 1 to 49, inclusive. The order in which the 6 integers will be chosen does not matter. In how many different ways can the 6 integers be chosen? 49! 6! / 43! 49! / 43! 49! / 6! 6! + 43!