Gordon, Henry and Sarah share £48 in a ratio 2:3:1. How much money does each person get?

x + x +2x + 2x = 64 is the right equation

How to check perimeter of rectangle ?

The formula for perimeter of rectangle is P = 2*(l+w)

we have perimeter , 64 = 2* (2x + x)

                                64  = x + x + 2x +2x

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The expected number of brewed coffee drinks to be sold is 209.

To find the number of brewed coffee drinks expected to be sold, we need to determine the proportion of brewed coffee drinks in the total number of coffee-based drinks sold.

The given ratio is 4:10:8:5, representing caramel macchiato, café latte, brewed coffee, and café americano, respectively.

To calculate the proportion of brewed coffee drinks, we can consider the ratio as fractions:

Proportion of brewed coffee drinks = 8 / (4 + 10 + 8 + 5) = 8 / 27

Now, we can find the number of brewed coffee drinks by multiplying the proportion by the total number of coffee-based drinks sold:

Number of brewed coffee drinks = (Proportion of brewed coffee drinks) * (total number of drinks)

Number of brewed coffee drinks = (8 / 27) * 710

Rounding off the answer to the nearest whole number, we get:

Number of brewed coffee drinks = (8 / 27) * 710 ≈ 209

Therefore, it is expected that approximately 209 brewed coffee drinks will be sold.

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Number of M&M bags with Danielle = 24

Number of jelly beans with her = 36

Number of snickers with her = 48

To find the highest number of candies each friend of Danielle will get, in a way in which all of them have the same number of candies , we have to find the HCF (highest common factor) of all the varieties of candy with Danielle.

Factors of 24 = 1,2,3,4,6,8,12,24

Factors of 36 = 1,2,3,4,6,9,12,18,36

Factors of 48 = 1,2,3,4,6,8,12,16,24,48

Highest common factor = 12

Which means the highest number of friends Danille can invite is 12 .

Number of M&M bags each friend will get :-

\( = 24 \div 12\)

\(\color{hotpink} = 2 \)

Which means each friend will get 2 M&M bags .

Number of jelly beans each friend of hers will get :-

\( = 36 \div 12\)

\(\color{hotpink} = 3\)

Which means each friend of Danielle will get 3 jelly beans.

Number of snickers each friend of hers will get :-

\( = 48 \div 12\)

\( \color{hotpink}= 4\)

Which means each friend of hers will get 4 snickers .

Therefore , the highest number of friends Danielle can invite = 12 and each of her friends will get 2 M&M bags , 3 jelly beans and 4 snickers .

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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The value 30 is not present in the given data set.The given data set is: 67,38,21,89,23,36,82,11,53,77,29,17

In order to search for the values 29 and 30 in the data set using binary search algorithm, the given data set should be sorted in ascending order.

Arranging the given data set in ascending order, we get11, 17, 21, 23, 29, 36, 38, 53, 67, 77, 82, 89

a) Search for value 29 Binary search algorithm for the value 29:

Step 1: Set L to 0 and R to n - 1, where L is the left index, R is the right index, and n is the number of elements in the data set.

Step 2: If L > R, then 29 is not present in the data set. Go to Step 7.

Step 3: Set mid to the value of ⌊(L + R) / 2⌋.Step 4: If x is equal to the value at index mid, then return mid as the index of the element being searched for.

Step 5: If x is less than the value at index mid, then set R to mid - 1 and go to Step 2. This sets a new right index that is one less than the current mid index.

Step 6: If x is greater than the value at index mid, then set L to mid + 1 and go to Step 2. This sets a new left index that is one more than the current mid index.

Step 7: Stop. The algorithm has searched the entire data set and 29 was not found in the given data set. The recursion diagram for the binary search algorithm for the value 29 is:We can see that the binary search algorithm for the value 29 has terminated in the fifth iteration.

Thus, the value 29 is present in the given data set.b) Search for value 30Binary search algorithm for the value 30:

Step 1: Set L to 0 and R to n - 1, where L is the left index, R is the right index, and n is the number of elements in the data set.

Step 2: If L > R, then 30 is not present in the data set. Go to Step 7.

Step 3: Set mid to the value of ⌊(L + R) / 2⌋.

Step 4: If x is equal to the value at index mid, then return mid as the index of the element being searched for.

Step 5: If x is less than the value at index mid, then set R to mid - 1 and go to Step 2. This sets a new right index that is one less than the current mid index.

