Here are the ingredients for a cake. 0.225 kg butter 225 g sugar 225 g flour 0.2 kg eggs 250 g berries How much do the ingredients weigh altogether?

We have number 422.44.

Then, we can evaluate each comparison. In the last comparison, we have that:

The value of the one-digit is 1/10 of the value of the tens digit.

Then, we have that:

In the ones, 2 represents 2.

In the tens 2 represents 20.

Therefore, the ones are:

Thus, the answer must be the last option:

The value of the one-digit is 1/10 of the value of the tens digit.

Since there are nine girls and seven boys, there are a total of 16 people entering the classroom.

The probability that a boy enters the classroom first is 7/16, because there are 7 boys out of the total 16 people entering.

The probability that a boy enters the classroom second after the first one was a boy is 6/15, because one person has already entered and it was a boy.

The probability that a boy enters the classroom third after the first two were boys is 5/14, because two people have already entered the classroom and they were boys.

The order in which the other people enter the classroom does not matter in this problem, so we will not consider it.

Since we've already deduced the probability of each even happening, the final probability will be

Thus, the probability that three boys are the first to enter the room is 0.06.

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Answer: 2sqrt(13)

Step-by-step explanation:

Using the distance formula, we get:

\(\sqrt{(9-5)^{2}+(3-(-3))^{2}}=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}\)

Answer: y=1.25

Step-by-step explanation:

First things first you have to find what is in the bracket things (i don’t know what it’s called) So 3 - 7 is -4y but since it’s absolute it’s going to be 4y.

So now you’ve got 4y - 10 = -5. Your going to want to eliminate 10 so, subtract 10 to both sides giving you 4y = -5

Lastly to get y by itself you need to divide it by its self so, 4y divided by 4. Do it to both sides. This gives you…

Y = 1.25

a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Given expression,

7 raised to the power 2 divided by 7 raised to the power 3

7 ^ 2 / 7 ^ 3

The value of a ^ m / a ^ n  = a ^ m-n

= 7 ^ (2-3)

= 7 ^ ( -1)

= 1 / 7 .

Therefore, The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

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Answer: x = 50

Step-by-step explanation:

In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.

To answer this question we will use the following two points formula for the equation of a line:

From the given graph we get that the line passes through (0,0) and (5,2), then its equation is:

Simplifying the above result we get:

Answer: Option D.

The volume of the sphere is approximately 8181.510 cm³.

The volume of a sphere is the amount of space that is enclosed within the surface of a sphere.

It is a measure of the three-dimensional space that is contained within the sphere.

The volume of a sphere is used in a variety of fields, such as physics, engineering, and architecture, to calculate the space enclosed by a sphere or a spherical object, such as a planet or a ball.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere. Substituting r = 12.5 cm and π = 3.14, we get:

V = (4/3) × 3.14 × (12.5 cm)³

V ≈ 8181.51 cm³

The volume of the sphere is approximately 8181.510 cm³.

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Answer:

She has 12 oranges left

Step-by-step explanation:

convert 3/5 to a decimal

3÷5=0.6

then multiply that by 20

0.6*20=12

Step-by-step explanation:

2/6=32/y

when you cross multiply, you will have

2y=6x32

2y=192

y=192/2

y= 96

Answer:

Below in bold.

Step-by-step explanation:

(a) Volume = volume of the cylinder + volume of hemisphere

= pi r^2 h + 1/2 * 4/3 pi r^3

= pi 2^2 3 + 2/3 pi 2^3

= 12pi + 16pi/3

= 52pi/3

= 52pi/3 in^3

= 54.45 in^3 to nearest hundredth.

(b) Surface area  = area of base + area of curved part + area of the hemisphere

= pi 2^2 + 3 * 2pi 2 + 2 pi 2^2

=  4pi + 8 pi + 12pi

= 24pi in^2

= 75.40 to nearest hundredth.

The population of the group in 2019 is 2,134,000 people

Let P represent the population in thousands of people in the year t after 2011

Given the equation:

\(P=1200(2)^{0.1038t}\)

a) The population of the group in 2019, that is t = 8(2019 - 2011):

\(P=1200(2)^{0.1038*8}=2134\)

b) The population of the group in 2029, that is t = 18(2029 - 2011):

\(P=1200(2)^{0.1038*18}=4382\)

The population of the group in 2019 is 2,134,000 people

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The Solution:

Given:

We are asked to find the two linear inequalities from the given inequality.

By the Modulus of inequality:

So,

Gives the following two linear inequalities:

Therefore, the correct answer is:

Given,

Two functions f(x) and g(x) are inverses if the composite functions are equal to the identity.

This means that:

f(g(x)) = g(f(x)) = x.

Now,

In this problem, we know that  f(x) and g(x) are inverse functions,

Using the above relation, we know that:

f(g(x)) = x

Hence the equation that satisfies the inverse relation between two functions is f(g(x)) = x

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Answer:

C: EAF Is the correct answer

Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Answer:

9 m²

Step-by-step explanation:

The perimeter of a square is 4x, where is the length of one side (because all the sides have the same length).

