Which value of x makes the equation 8x + 38 = 2(11x + 5) true?

Answer:

991 is the correct answer

Answer:

(B) 3

Step-by-step explanation:

24/(10-2)

24/8 is 3

Answer:

\( x = 2.5 \)

Step-by-step explanation:

Surface area of cylinder = 2πr(h + r)

Volume of cylinder = πr²h

Given that S.A = Volume of the cylinder, therefore, we have:

2πr(h + r) = πr²h

Radius (r) is given as 2.5 cm

height (h) = x cm

Input the values and solve for x

2πr(h + r) = πr²h

2πr(h + r) = πr(rh)

2(h + r) = rh (πr cancels πr)

\( 2(x + 2.5) = 2.5*x \)

\( 2x + 5 = 2.5x \)

Subtract 2x from both sides

\( 2x + 5 - 2x = 2.5x - 2x \)

\( 5 = 0.5x \)

Divide both sides by 0.5

\( \frac{5}{0.5} = \frac{0.5x}{0.5} \)

\( 2.5 = x \)

\( x = 2.5 \)

Answer:

41m, 30m, 15m

Step-by-step explanation:

A triangle can only be formed if the sum of any 2 side lengths adds up to be greater than the length of the other side.

The combination 41m, 30m, 15m is the only one where any 2 side lengths adds up to be greater than the other side.

We can test this:

41 + 30 > 15

30 + 15 > 41

The solution is Option C.

The sides of the triangles are 15 m , 30 m and 45 m

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Now , the measure of the sides of the triangle are

a)

AB = 8 m

BC = 10 m

AC = 20 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

20 < 10 + 8

20 < 18 which is FALSE

b)

AB = 2.5 m

BC = 2.5 m

AC = 8 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

8 < 2.5 + 2.5

8 < 5 which is FALSE

c)

AB = 15 m

BC = 30 m

AC = 41 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

41 < 30 + 15

41 < 45 which is TRUE

So , triangle ABC with sides 15 m , 30 m and 41 m is a triangle

d)

AB = 25 m

BC = 25m

AC = 75 m

Now , for a triangle AC < AB + BC

So , substituting the values in the equation , we get

75 < 25 + 25

75 < 50 which is FALSE

Hence , the triangle is with sides 15 m , 30 m and 41 m

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Answer: $22.50

Step-by-step explanation

In this case, x is what the original number was in case you didn’t know.

x - (x * 20/100) = 18

x -0.2x=18

0.8x=18

18/0.8=x

X = 22.5

Heather and her family purchased a home for 450,000, which is right in the middle of the range of homes in the area, which have a mean price of 450,000 and a standard deviation of 50,000.

The mean price of the homes in the area is the average price of all homes in the area and can be calculated by adding up all of the prices of the homes and then dividing by the total number of homes. In this example, the mean price is 450,000. The standard deviation is a measure of how much variation there is in a set of data. It is calculated by taking the square root of the sum of the squared differences of each data point from the mean, divided by the total number of data points. In this example, the standard deviation is 50,000. So, the mean price of the homes in the area is 450,000, plus or minus 50,000. This means that the majority of homes in the area cost between 400,000 and 500,000. Heather and her family purchased a home that cost 450,000, which is right in the middle of the range.

Heather and her family purchased a home for 450,000, which is right in the middle of the range of homes in the area, which have a mean price of 450,000 and a standard deviation of 50,000.

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Answer:

1/4 and 2/8

Step-by-step explanation:

Answer:

Flagpole height is 50 ft.

Explanation:

This is a ratio problem

Answer:

14 [m].

Step-by-step explanation:

1) in the square ABCD AC is diagonal, its length can be calculated as AB*√2;

2) the length of AB can be calculated:

AB=√Area(ABCD); ⇒ AB=√98;

Then

3) AC=√98*√2=14 [m].

Answer:

\(14\:m\)

Step-by-step explanation:

ABCD is a square. (Given)

\( \implies \: A(square) = \overline{AB} ^{2} \\ \\ \implies \: 98 = \overline{AB} ^{2} \\ \\ \implies \: \overline{AB} = \sqrt{98} \\ \\ \implies \: \overline{AB} = \sqrt{ {7}^{2} \times 2} \\ \\ \implies \: \overline{AB} = 7\sqrt{ 2}\\\\\implies \overline{AC}= \overline{AB} \times \sqrt 2 \\\\\implies \overline{AC}= 7\sqrt{ 2} \times \sqrt 2\\\\\implies \overline{AC}= 14\: m\)

Answer:

see explanation

Step-by-step explanation:

cos C = \(\frac{adjacent}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{24}{51}\) = \(\frac{8}{17}\)

-----------------------------------------------------

tan Z = \(\frac{opposite}{adjacent}\) = \(\frac{XY}{ZY}\) = \(\frac{15}{20}\) = \(\frac{3}{4}\)