Step 6: If x is greater than the value at index mid, then set L to mid + 1 and go to Step 2. This sets a new left index that is one more than the current mid index.

Step 7: Stop. The algorithm has searched the entire data set and 30 was not found in the given data set. The recursion diagram for the binary search algorithm for the value 30 is:

We can see that the binary search algorithm for the value 30 has terminated in the fifth iteration.

Thus, the value 30 is not present in the given data set.

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The two most generic and widely used valuation multiples in finance and investment analysis are the price-to-earnings (P/E) ratio and the enterprise value-to-earnings before interest, taxes, depreciation, and amortization (EV/EBITDA) multiple.

1. Price-to-Earnings (P/E) Ratio: The P/E ratio is calculated by dividing the market price per share of a company's stock by its earnings per share (EPS). It provides a measure of how much investors are willing to pay for each dollar of earnings generated by the company.

A high P/E ratio suggests that investors have high expectations for future growth and are willing to pay a premium for the stock. On the other hand, a low P/E ratio may indicate that the stock is undervalued or that investors have low expectations for future growth.

2. Enterprise Value-to-EBITDA (EV/EBITDA) Multiple: The EV/EBITDA multiple is calculated by dividing the enterprise value (EV) of a company by its earnings before interest, taxes, depreciation, and amortization (EBITDA).

The EV is the total market value of a company's equity and debt, minus its cash and cash equivalents. EBITDA represents the company's operating earnings before accounting for interest, taxes, depreciation, and amortization.

The EV/EBITDA multiple is commonly used in evaluating the valuation of companies, especially in the context of mergers and acquisitions. It provides a measure of a company's overall value relative to its earnings, without being affected by capital structure or tax considerations.

Both the P/E ratio and EV/EBITDA multiple are widely used because they are relatively easy to calculate and understand. However, it's important to note that these multiples have limitations and should be used in conjunction with other valuation methods and qualitative analysis to make informed investment decisions.

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Answer:

Calculation:

Frequency table

Other statistical characteristics:

Average (mean): μ=93.9

Absolute deviation: 153.4

Mean deviation: 5.1133333333333

Minimum: 78

Maximum: 104

Variance: 40.956666666667

Standard deviation σ=6.3997395780349

Corrected sample standard deviation s=6.5091447608147

Coefficient of variation cV=0.069319965503884

Signal-to-noise ratio SNR=14.42585830404

Median: 95

Quartile Q1: 89.75

Quartile Q2: 95

Quartile Q3: 99

1st decile: 85.2

2nd decile: 88.2

3rd decile: 91.3

4th decile: 93

5th decile: 95

6th decile: 97

7th decile: 97.7

8th decile: 99

9th decile: 101.9

Interquartile range IQR: 9.25

Quartile Deviation QD: 4.625

Coefficient of Quartile Deviation CQD: 0.049006622516556

Lower fence: 75.875

Upper fence: 112.875

Set of outliers: {} - empty set - no outliers found

Interdecile range IDR: 16.7

Mode: 97 - unimodal

Geometric mean: 93.673540144338

Harmonic mean: 93.43824696186

Sum: 2817

Sum of squares: 1228.7

Sum of absolute values: 2817

Average absolute deviation: 5.1133333333333

Range: 26

Frequency table :

Z-score: {-0.1406, -1.3907, 0.4844, -2.3282, 1.5782, -0.9219, -0.2969, 0.0156, 0.4844, -1.0782, -2.4845, 0.1719, 1.1094, -0.1406, 0.4844, 0.7969, -1.0782, 1.4219, -0.6094, 0.1719, 1.2657, 0.4844, 0.7969, -0.4531, 0.1719, -0.2969, 1.1094, -0.7657, 0.7969, 0.6407}

Count items: 30

Answer:

27. 18.62

28. 200%

29. 136

30. 50

31. 12.5%

32. 750

33. 5.4

Step-by-step explanation:

The slant height of the triangular pyramid is 8.7 feet.

Given a triangular pyramid.

The surface area of the triangular pyramid = 174 square feet

A triangular pyramid consists of 4 triangular faces.

Given that all the triangular faces are equilateral triangle with a length of side as 10 feet.

We have to find the slant height of the pyramid.

