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Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

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Explanation:

The key thing to focus on is the phrasing "starting at the age of 8"

Specifically, your teacher wants the starting height when Mia was 8 years old. That height being 52 inches.

The 7 inches refers to how much she had grown over the 2 years, which is part of the rate of change (and will be part of the slope).

Side note: 52 inches = 4 ft, 4 inches

Solution

- The solution steps are given below:

Final Answer

The answer is 4

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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We have found that: AB = (BD/2) * (XZ/AY) and we can solve for BD:

BD = 2 * AB * AY / XZ

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Since BD is a median of triangle ABC, it divides side AC into two equal parts. Let's label the midpoint of AC as M. Similarly, YW is a median of triangle XYZ and it divides side XZ into two equal parts, with the midpoint labeled as N.

Since AABC~AXYZ, we know that the corresponding sides are proportional. Thus,

AB/AX = AC/AY = BC/BZ

Since AB = BC (given that B is a vertex of both triangles), we have:

AB/AX = AC/AY

We can rewrite this equation as:

AB/AC = AX/AY ----(1)

Since BD is a median of triangle ABC, we have:

BD = 1/2 AC ----(2)

Similarly, since YW is a median of triangle XYZ, we have:

YW = 1/2 XZ ----(3)

From equation (1), we have:

AB/AC = AX/AY

Multiplying both sides by AC, we get:

AB = AX * (AC/AY)

Now, using equation (2), we can substitute AC/2 for BD:

AB = AX * BD/AY

Finally, using equation (3), we can substitute XZ/2 for YW:

AB = (BD/2) * (XZ/AY)

Therefore, we have found that:

AB = (BD/2) * (XZ/AY)

Hence, we can solve for BD:

BD = 2 * AB * AY / XZ

Note that we need to know the actual values of AB, AY, and XZ to find BD.

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Answer:

22° + m<C = 90°

Step-by-step explanation:

We are given that <A (which is equal to 22°) and <B are vertical angles, and that <B is complementary to <C.

We want to write an equation that will help us solve <C.

Recall that vertical angles are congruent by vertical angles theorem.

This means that <A ≅ <B; it also means that the measure of <B is also 22°.

Also recall that complementary angles add up to 90°.

This means that m<B + m<C = 90°.

Since we deduced that m<B is 22°, we can substitute that value into the equation.

Hence, an equation that can be used to solve for <C is:

22° + m<C = 90°

a) The function of h in terms of r is h=1400/(πr²).

b) The surface area of the can in terms of r is 2800/r+2πr².

c) The corresponding values of r and h that minimize the amount of required material are r≈14.04 cm and h≈2.98 cm.

a) The volume of a cylinder is given by

V = πr²h.

In this case, the volume of the can is

1400 cm³

So we have

1400 = πr²h.

Solving for h, we get

h = 1400/(πr²).

b) The surface area of a cylinder is given by

A = 2πrh+2πr².

Using the expression we obtained for h in part (a), we can substitute it in the equation and get

A = 2πr(1400/(πr²))+2πr²

= 2800/r+2πr².

c) To minimize the amount of required material, we need to find the value of r that minimizes the surface area.
To do this, we take the derivative of the surface area expression with respect to r and set it equal to zero:

dA/dr = -2800/r²+4πr = 0.

Solving for r, we get

r = √(700/π), which is approximately 14.04 cm.

Substituting this value in the expression for h that we obtained in part (a), we get

h = 1400/(π(14.04)²), which is approximately 2.98 cm.

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Answer:

The function is an odd function.

Step-by-step explanation:

A function f is odd if the following equation holds for all x and −x in the domain of f : −f(x)=f(−x) − f ( x ) = f ( − x ).

This equation holds for the function in the question.

Also, the function is a sin function so it is known to be odd.

Answer: 31.25%

Step-by-step explanation:

Draw a Ven diagram in a rectangle with 2 circles one for F and the other for C. The intersection overlap will have the 10 who play both outside the circles but within the rectangle the 7 who do neither so then fill the rest of F with 4 to give a total of 14 and 11 for the C to total 21. When you add all the numbers you’ll get a class total of 32. Then the % who play both F and C is = (10/32)*100 = 31.25%

Answer:

MAD would be more similar than mean

Step-by-step explanation:

Without doing any calculations, I assumed that the average value for each neighbor is different since their dot plots surround different areas. The MAD is the mean absolute deviation where it shows how distributed are the dot plots compared to the average value. In this case, I can tell that both neighborhoods having a very similar distribution of dot plots relative to their average/mean. Hope this helps!

Answer:

$54.67

Step-by-step explanation: sorry if im wrong i tried

Answer:

A would be correct

Step-by-step explanation:

the answer is A.

Answer:

4.475

Step-by-step explanation:

Answer:

(5,6) (6,7)

Step-by-step explanation:

The volume of the composite figure is 240 mm³.

What is a  composite figure?

When broken down, a composite shape (or composite figure), also referred to as a compound shape, is composed of numerous other shapes.

Any shape that is constructed from two or more geometric shapes is referred to as a composite or compound shape.

The composite figure consists of three rectangular prisms.

The length, width, and height of the top rectangular prism are 6 mm, 3 mm, 4 mm respectively.

The length, width, and height of the middle rectangular prism are (5 + 6) mm = 11 mm, 3 mm, and 4 mm respectively.

The length, width, and height of the bottom rectangular prism are 3 mm, 3 mm, and 4 mm respectively.

