He prepared a mixture of water from two buckets by taking same quantity and observed the thermometer reading of mixture as
A. 25° C
B. 37.5°C
C. 37.5°F
D. 50° C​

Answer:

129.25

Step-by-step explanation:

Area of the rectangle

Area = L * W

L = 10

W = 9

Area = 9 * 10 =                                                         90

Area of the1/2 circle

Area of a whole circle = pi * r^2

Area of a 1/2 circle = pi * r^2 /2

d = 10

r = d/2

r = 10/2

r = 5

Area of the 1/2 circle = 3.14 * 5^2 /2       =         39.25

Total                                                                    129.25

Answer:

y = -2x - 2

Step-by-step explanation:

From the graph attached,

If the line 'l' passes through two points A(0, -1) and B(4, 1).

Rule for the rotation of any point (x, y), 90° clockwise about the origin is,

(x, y) → (y, -x)

By this rule,

A(0, -1) → A'(-1, 0)

B(4, 1) → B'(1, -4)

Let the equation of the line A'B' is,

y - y' = m(x - x')

where m = slope of the line A'B'

And (x', y') is a point lying on the line.

Slope of the line passing through A' and B' will be,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

m = \(\frac{0+4}{-1-1}\)

m = -2

Therefore, equation of the line passing through (-1, 0) and slope = -2,

y - 0 = (-2)(x + 1)

y = -2x - 2

So the equation of the line after rotation of lie 'l' by 90° clockwise will be,

y = -2x - 2

Answer:

learning task 3.4

1) p-3

2) (8÷d)+6

3) 11-(9×4)

4) 4÷2

5) (10+6)÷4

Answer:

0

Step-by-step explanation:

Plug 2 in for x

\(2(2) -4\)

Simplify

\(4-4\)

\(=0\)

Answer:

Step-by-step explanation:

Answer:13

Step-by-step explanation:

The points which represents a the solution are: A, C, D and K

What are coordinates?

Coordinates can be defined as the ordered pairs in which it is used to locate any points in 2D.

The given inequalities:  y ≤ −2x + 10 & y > 1/(2x − 2)

The given points: A(-5,4), B(4,7), C(-2,7), D(-7,1), E(4,-2),

F(1,-6), G(-3,-10), H(-4,-4), I(9,3), J(7,-4) and K(2,3).

The attached figure represents the graph of the given inequalities.

The shaded area represents the solution of the inequalities.

So, the points lies in the shaded area represents the solution of the inequalities.

So, points A, C, D and K are a solution to the system of inequalities.

Note only if

If the given inequalities:  y ≤ −2x + 10 & y > (1/2x) - 2

It will be the same solution.

Hence, The  points A, C, D and K are a solution to the system of inequalities.

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Answer: x = 0.65

Step-by-step explanation: 3.6 - 0.65 = 2.95

Answer:

100

Step-by-step explanation:

60*2=120

10 seats taken up on 2 buses=20

120-20=100

Answer:

the last one (100) 60+60 equals120 10+ 10 equals 20 120-20 equals 100

The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

To learn more about  Convergent integral :

Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

The probability that a person who tests positive actually has the disease is 0.006%

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

The probability that a person who tests positive actually has the disease is represented as

Probability = Incidence rate * False positive rate

Substitute the known values in the above equation, so, we have the following representation

Probability = 0.3% * 2%

Evaluate the products

Probability = 0.006%

Hence, the probability is 0.006%

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The equation M = 8 + 8 represents the given information. Maria has 16 scarves.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's let "M" represent the number of scarves that Maria has.

According to the problem, "Maria has 8 more scarves than Lucy." We know that Lucy has 8 scarves. So, Maria has 8 more than that.

We can represent this information in an equation:

M = 8 + 8

We add 8 to Lucy's 8 scarves to get the total number of scarves that Maria has, which is 16.

So, Maria has 16 scarves.

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The required Maria has 16 scarves, and the expression models the situation is given as M = 8 + L.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's use the variable "M" to represent the number of scarves that Maria has. Since Maria has 8 more scarves than Lucy, and Lucy has 8 scarves, we can write an equation as,

M = 8 + L

where L is the number of scarves that Lucy has. Substituting L = 8 into this equation, we get:

M = 8 + 8

M = 16

Therefore, Maria has 16 scarves.

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Answer:

welp-_- in 1 yard theres 3 so..........in 5 yards there 15 feet + 1 is 16 your welcome

Step-by-step explanation:

but..................subscribe to my channel

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*take the space out*

The correct value of inequality is x lies between (−∞,−1]∪[3,+∞).

What is inequality?

In arithmetic, the relationship between 2 values that don't seem to be equal is outlined by inequalities. difference means that not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”

As it contains modulus function so,

A modulus function is a function which gives the absolute value of a number or variable.

Since ∣x∣=x and −x

Therefore, ∣x−1∣>=2 may be calculated as:

x−1>=2 and −(x−1)>=2

⇒x>=2+1 and −x+1>=2

⇒x>=3 and −x>=2−1

⇒x>=3 and −x>=1

⇒x>=3 and x<=−1

Therefore, x lies between (−∞,−1]∪[3,+∞).

Hence, option C is correct.

the complete question is:

Solve the inequality with absolute value

∣x−1∣≥2

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Answer:

x-intercepts: (1,0), (−2,0) and (2,0)

y-intercept: (0,4)

The graph is rising and crosses 3 times the x-axis and 1 time the y-axis as shown above.

Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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Answer:

32 ounces

Step-by-step explanation:

1 lb = 16 ounces

2 lbs = 2 * 16 = 32 ounces

Answer:

707,957

Step-by-step explanation:

x= 518*tan(42°) + 518*tan(25°) =518*(tan(42°)+tan(25°))≈518*1.367=707.957

Answer:

707,957

Step-by-step explanation:

The answer is in the image

Answer:

The range is from 1.62 to 1.98.

Step-by-step explanation:

We have to solve for the percentage of the particular value if the range of the answer should be +/- 10% of the particular value.

The value given is 1.8, we thus want to find 10% of that: 1.8 * 10/100 = 0.18

Then, add this value to the original value of 1.8: 1.8+0.18 = 1.98

Furthermore, subtract .18 from from the original value of 1.8: 1.8-0.18 = 1.62

The range will be between these two numbers, so the range is from 1.62 to 1.98.

Answer:

The total price before discount was £63.

The price of the watch before discount was £25.

Step-by-step explanation:

Let the total original price before discount be x.

The total of £53.55 included a 15% discount. That means he paid only 85% of the original total price before the discount.

85% of x = £53.55

0.85x = 53.55

x = 63

The total before discount was £63.

£63 - £38 = £25

The total price before discount was £63.

The price of the watch before discount was £25.

Answer:

\(V_c=452.16\ mm^3\)

Step-by-step explanation:

Given that,

The volume of a sphere is 904.32 mm³.

The volume of a cone that has the same height and circular base with the same diameter is:

\(V_c=\dfrac{1}{3}\pi r^2 \times 2r=\dfrac{2}{3}\pi r^3\)

The volume of a sphere with the same radius is:

\(V_s=\dfrac{4}{3}\pi r^3=2\times \dfrac{2}{3}\pi r^3\)

So, the volume of sphere is :

\(V_c=\dfrac{V_s}{2}\\\\V_c=\dfrac{904.32 }{2}\\\\V_c=452.16\ mm^3\)

So, the volume of the cone is \(452.16\ mm^3\).

Answer:

x = 21

Step-by-step explanation:

equation:

⇒ 44 + 6x + 10 = 180

add like terms:

⇒ 44 + 6x + 10 = 180

⇒ 54 + 6x = 180

subtract 54 on both sides

⇒ 54 - 54 + 6x = 180 - 54

⇒ 6x = 126

divide 6 on both sides

⇒ \(\frac{6x}{6} = \frac{126}{6}\)

⇒ x = 21

to check:

44 + (6x + 10) = 180

44 + (6 x 21 + 10) = 180

44 + 136 = 180

180 = 180

Answer:

sin(100°) = 0.985

sin(-100°) = -0.985

Step-by-step explanation:

In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).

Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:

\(\boxed{\sin(100^{\circ}) = 0.985}\)

Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:

\(\boxed{\sin(-100^{\circ}) = -0.985}\)

In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

The value of the sine of the angles is calculated by applying the following formula as follows;

The value of sin (100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.

sin (100) = 0.985

The value of sin (-100) is calculated as follows;

sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.

sin (-100) = -0.985

Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.

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Answer:

x>4

Step-by-step explanation:

Option (c) is correct that is 19. Value 2 will be inserted in left sub tree of binary heap. Thus the right sub tree will remain unchanged.

Given that,

In the picture we have a tree.

Given the following binary heap (minheap).

We have to find what will the value in the red square be if we add value 2 to this heap and let it brew up.

We know that,

There are many other kinds of heaps, however in this chapter we'll talk about binary heap. A data structure that resembles a full binary tree is called a binary heap. The ordering features of the heap data structure are covered below. An array is frequently used to represent a heap. In this chapter, H is used to represent a heap.

Therefore, Option (c) is correct that is 19. Value 2 will be inserted in left sub tree of binary heap. Thus the right sub tree will remain unchanged.

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The most accurate way to estimate the percentage of the given value = ¼×66. Which is option C

Percentage is defined as the representation of a given value all over 100 and is given with a symbol of %.

The given value.= 66

The 26% of 66 would be given as follows;

26/100 × 66/1

= 1716/100

= 17.16

Therefore, the most accurate way to represent 26 percentage of 66 would be = ¼ × 66 which would be = 16.5 and is approximately 17.

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Complete question:

Which is the most accurate way to estimate 26% of 66

¼×64

⅔×60

¼×66

⅔×60

Answer:

(x - 7)² + (y - 5)² = 116

Step-by-step explanation:

equation of a circle:

(x - h)² + (y - k)² = r²

where (h,k) is the centre and r is the radius

centre is the midpoint of the diameter:

(h,k) = (11+3)/2 , (-5+15)/2

(h,k) = (7,5)

diameter = sqrt[(15--5)² + (3-11)²]

diameter = sqrt(464) = 4sqrt(29)

radius = ½ diameter

radius = 2sqrt(29)

r² = 116

equation:

(x - 7)² + (y - 5)² = 116

Answer:

[x-7]^2 + [y-5]^2= 116

Step-by-step explanation:

General equation of a circle is

[x2 - xo]^2 + [y2- yo]^2 = r^2

Where xo and yo are coordinates of the circle at the origin.

But xo = [x2 + x1]/2

= 11 + 3 / 2 = 7

yo = [y2 + y1] / 2 = [-5 + 15] /2 = 5

x2= 11, x2= 3; y1= -5, y2= 15

[11-7]^2 + [15-5]^2 =

16+ 100=116 = r^2

From the expression below;

[x2-xo]^2 + [y2-yo] ^2 = r^2

[x1-xo]^2 + [y1-yo] ^2 = r^2

[x-7]^2 + [y-5]^2= 116

Solution:

Given the polynomial

To factor out the GCF, we have

Thus,

Description:

Chris made mistakes in his division.