The formula to find the surface area of the triangular pyramid is,

Surface area = base area + 1/2 (perimeter × slant height)

Base area = 1/2 × 10 × √(10² - 5²) = 5√75 feet²

Perimeter = 3 × 10 = 30 feet

Substituting,

174 = 5√75 + 1/2 (30h)

174 = 5√75 + 15h

h = (174 - 5√75) / 15

h = 8.7 feet

Hence the slant height is 8.7 feet.

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Answer:

x < 1/6

Step-by-step explanation:

In the equation 10 – 2(3x – 1) > 6x + 10, start by using the distributive property. Once you've done that, you'd now get 10-6x+2 > 6x+10.

Now, add 10 and 2 togther to get -6x+12 > 6x+10.

Subtract 6x to both sides and subtract 12 to both sides and now you'll get

-12x > -2.

Now, divide each side by -12 to get x < 2/12 or 1/6. Notice how the sign is flipped since you divided by a -.

The  probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

Using the binomial probability formula, the probability of x successes in n independent trials with a probability of success p can be calculated as:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where "n choose x" represents the number of ways to choose x items from a set of n items, and is calculated as:

(n choose x) = n! / (x! * (n-x)!)

So, for the given parameters nequals=7, pequals=0.65, xequals=6, we have:

P(6) = (7 choose 6) * 0.65^6 * (1-0.65)^(7-6)
     = 7 * 0.65^6 * 0.35^1
     = 0.3052

Therefore, the probability of 6 successes in 7 independent trials with a probability of success 0.65 is 0.3052.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

\(Blue = \frac{8}{9}\)

Step-by-step explanation:

Given

\(Yellow = 1ft^2\)

\(Blue = 8z^{-1\)

Required

Evaluate Blue when z = 9

To do this, we simply substitute 9 for z in \(Blue = 8z^{-1\)

\(Blue = 8 * 9^{-1\)

Convert indices to fraction

\(Blue = 8 * \frac{1}{9}\)

\(Blue = \frac{8}{9}\)

Hence, the blue section has an area of \(\frac{8}{9}ft^2\)

The probability of drawing a second black bead, given that the first bead is black, is 1/3 or 0.33.

The probability of drawing two black beads from a bag without replacement is given as 335. The probability of drawing one black bead is also given as 310. To calculate the probability of drawing a second black bead, given that the first bead is black, we can use the formula P(B2|B1) = P(B1 and B2) / P(B1). The probability of drawing one black bead is P(B1) = 310. The probability of drawing the two black beads is P(B1 and B2) = 335. Therefore, P(B2|B1) = 335 / 310 = 1/3 = 0.33.

The probability of drawing two black beads from a bag without replacement is given as P(B1 and B2) = 335. This means that, out of all the possible combinations of beads in the bag, 335 of them contain two black beads. The probability of drawing one black bead is given as P(B1) = 310. This means that, out of all the possible combinations of beads in the bag, 310 of them contain one black bead. To calculate the probability of drawing a second black bead, given that the first bead is black, we can use the formula P(B2|B1) = P(B1 and B2) / P(B1). The probability of drawing one black bead is P(B1) = 310. The probability of drawing two black beads is P(B1 and B2) = 335. Therefore, P(B2|B1) = 335 / 310 = 1/3 = 0.33. This means that the probability of drawing a second black bead, given that the first bead is black, is 1/3 or 0.33.

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Answer: 126

Step-by-step explanation:

11+5=16

Step-by-step explanation:

square root of 121 is 11 and cube root of 125 is 5 i.e

11^2=121 and 5^3=125

It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

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Answer:

\(\frac{47}{2} \to 6\)

\(\frac{60}{12} \to 5\)

\(\frac{40}{10} \to 4\)

\(\frac{56}{8} \to 7\)

\(\frac{64}{8} \to 8\)

Step-by-step explanation:

Given

See attachment

Required

Complete the blanks

To do this, we simply carry out the division operation.

So, we have:

\(\frac{47}{2} \to 6\)

\(\frac{60}{12} \to 5\)

\(\frac{40}{10} \to 4\)

\(\frac{56}{8} \to 7\)

\(\frac{64}{8} \to 8\)

The rates of the given equivalent unit rates are properly matched as follows:

42/7 = 6

60/12 = 5

40/10 = 4

56/8 = 7

64/8 = 8

To find the unit rate, the numerator is divided by the denominator such that the denominator is reduced to 1.

Thus, let's find the unit rates that matches with the equivalent rates given (see attachment below).

Divide the numerators by the denominators such that the value of the denominators are reduced to 1.