---------------------------------------------------

sin C = \(\frac{opposite}{hypotenuse}\) = \(\frac{AB}{AC}\) = \(\frac{60}{65}\) = \(\frac{12}{13}\)

Answer:

y=36.25

Step-by-step explanation:

substitute x

y=7.25(5)

y=36.25

Answer:

y=36.25

Step-by-step explanation:

We are given

y= 7.25x

and

x=5

We know that x is equal to 5, therefore we can substitute 5 in for x.

y= 7.25x

y=7.25(5)

Multiply 7.25 and 5

y=36.25

Remainder theorem can be used to check if a given number is root or not. The factors of the polynomial function given are: (x-2), (x+4), (x-6).

When a polynomial f(x) is divided by (x-a), the remainder is f(a)

The given polynomial function is

\(f(x) = x^3 -4x^2 - 20x + 48\)

One root is x = 6, thus, (x-6) is one of the factor (since, by remainder theorem the remainder of f(x)/(x-6) is f(6) which is 0 since x = 6 is a root. And for those divisions, who leave no remainder, are division by factors.)

Getting other two factors:

\(f(x) = x^3 -4x^2 - 20x + 48\\\\f(x) = x^3 -6x^2 + 2x^2 - 12x - 8x + 48\\\\f(x) = x^2(x-6) + 2x(x-6) - 8(x-6)\\\\f(x) = (x-6)(x^2 + 2x -8) = (x-6)(x^2 + 4x - 2x -8) = (x-6)(x(x+4)-2(x+4))\\\\f(x) = (x-6)(x+4)(x-2) = (x-2)(x+4)(x-6)\)

Thus, the factors of the polynomial function given are: (x-2), (x+4), (x-6).

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Answer:

C: x-2  x+4  x-6

Step-by-step explanation:

As per the ratio, the number of men on the sight-seeing tour is 4.

In the given sight-seeing tour, we are told that there were 14 people in total. We are also given the ratio of women to children, which is 5 to 2. This means that for every 5 women on the tour, there were 2 children.

To find the number of men on the tour, we need to first find the number of women and children. We can do this by dividing the total number of people by the ratio of women to children.

Let's use a variable to represent the number of sets of 5 women and 2 children. We'll call this variable "x".

So, the number of women on the tour is 5x and the number of children is 2x.

Now, we can set up an equation to find the value of x:

5x + 2x = 14

This equation represents the total number of women and children on the tour, which is equal to 14.

Simplifying the equation, we get:

7x = 14

Dividing both sides by 7, we get:

x = 2

This means that there were 2 sets of 5 women and 2 children on the tour. So, the number of women is:

5x = 5(2) = 10

The number of children is:

2x = 2(2) = 4

Now, we can find the number of men by subtracting the number of women and children from the total number of people:

14 - 10 = 4

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Answer:

ummm maybe 25 :/ im not completely sure.

Step-by-step explanation:

Answer: answer is 10

Step-by-step explanation: Give brainliest pls

Answer:

I think its an obtuse triangle

Answer:

Finding x-intercepts and y-intercepts

To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y. ...

To find the x-intercept, set y = 0 \displaystyle y=0 y=0.

To find the y-intercept, set x = 0 \displaystyle x=0 x=0.

Step-by-step explanation:

Answer:

Length of the side of the square is 12 cm.

Step-by-step explanation:

Given information:

\(\text{side}_1 = 8a \text{ cm (side of a rectangle)}\\\text{side}_2 = 7a \text{ cm (side of a rectangle)}\\P_\text{rec} = 42 + P_\text{sq} \text{ cm } (P_\text{rec} \text{ is perimeter of the rectangle and } \\P_\text{sq} \text{ is the perimeter of the square)}\\\text{side}_\text{sq} = 4a \text{ cm (side of a square)}\)

Our mission is to find the length of the side of the square. We know that the side of the square is 4a cm, so to be able to answer we have to find the value of a first.

Step 1: Finding the value of a

Key to finding the value of a is the perimeter of the rectangle. Notice that we can calculate the perimeter of the rectangle in two different ways.

One way was given in the question:
\(P_\text{rec} = 42 + P_\text{sq}\)

We want equations in terms of a, so we can calculate a. Perimeter of the square can be calculated as:

\(\text{perimeter}_\text{square} = 4 \times \text{side}\)

Substituting the values in equation:

\(P_\text{sq} = 4 \times 4a\\P_\text{sq} = 16a\)

Therefore the first equation for perimeter of the rectangle becomes:

\(P_\text{rec} = 42 + P_\text{sq}\\\fbox{\begin{test}P_\text{rec} = 42 + 16a\end{test}}\)

For the second way we use formula for the perimeter of rectangle which is:
\(\text{perimeter}_\text{rectangle} = 2 \times \text{width} + 2 \times \text{length}\)

Substituting the values in equation:
\(P_\text{rec} = 2 \times 7a + 2 \times 8a\\P_\text{rec} = 14a + 16a\\\fbox{\begin{test}P_\text{rec} = 30a\end{test}}\)

Now let's equate both perimeters of the rectangle.

\(P_\text{rec} = P_\text{rec}\\42+16a = 30a\\42 =14a\\3 = a\)

Step 2: Find the length of the side of the square

It's given that side of the square is 4a cm. All we have to do is substituting a with its value, which we got in the previous step.

\(\text{side}_\text{sq} = 4a\\\text{side}_\text{sq} = 4(3)\\\text{side}_\text{sq} = 12 \text{ cm}\)

The marginal frequencies of chocolate and strawberry are 0.75 and 0.25 and chocolate is greater by 0.5

Marginal frequency is the ratio between either a column total or a row total and the total sample size.

For example, in a table of students classified by sex and area of study, the number of female students, regardless of area of study, would be one marginal frequency.

The marginal frequency of chocolate is calculated as;

The total frequency of chocolate = 30+45 = 75

The grand frequency = 75+25 = 100

marginal frequency of chocolate = 75/100

= 0.75

The marginal frequency of strawberry = 25/100

= 0.25

The difference in the marginal frequencies of chocolate and strawberry = 0.75 - 0.25 = 0.50

Therefore the marginal frequency of chocolate is greater than strawberry by 0.5

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The correct option is b) Label.

In a chart, each data point, bar, slice, and so on has a unique label. This label is used to identify and differentiate the different elements within the chart. It provides a clear and concise description of what each element represents.

For example, in a bar chart that shows the sales of different products, each bar would have a label indicating the specific product it represents. This allows the viewer to easily understand which product corresponds to each bar.

The label is crucial in making the chart understandable and meaningful. Without it, the chart would be confusing and difficult to interpret. It helps to provide context and clarity to the data being presented.

While color, size, and position can also be used to distinguish between elements in a chart, they do not provide the same level of specificity as a label. Color, for instance, may be used to represent different categories, but it does not provide specific information about each individual element.

In summary, the unique label assigned to each data point, bar, slice, or other element in a chart is what helps identify and differentiate them. It provides a clear description of what each element represents, making the chart more understandable and meaningful.

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a. Mixed cost - the cost per unit decreases with increase in units sold.

b. Variable cost - the expense increases with increase in units sold

c. Fixed cost - expense is constant with increase in units sold.

d. Fixed cost - cost is constant with increase in units sold.

e. Variable cost - cost increases with increase in units sold

f. Variable cost - cost increases with increase in units sold

g. Mixed cost- depreciation cost decreases with increase in units sold.

h. Fixed cost - cost is constant with increase in units sold.

i. Variable cost - cost increases with increase in units sold

j. Fixed cost- cost is constant with increase in units sold.

According to the given question;

Mixed costs: That has a high initial cost generally because they contain some fixed components and change in proportion because they contain some variable components.

Fixed costs: Costs that are consistent or constant are known as fixed costs.

Variable costs: These alter as the quantity of units changes.

(a) The price is fixed. This is because even while the price per unit fluctuates, the overall price does not. For instance, the total cost for 20 units is $720 ($36 x 20 units), and the total cost for 100 units is $720 ($7.2 x 100 units).

(b) The overall cost of the phone is mixed. On the basis of unit cost fluctuations, it may be claimed that the first 20 units have a fixed component and that subsequent 20 units have an equal distribution of fixed and variable costs.

(c) The price is vary. Supply costs are fixed regardless of quantity changes, and variable cost per unit is also fixed regardless of quantity changes that affect changes in the aggregate but not in the individual.

(d) The fact that the overall insurance cost remains constant as the quantity changes suggests that it is a fixed cost.

(e) Total salary expenses are mixed costs since they have a higher initial cost due to the inclusion of some fixed costs and ratio changes as a result of the addition of variable costs.

(f) Variable expenses, which rise in line with an increase in quantity, make up the entire cost of items sold.

(g) Depreciation is a fixed cost because, despite the fact that unit cost reduces as quantity increases, total cost remains constant.

(h) The total rent expense is constant despite changes in quantity, indicating that it is a fixed expense.

(i) The price of shopping bags is variable since the price and total fluctuate when the amount changes.

(j) Since individual unit expenses are constant per unit, the cost per unit of goods sold is variable.

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The write question is given below:

Answer:

all the answers are there in safari and also can refer to your text book

Step-by-step explanation:

One way to decompose the fraction of the day 27 over 6 is: 27/6 = 4 + 3/6.

This means that there are four whole parts of the day, plus an additional three-sixths of a part.

To understand this, we can think of the day as being divided into six equal parts, such as hours. Each part would be 1/6 of the day, so 27/6 would represent 4 and a half hours.

We can simplify this further by recognizing that 4 hours is equivalent to 4 times 1/6, or 4/6. So, we can subtract 4/6 from 27/6 to get the remaining fraction of a part, which is 3/6.

The fraction sentence 27/6 = 4 + 3/6 means that there are four whole parts of the day plus three-sixths of another part, which is equivalent to 4 and a half hours. Decomposing fractions like this can help us better understand the value and relationship between different parts of a whole.

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Answer:

See graph below.

When a function is even, it has symmetry about the y-axis, meaning that the graph of a function is symmetrical about the y-axis.

Suppose that the graph of a function f is known. Then the graph of y=f( – x) may be obtained by a reflection about the y-axis of the graph of the function y = f(x). In order to obtain the graph of y = f(-x) by a reflection about the y-axis of the graph of the function y = f(x), the positive x-values should be replaced with their corresponding negative values. Then we can obtain the graph of y = f(-x) by reflecting the part of the graph about the y-axis.

Since the x-axis does not change during the transformation, a reflection about the y-axis is also known as an "even function." When a function is even, it has symmetry about the y-axis, meaning that the graph of a function is symmetrical about the y-axis.

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a) When Lily's age is 20, and Raphael's age is divided by 3 then the expression of Lily's age in terms of h is h < 10.

b) Ethan's age is half of Raphael's age therefore, Ethan's age is half Raphael's age.

a) If Raphael is twice as old as his sister Lily, we can represent their ages as 2h and h, respectively, where h is Lily's age. The sum of their ages is less than 30, so we can write the equation:

2h + h < 30

Combining like terms, we get:

3h < 30

Dividing both sides by 3, we get:

h < 10

This is an expression of Lily's age in terms of h.

b) If Ethan's age is 16, and Raphael's age is twice Ethan's age, we can represent Raphael's age as 2 × 16 = 32.

Ethan's age is 16, which is half of Raphael's age of 32. Therefore, Ethan's age is half of Raphael's age.

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The question is -

Raphael is twice as old as his sister. The sum of their ages is less than 30.

a) Lily's age is 20, and Raphael's age is divided by 3. Write an expression in terms of h for Lily's age.

b) An expression for Ethan's age 16. Write a sentence to describe how Ethan's age compares with Raphael's age.

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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There are 2475 ways to place 10 identical red balls and 10 identical blue balls into 4 distinct urns, given the condition for the first urn.

We want to place 10 identical red balls and 10 identical blue balls into 4 distinct urns with the condition that the first urn has at least 1 red ball and at least 2 blue balls.

Step 1: Place the minimum number of balls in the first urn.
Let's place 1 red ball and 2 blue balls in the first urn. Now we have 9 red balls and 8 blue balls left to distribute.

Step 2: Use the stars and bars method to distribute the remaining balls.
For the remaining 9 red balls, we will use the stars and bars method. There are 3 urns left to place the balls, so we will have 2 "bars" to divide them. In total, we have 9 stars (red balls) and 2 bars, so there are C(11, 2) ways to distribute the red balls, where C(n, k) represents combinations.

If the first urn has no red balls, then we need to place all 10 red balls into the other 3 urns, and the blue balls can go into any of the 4 urns. There are 3^10 ways to place the red balls and 4^10 ways to place the blue balls, so there are 3^10 * 4^10 ways to violate the condition in this way.

If the first urn has exactly 1 red ball and fewer than 2 blue balls, then we need to place the other 9 red balls and the remaining blue balls into the other 3 urns. There are 3^9 ways to place the red balls, and (4 choose 2) * 3^8 ways to place the blue balls (since we need to choose 2 of the remaining 3 urns to put the blue balls in). So there are 3^9 * (4 choose 2) * 3^8 ways to violate the condition in this way.

For the 8 blue balls, we also use the stars and bars method. Again, there are 3 urns left, so we will have 2 "bars" to divide them. We have 8 stars (blue balls) and 2 bars, so there are C(10, 2) ways to distribute the blue balls.

Step 3: Calculate the total ways to distribute the balls.
Since the ways to distribute red balls and blue balls are independent, we multiply the number of ways to distribute the red balls by the number of ways to distribute the blue balls.
Using the principle of inclusion-exclusion, the total number of ways to place the balls into the urns that satisfy the condition is:

4^20 - 3^10 * 4^10 - 3^9 * (4 choose 2) * 3^8

= 2,922,821,387,520 - 3,486,784,401,920 - 312,491,796,480

= 123,544,189,120
Total ways = C(11, 2) * C(10, 2) = 55 * 45 = 2475

So, there are 2475 ways to place 10 identical red balls and 10 identical blue balls into 4 distinct urns, given the condition for the first urn.

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