This means that 4x = 12, so x = 3, in other words the length of one side of the square is 3 m.

To work out the area of the square, multiply the length and the width together: 3 x 3 = 9 m²

Hope this helps!

\( \boxed{\sf Option \: A\text{:} \: \dfrac{1 + \sqrt{-32}}{4} = \dfrac{1}{4} + \sqrt{2}i} \)

\( \\ \\ \)

We are asked to express the given number in the form a + ib, also known as the algebraic form.

\( \\ \\ \)

\( \\ \\ \)

\( \sf z = a + ib \\\)

Where:

✰ a and b are real numbers and are the complex number's real part and imaginary part, respectively.

\( \\ \\ \)

✰ i is the imaginary unit number and can be expressed as follows:

\( \\ \sf i= \sqrt{-1}\)

\( \\ \\ \)

\( \\ \\ \)

\( \sf z = \dfrac{1 + \sqrt{-32}}{4} = \dfrac{1 + \sqrt{32 \times (-1)}}{4} \\ \\ \\ \sf \diamond \: We \: know \: that \: \sqrt{ab} = \sqrt{a} \times \sqrt{b}. \\ \\ \implies \dfrac{1 + \sqrt{32 \times (-1)}}{4} = \dfrac{1 + \sqrt{32}\times \sqrt{-1}}{4}\)

\( \\ \\ \sf \implies \dfrac{1 + \sqrt{32}\times \sqrt{-1}}{4} = \dfrac{1 + \sqrt{16 \times 2} \times \sqrt{-1}}{4} = \dfrac{1 + 4\sqrt{2} \times \sqrt{-1}}{4}\)

\( \\ \\\)

\( \diamond \: \sf Substitute \: \sqrt{-1} = i. \\ \\ \implies \sf \dfrac{1 + 4\sqrt{2}\times \sqrt{-1}}{4} = \dfrac{1 + 4\sqrt{2} \times i}{4} = \dfrac{1 + 4i\sqrt{2}}{4} \)

\( \\ \\ \: \sf \diamond \: Simplify \: knowing \: that \: \dfrac{a + b}{c} = \dfrac{a}{c}+\dfrac{b}{c}. \)

\( \\ \\ \\ \implies \: \sf \dfrac{1 + 4i\sqrt{2}}{4} = \dfrac{1}{4} + \dfrac{4i\sqrt{2}}{4} = \boxed{\sf \dfrac{1}{4} + \sqrt{2}i} \)

\( \\ \)

Therefore, the first option is correct.

\( \\ \\ \\ \)

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Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

The value of x is 21.4.

What is right-angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x. The measure of the angle opposite to height is 31°.

The sine of an angle is the ratio of height to the hypotenuse.

Therefore,

sin 31° = height/hypotenuse

sin 31° = 11/x

Multiply x with both sides:

x sin 31° = 11

Divide sin 31° with both sides:

x = 11/ sin 31°

x = 21.35

x ≈ 21.4 units

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The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

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The given sequence does not follow a simple arithmetic or geometric pattern, making it challenging to determine an explicit rule based on the given terms.

To identify the type of sequence and write the explicit rule, we need to examine the pattern of the given sequence: -39, -45, 51, 57, ...

By observing the differences between consecutive terms, we can determine if it follows an arithmetic or geometric pattern.

Arithmetic sequences have a common difference between each term, meaning that by adding (or subtracting) the same value repeatedly, we can generate the sequence. Geometric sequences, on the other hand, have a common ratio between each term, meaning that by multiplying (or dividing) by the same value repeatedly, we can generate the sequence.

Let's calculate the differences between consecutive terms:

-45 - (-39) = -6

51 - (-45) = 96

57 - 51 = 6

From the differences, we can see that the sequence is not arithmetic since the differences are not constant. However, the differences alternate between -6 and 6, indicating a possible geometric pattern.

Let's calculate the ratios between consecutive terms:

-45 / (-39) ≈ 1.1538

51 / (-45) ≈ -1.1333

57 / 51 ≈ 1.1176

The ratios are not constant, indicating that the sequence is neither geometric nor arithmetic.

Therefore, the given sequence does not follow a simple arithmetic or geometric pattern, and it is difficult to determine the explicit rule based on the given terms. It is possible that the sequence follows a more complex pattern or rule that is not apparent from the given terms.

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Answer:

The radius is 18 inches

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

36 pi = 2 * pi *r

Divide each side by pi

36 = 2r

Divide each side by 2

18 =r

Answer:

Step-by-step explanation:

Circumference of a circle = 2πr

where

r is the radius of the circle

From the question

Circumference = 36π inches

To find the radius substitute the value of the circumference into the above formula and solve for the radius

That's

Divide both sides by 2π

We have

We have the final answer as

Hope this helps you