Johan works in a cafe.
One morning he sells 48 cups of tea and 12 cups of coffee.
Write down the ratio of the number of cups of tea to the number of cups of coffee.
Write your answer in its simplest form.

Answer:

The correct answer is A or option 1

Answer:

Step-by-step explanation:

The frequency distribution table can now be converted to a cumulative frequency table as shown below:S/NValueFrequencyCumulative Frequency11 13 21 25 32 41 52 62 72 83 98 105 109 112 123 133 145 1516 167 173 186 197 201 213 224 235 246 2511 265 272 281 291 305 318 329 3310 341 356 366 377 388 394 401 416 421 432 447 45.

A frequency distribution table is a table that indicates the number of times a value or score occurs in a given data set. It is usually arranged in a tabular form with the scores arranged in ascending order of magnitude and the frequency beside them. The cumulative frequency table, on the other hand, shows the frequency of values up to a particular score in the data set.

It is obtained by adding the frequency of each value in the frequency distribution table cumulatively from the bottom up to the top.The frequency distribution table for the data set is shown below:S/NValueFrequency11 13 21 25 32 41 52 62 72 83 98 105 109 112 123 133 145 1516 167 173 186 197 201 213 224 235 246 2511 265 272 281 291 305 318 329 3310 341 356 366 377 388 394 401 416 421 432 447 45The class interval for this distribution can be obtained by subtracting the smallest value (1) from the largest value (10) and dividing by the number of classes.

In this case, we have 10 - 1 = 9 and 9 / 10 = 0.9. Therefore, the class interval is 1.0 - 1.9, 2.0 - 2.9, 3.0 - 3.9, and so on.

The frequency distribution table can now be converted to a cumulative frequency table as shown below:S/NValueFrequencyCumulative Frequency11 13 21 25 32 41 52 62 72 83 98 105 109 112 123 133 145 1516 167 173 186 197 201 213 224 235 246 2511 265 272 281 291 305 318 329 3310 341 356 366 377 388 394 401 416 421 432 447 45.The cumulative frequency column is obtained by adding the frequency of each value cumulatively from the bottom up to the top.

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Using Rank theorem , the dimensions of col A and Null A add up to the number of colmns in A. It is true statement.

The rank of matrix A denoted as rank(A) is the dimension of the column space Col(A).

The nullity of matrix A written as nullity(A) is the dimension of the null space Nul(A)

Rank Theorem:

If A is a matrix with n columns, then

Rank (A) + nullity (A) = n

In other words we can say that

dim (Col(A) ) in column space + dim (Nul(A)) in empty space = total number of columns in A

The rank theorem is really important theorem.

It is gives a strong relationship between the Null space ( all possible vector x such that Ax = 0) and the column space (the set of vectors b matching Ax=b) explain the two main objectives. The more freedom we have for choosing x, the less freedom we have for choosing b, and vice versa.

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Answer:

2x+2y+z

Step-by-step explanation:

The one that has the most circles in a group :D

There are a total of 212 pounds of berries, and the number of friends sharing the berries is equal to 4.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

The total amount of berries = 212 pounds

The number of berries received by each one = 54 pounds

Then, the number of friends sharing the berries is:

212/54 = 3.92 ≈ 4 friends.

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To calculate the amount Aubrey will have in her savings account after 3 years, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:

A is the balance (final amount)

P is the principal (starting amount)

r is the interest rate expressed as a decimal

n is the number of times per year that the interest is compounded

t is the time in years

In this case, Aubrey deposited $800.00 into her savings account, the interest rate is 9% (or 0.09 as a decimal), and the interest is compounded annually (n = 1). She wants to know how much she will have after 3 years.

Substituting the given values into the formula:

A = $800(1 + 0.09/1)^(1*3)

Simplifying the expression inside the parentheses:

A = $800(1 + 0.09)^3

Calculating the value inside the parentheses:

A = $800(1.09)^3

Calculating the value raised to the power of 3:

A ≈ $800(1.295029)

Calculating the final amount:

A ≈ $1036.02

Therefore, Aubrey will be able to spend approximately $1036.02 on the new bicycle from her savings account after 3 years, rounded to the nearest cent

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The foil method is an effective method because you are able to successfully remember the other at which you multiply the brackets to open them using F.O.I.L, so its not only easy to remember but very good to use for quadratic, cubic and to an extent, polynomials.