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Answer:

3/20 is the answer.......

Answer: The slope is 1.5. The equation of the line is y=1.5x+3

Step-by-step explanation:

Slope is the "Rise" over the "Run" of a line. The rise is the change in y. The run is the cange in x. Take any two points. I picked (0,3) and (4,9) since they were clearly on whokle number lines. The rise is (9-3) or 6. The run is (4-0) or 4. Rise/Run = 6/4 or 1.5. The y intercept is at 3 (the value of y when x=0). The full line equation is thus y = 1.5x+3.

To find the number of ways to pick a set of six balls from the bin in which at least one ball has an odd number, we can use the principle of inclusion-exclusion.

First, we find the total number of ways to pick a set of six balls from the bin, which is 21 choose 6 (written as C(21,6)) = 54264.

Next, we find the number of ways to pick a set of six balls from the bin in which all the balls have even numbers. There are only 10 even-numbered balls in the bin, so the number of ways to pick a set of six even-numbered balls is 10 choose 6 (written as C(10,6)) = 210.

Therefore, the number of ways to pick a set of six balls from the bin in which at least one ball has an odd number is:

C(21,6) - C(10,6) = 54264 - 210 = 54054.

So there are 54054 ways to pick a set of six balls from the bin in which at least one ball has an odd number.e

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The correct option regarding how a business might encourage its employees to participate in a retirement investment plan is given as follows:

By offering a large variety of plan options.

Retirement investment plans are plans in a which a part of the employee's salary goes towards savings, which are retirement plans, as the monetary amount is saved, generating investment, and then when the employee retires this amount with interest is deposed from the bank account.

The most well know retirement plan is the 401k, and the company should offer various options to it's employees, as they may have different interests, such as how long it will take for them to retire, or the amount they want to save, depending on their costs of living.

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if  Lines p and q are also parallel to each other then value of x is 100, option C is correct.

Parallel lines are coplanar infinite straight lines that do not intersect at any point.

The known angle is supplementary with angle A (Look at the attachment), that means that the sum of the known angle and A is 180°, therefore the value of angle A is 80°

Angle A and B are corresponding angles, which means that they have the same value, that happens because p and q are parallels and both cut line n  in the same way. the value of the angles B is 80°

Angles B and C are corresponding too, so the value of the angle C is 80°.

Angles C and X are supplementary too for which the sum of X and C  is 180°, so the value of X is 100°

Hence, if  Lines p and q are also parallel to each other then value of x is 100, option C is correct.

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In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.

This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.

The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.

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Answer:

2(x-4)  = 3

Step-by-step explanation:

The probability that the randomly selected sample is vulnerable or critically endangered is equal to 0.76

The probability can be determined using the following formula;

probability = number of desired events or outcomes ÷ total number of events or outcomes

The total is known to be 45, the favorable or desired outcomes can be calculated as follows;

number of desired outcomes = number of vulnerable species + number of critically endangered species

number of desired outcomes = 12 + 22

number of desired outcomes = 34

Now we calculate the probability by using the above formula;

probability = 34 ÷ 45

probability = 0.76

Therefore, 0.76 is the probability that the randomly selected species is vulnerable or critically endangered.

Although a part of your question is missing, you might be referring to this question:

In a random sample of 45 endangered species, 12 are categorized as vulnerable, 11 are categorized as endangered, and 22 are categorized as critically endangered. what is the probability that a randomly selected species from this sample is vulnerable or critically endangered? group of answer choices

11/45

0.24

0.83

0.76

12/45

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To define a default field value in a form or a database, you can use the attribute "default". When you add the "default" attribute to a field, it will automatically assign the specified value to that field if no other value is provided by the user or system.

This can be particularly useful when designing forms or databases that require certain fields to have a value even when the user does not provide one.
For example, in a web form, you might have a "Country" field that requires users to select their country from a dropdown list. By setting a default value for this field, such as "United States," the system ensures that there is always a value associated with that field even if the user does not make a selection.
Similarly, in a database schema, you might have a "DateCreated" field that automatically assigns the current date and time as the default value. This ensures that the date and time are always recorded for each new entry, even if the user does not manually input a value.
In both cases, the "default" attribute allows you to streamline the data collection process and ensure that your forms and databases maintain consistent and complete data. Using default values can also improve the user experience by reducing the amount of input required, making it easier for users to complete forms and submit their data.

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