The volume of a rectangular prism is the product of length, width, and height.

The volume of the top rectangular prism is (6×3×4) mm³ = 72 mm³

The volume of the middle rectangular prism is (11×3×4) mm³ = 132 mm³.

The volume of the bottom rectangular prism is (3×3×4) mm³ = 36 mm³.

The total volume of  composite figure is (72 + 132 + 36) mm³

= 240 mm³

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Answer:

88% decrease

Step-by-step explanation:

3 is only 12% of 25 so there was a 88% decrease

The percentage of the distance Dominic is on the path is his distance

travelled as a fraction of the total distance when equivalent to 100.

The distance he has travelled on the path is 8.75 miles.

The given parameter are;

Length of Dominic's path = 12.5 miles

The length of the way Dominic is to the end = 70%

Required:

The distance Dominic has travelled on the path

The distance Dominic has travelled, D is 70% of 12.5 miles.

70% of 12.5 miles = 70% × 12.5 miles = 8.75 miles

The distance Dominic has travelled on the path, D = 8.75 miles

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Answer:

y=115+35x

Step-by-step explanation:

Answer:

Mean = 59.1, Median = 61

(there might have been a mistake in calculation (a lot of numbers!))

Step-by-step explanation:

The sample size is 40,

Now, the formula for the mean is,

Mean = (sum of the sample values)/(sample size)

so we get,

\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)

To find the median, we have to sort the list in ascending (or descending)order,

we get the list,

22,25,37,39,39,41,41,45,48,49,

49,51,52, 52,55,58, 58, 59, 59, 61,

61, 61, 61, 63, 63, 63, 65, 68, 71, 72,

72, 75, 75, 75, 75, 78, 78, 81, 82, 85

Now, we have to find the median,

since there are 40 values, we divide by 2 to get, 40/2 = 20

now, to find the median, we takethe average of the values above and below this value,

\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)

And the (n+1)th value is the 21st value

Now,

The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,

Median = (61+61)/2

Median = 61

The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

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The solution of the given system of equations is (-1, -2).

We are aware that a linear system of equations can be solved using a substitution method.

The intersection of the two lines represents the system's solution.

The given equations are-

y = 3x+1 ...eq 1

y = -2x-4  ...eq 2

Put the value of eq 1 in eq2 .

3x+1  = -2x-4

3x + 2x = -4 - 1

5x = -5

x = -5/5

x = -1

Put the x in eq 1.

y = 3(-1)+1

y = -2

Thus, the solution of the given system of equations is (-1, -2).

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The complete question is-

What is the solution to the system of equations-

y=3x+1 ;

y=-2x-4

Answer:

Step-by-step explanation:

If J is between H and K then HJ + JK = HK

Given

HJ=6x-5

JK=4x-6

KH=129

Required

The value of x

Substituting the given parametrs into the formula;

6x-5+4x-6 = 129

6x+4x-5-6 = 29

10x-11 = 129

add 11 to both sides

10x-11+11 = 129+11

10x = 140

divide both sides by 10

10x/10 = 140/10

x = 10

Hence the value of x is 10

Step-by-step explanation:

we first of all move 20 behind the comma for it to become -20 +3 and we get -17.

then use the product =-34

sum = 3

factors then continue

Answer:

\(x= \frac{-3 - \sqrt{145} }{4} \ \ or\ \ x= \frac{-3 + \sqrt{145} }{4}\)

Step-by-step explanation:

2x² + 3x + 3 = 20​

⇔ 2x² + 3x + 3 - 20 = 0

⇔ 2x² + 3x - 17 = 0

Using the Quadratic Formula to solve a Quadratic Equation :

\(x= \frac{-b \pm \sqrt{b^{2}-4ac} }{2a}\)

In the equation 2x² + 3x - 17 = 0

a = 2  ,  b = 3  and c = -17

Then

b² - 4ac = 3² - 4×2×(-17)

           = 9 + 8 × 17    

           = 9 + 136    

           = 145

Then

b² - 4ac > 0

Then

\(x= \frac{-3 \pm \sqrt{145} }{2 \times 2}\)

Then

\(x= \frac{-3 \pm \sqrt{145} }{4}\)

Answer:

The function is increasing during the interval 0 < x < 5.

Step-by-step explanation:

“The domain on which the function is increasing” is just a fancy way of saying, over what X values is the f(x), or y, of the function increasing! When looking at a graph, whenever the function line is going up, that is when the function is increasing. All you need to to is find the X values over this time. Then, just format them in the [lowest x] < x < [highest x] format.

With this function, we can see that the f(x), or y, is increasing between X = 0 and X = 5. We would write 0 < x < 5. This shows that x is more than 0, but is less than 5 over the interval where it is increasing.

Let me know if you have any questions!

Answer:

Since there are 2 possibilities for each bat (hit or out), the amount of total possibilities is 2 * 2 * 2 = 8. There is only one possibility out of those eight that gives us three hits, therefore the probability is 1 / 8 or 0.125.

Step-by-step explanation:

Heron's formula when all 3 sides (a, b, c) are given :

s = (a + b + c)/2

A = sqrt(s(s-a)(s-b)(s-c))

in our case

s = (34+73+89)/2 = 98

A = sqrt(98(98-34)(98-73)(98-89)) =

= sqrt(98×64×25×9) = sqrt(98)×8×5×3 =

= sqrt(2×49)×120 = sqrt(2)×7×120 =

= sqrt(2)×840 = 1,187.939392... ≈ 1,188 in²