The FOIL Method stands for First Outer Inner Last. This is a standard method for multiplying two binomials together. It is also a valid method for solving quadratic equations and simplifying expressions.

The FOIL method is a valid method because it helps to simplify complicated expressions, and it is easy to use. It is used to multiply two binomials together.

By following the steps, the user can easily find the product of two binomials. The steps are as follows:

The FOIL method is valid because it helps to simplify expressions by breaking them down into smaller parts. This makes it easier to see how the parts relate to each other and how they combine to create the final expression. It is a straightforward method, and it is easy to use.

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Applying the triangle proportionality theorem, the length of AD that will make DE║AB is: AD = 60.

According to the triangle proportionality theorem, the equation or proportion we can create to find x is expressed as:

(2x - 4) / 5x = 3x / 8x

Cross multiply:

8x(2x - 4) = (3x)(5x)

16x² - 32x = 15x²

x² - 32x = 0

Solve to find x by factoring:

The equation x² - 32x = 0 can be solved by factoring:

x(x - 32) = 0

So either x = 0 or x - 32 = 0, meaning x = 32.

The solutions to the equation are x = 0 and x = 32.

Using x = 32:

AD = 2x - 4 = 2(32) - 4

AD = 60

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Answer:

27/.6=45 total in collection

45-27=18

18/3 per week=6 weeks

Step-by-step explanation:

The number of weeks until your collection is complete should be 6 weeks.

Since You purchase 3 action figures per week. You have 27 action figures, which is 60% of the total number of action

So here total collection should be

\(27\div 0.60\) = 45

Now the number of weeks should be

\(= (45 - 27) \div 3\)

= 6

hence, The number of weeks until your collection is complete should be 6 weeks.

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\( \bf \implies{\angle{JND} = 57 \degree}\)

\( \bf \longrightarrow{\angle{BNL} = 33 \degree}\)

\( \bf \longrightarrow{\angle{JND} = \: ?}\)

\( \bf \longrightarrow \: \: \: \angle{BNL} = \angle{DNS} \: \\ \: \: \: \bf [Verically \: Opposite \: Angle]\)

\( \bf \therefore\angle{DNS } = 33 \degree\)

\( \bf \longrightarrow \angle{JND} + \angle{ DNS} = 90 \degree \\ \bf \: \: \: \: \: \: \: \: \: [form \: a \: right \: angle]\)

\( \bf \longrightarrow \angle{JND} +33 \degree= 90 \degree\)

\( \bf \longrightarrow \angle{JND}= 90 \degree - 33 \degree\)

\( \bf \longrightarrow \angle{JND}= 57 \degree \)

The given exponential function equation is A = P(1+r)t, where P represents the principal amount, A represents the final amount, r represents the annual interest rate, and t represents the time in years.a.

The independent variable is t (time in years) while the dependent variable is A (final amount).b. The growth factor can be obtained by dividing A by P. Therefore, Growth factor = A/PLet us assume P=100, r=20%, and t=1. Then we can find A as follows:A = P(1+r)tA = 100(1+0.2)1A = 100(1.2)A = 120Therefore, the growth factor is:A/P = 120/100 = 1.2If we assume P=150, r=5%, and t=2, thenA = P(1+r)t = 150(1+0.05)2= 150(1.1025)= 165.375The growth factor is:A/P = 165.375/150 = 1.1025

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To find ,we can break down each vector into its horizontal and vertical components. The horizontal component represents the vector's magnitude in the x-axis , and the vertical component the magnitude in the y-axis direction.

To verify the sum of vectors using the components method, we can add the horizontal components together and the vertical components together. If the resultant sum of the horizontal components equals the horizontal component of the resultant vector, and the sum of the vertical components equals the vertical component of the resultant vector, then the components method is verified.

To find the vector components, we typically use trigonometry. Given a vector with magnitude (r) and an angle (θ) measured counterclockwise from the positive x-axis, we can find the horizontal component (x-component) and the vertical component (y-component) using the following equations:

x-component = r * cos(θ)

y-component = r * sin(θ)

To verify the sum of vectors using the components method, we add the horizontal components together and the vertical components together. Let's say we have two vectors A and B. The components of vector A are (A₁, A₂), and the components of vector B are (B₁, B₂). The components of the resultant vector R would be (A₁ + B₁, A₂ + B₂).

To verify the sum, we check if the sum of the horizontal components (A₁ + B₁) equals the horizontal component of the resultant vector R, and the sum of the vertical components (A₂ + B₂) equals the vertical component of the resultant vector R. If these conditions are satisfied, the sum of vectors using the components method is verified.

In summary, vector components can be found by breaking down vectors into their horizontal and vertical components. To verify the sum of vectors using the components method, we add the horizontal and  vertical components separately and check if they match the components of the resultant vector.

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The decimal form of the given number which is 5 3/4 is 5.75.

Given number = 5 3/4.

The given number is a fractional number, which is looking like a mixed fraction.

To write the mixed fraction into decimal form first, we have to write it into normal fraction, later we divide it to get the required decimal form.

To convert mixed fraction into normal fraction,

5 3/4 = ((4*5) + 3) / 4 = 23/4

So, the fraction is 23/4.

To convert the fraction into a decimal, we have to divide the numerator by the denominator as shown below,

23/4 = 5.75

From the above analysis, we can conclude that the decimal form of 5 3/4 is 5.75.

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To prove the properties of the projection matrix, we'll assume that p is the projection matrix corresponding to a subspace S of \(R^{m}\).

(a) p² = p

To show that p² = p, we need to demonstrate that applying the projection matrix p twice is equivalent to applying it once.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, if we apply the projection matrix p again to p(x), we have:

p(p(x)) = projection of p(x) onto S

Since p(x) is already the projection of x onto S, applying the projection matrix p once more won't change the result. Hence, we can write:

p(p(x)) = p(x)

This equation holds for any vector x in \(R^{m}\), meaning that p² = p.

(b) \(p^{T}\) = p

To prove that \(p^{T}\) = p, we need to show that the transpose of the projection matrix p is equal to p.

Let's consider an arbitrary vector x in \(R^{m}\). Applying the projection matrix p to x yields its projection onto the subspace S:

p(x) = projection of x onto S

Now, let's compute the transpose of p(x):

\((p(x))^{T}\) = \((projection of x onto S)^T\)

The transpose of a projection onto a subspace doesn't change the result because it only affects the column vectors of the projection matrix. The transpose of p(x) is still the projection of x onto S. Hence, we can write:

\((p(x))^T\) = p(x)

Since this equation holds for any vector x in \(R^{m}\), we can conclude that \(p^T\) = p.

Therefore, we have shown that (a) p² = p and (b) \(p^T\) = p, proving the properties of the projection matrix corresponding to a subspace S of \(R^{m}\).

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Answer:

x ≥ - 1

Step-by-step explanation:

10x + 5 ≥ 2x - 3 ( subtract 2x from both sides )

8x + 5 ≥ - 3 ( subtract 5 from both sides )

8x ≥ - 8 ( divide both sides by 8 )

x ≥ - 1

\(\boxed{Average\:speed=\frac{Total\:distance}{Total\:time\:taken}}\)

\(\bold{\underline{\underline{As\:we\:know\:all\:the\:units\:are\:in\:hr}}}\)

\(\rm{So,40\:minutes=\frac{40}{60}=\frac{2}{3}}\)

\(\sf{\underline{\underline{Now,putting\:values\:in\:the\:given\:formula:}}}\)

\(\rm{21km/h=\frac{Distance}{\frac{2}{3}}}\)

\(\rm→{21×\frac{2}{3}=Distance}\)

\(\rm{→14=Distance}\)

\( \large{ \underline{ \overline{ \mid{ \rm{ \red{Answer→Distance=14\:\:km}} \mid}}}}\)

Answer:

\(we \: have \: avarage \: speed= \frac{distance}{time \: } \\ here \: time \: is \: in \: \: minute \: convert \: \\ it \: in \: to \: hour \\ so \: \frac{40}{60} \: hour \\ = \frac{2}{3} hour \\ distance = avarage \: speed \times time \\ = 21 \times \frac{2}{3} = 7 ×2 = 14km\\ thank \: you\)

Answer: D.

Step-by-step explanation:

You can start out with the form AX = B and solve for matrix X that would yield the answer

Then X = (A^-1)(B)

A = [1    -1]

      [1     1]

A^-1 = (1/(1 - (1)(-1)))*[1    1]

                             [-1   1]

which can be written as (1/2) * [1    1]

                                                  [-1   1]

B = [26]

     [6]

(A^-1)(B) = (1/2)*[1    1] [6]

                        [-1   1] [26]

= (1/2)*[32]

          [20]

= [16]

  [10]

The restriction on x when x³ - 4x² + 5x - 6 is divided by x - 1 is x = 1.

When we divide x³ - 4x² + 5x - 6 by x - 1, we perform polynomial long division or synthetic division to find the quotient and remainder.

In this case, the remainder is zero, indicating that (x - 1) is a factor of the polynomial.

To find the restriction on x, we set the divisor, x - 1, equal to zero and solve for x.

Therefore, x - 1 = 0, which gives us x = 1.

Hence, the value of x that satisfies the restriction when x³ - 4x² + 5x - 6 is divided by x - 1 is x = 1.

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99.85% of adults in the city have a systolic blood pressure of less than 110 mmHg.

Using 68-95-99.7 rule, we know that

99.7% of values lie between the interval (mean - 3 × standard deviation, mean + 3 × standard deviation)

(100 - 99.7) = 0.3% values lie outside the interval (mean - 3 × standard deviation, mean + 3 × standard deviation).

Since the normal distribution is bell-curved and symmetrical,

we can say

0.3/2 = 0.15% values are less than the mean - 3 × standard deviation

and 0.3/2 = 0.15% values are greater than mean + 3 × standard deviation.

Here,

Mean + 3 × standard deviation.

= 110 + 3 × 10 = 140

So, 0.15% of values  are greater than 140

So, (100 - 0.15) = 99.85% values are less than 140.

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Answer:

36 years

Step-by-step explanation:

Let

x = Elga's age

Alvin's age = x + 7

Sum of their ages = 79

Sum of their ages = Alvin's age + Elga's age

79 = (x + 7) + x

79 = x + 7 + x

79 = 2x + 7

79 - 7 = 2x

72 = 2x

x = 72/2

x = 36

Elga's age = x = 36 years

Alvin's age = x + 7

= 36 + 7

= 43 years

Answer:

The total work done is approximately 2,114.308 J

Step-by-step explanation:

The mass of the trunk = 35 kg

The height to which the trunk is dragged, d₁ = 10 m

The inclination of the plane on which the trunk is dragged = 12°

The applied force F = 90 N

The angle of inclination of the force to the ramp = 20°

The distance the trunk is dragged horizontally at the top of the ramp, d₂ = 15 m

Work = Force × Distance

The work done along the inclined plane, W₁ = 90 N × cos(20°) × 10 m ≈ 845.723 J

The work done along the horizontal, W₂ = 90 N × cos(20°) × 15 m ≈ 1,268.585 J

The total work done, W = W₁ + W₂

∴ W = 845.723 J + 1,268.585 J = 2,114.308 J

Answer:

∑[ (250)2 (400)2 (250)2 (350)^2 (100)2 (50)2] = 420,000.

Step-by-step explanation:

You first calculate the mean which is  is 2150.

You then subtract 2150 from the 6 values in turn

The first one = 2400 - 2150 = 250.

Then you square each of the 6 results and add them up - this comes to 420,000.

Weak positive term describes the correlation  .

What does a weak positive indicate?

A weak positive graph is what?

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Answer: 121

Step-by-step explanation:

The formula for the square of sums is \((a+b)^2=a^2+2ab+b^2\).

Applying the formula, we see that the only option for b is 11 squared, or 121.

Answer:

3rd graph

Step-by-step explanation:

Answer:

The third one

Step-by-step explanation: