A room has a length of 7 m.
A scale diagram is drawn of the room.
In the diagram, the room has a length of 1 cm.
What is the scale of the diagram?
Give your answer as a ratio in the form 1 : k, where k is an integer.

Answer:

Step-by-step explanation:

For each value of y, the number of value of x must be one. Then the correct options is D.

The complete question is attached below.

The relation function is given as, for every independent value, there is a dependent value.

Let the function be y = f(x).

For each value of x, the number of value of y may one or two.

But for each value of y, the number of value of x must be one.

Then the correct options is D.

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Answer:

Please mark as brainliest!!

Step-by-step explanation:

range = maximum value -minimum value

35-12=23

Considering the curve x³y + y³ = sin y - x, the final i is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

Implicit differentiation is a technique used to differentiate equations that are not explicitly expressed in terms of one variable. It is particularly useful when you have an equation that defines a relationship between two or more variables, and you want to find the derivatives of those variables with respect to each other.

To find dy/dx for the curve x³y + y³ = sin y - x², the implicit differentiation will be used which involves differentiating both sides of the equation with respect to x.

It is expressed as follows;

\(\frac{d}{dx} x^3y + \frac{d}{dx} y^3 = \frac{d}{dx} sin(y) - \frac{d}{dx} x^2\)

Then we'll differentiate each term:

For the first term, x^3y, we'll use the product rule

\(\frac{d}{dx} x^3y = 3x^2y + x^3 \frac{dy}{dx}\)

For the second term, y^3, we'll also use the chain rule

\(\frac{d}{dx} y^3 = 3y^2 \frac{dy}{dx}\)

For the third term, sin(y), we'll again use the chain rule

\(\frac{d}{dx} sin(y) = cos(y) \frac{dy}{dx}\)

For the fourth term, x², we'll use the power rule

\(\frac{d}{dx} x^2 = 2x\)

Substituting these expressions back into the original equation, we get:

3x²y + x³(dy/dx) + 3y²(dy/dx) = cos(y)(dy/dx) - 2x

Simplifying the equation:3x²y + x³(dy/dx) + 3y²(dy/dx) - cos(y)(dy/dx) = -2x

Dividing both sides by 3y² - cos(y), we get:(x³ - cos(y))(dy/dx) = -2x / (3y² - cos(y))

Hence, the final answer is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

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Answer:

XY = 30 units

∠XYZ = 90°

Step-by-step explanation:

The term congruent means to be in the exact same shape or size thus,

WX = XY and ∠ZWX = ∠XYZ

Answer: Cylinder B is 50% bigger than cylinder A

Cylinder A volume:

= πr²h

= π(10)²(5)

= 500π

Cylinder B volume:

= 750π

Cylinder B bigger than Cylinder A by:

= (750π - 500π)/500π × 100 = 50%

\(\hrulefill\)

Hence, cylinder B is bigger than cylinder A by 50%

Answer:

Cylinder B is 50% bigger than Cylinder A

Step-by-step explanation:

\(\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}\)

Cylinder A

Given:

Substituting the given values into the formula:

\(\implies \sf Volume_A=\pi (10)^2(5)=500\pi \:in^3\)

Cylinder B

Given:

\(\implies \sf Volume_B=750\pi \:in^3\)

Percentage Change

\(\begin{aligned}\sf percentage\:change & =\sf \dfrac{final\:value-initial\:value}{initial\:value} \times 100\\\\& = \sf \dfrac{Volume_B-Volume_A}{Volume_A} \times 100\\\\& = \sf \dfrac{750\pi-500\pi}{500\pi} \times 100\\\\& = \sf \dfrac{1}{2} \times 100\\\\& = \sf 50\%\end{aligned}\)

Therefore, Cylinder B is 50% bigger than Cylinder A

These disadvantages can impact the validity and reliability of the data collected using this type of data collection method. To mitigate these issues, researchers should design the survey carefully, ensure a representative sample, and provide clear instructions to respondents.

There are several disadvantages of using the mentioned type of data collection, which could affect the quality and reliability of the data gathered.

1. Respondents may exaggerate or distort facts: It is possible that some respondents may not provide accurate information, either due to the desire to present themselves in a better light or misremembering details. This can lead to biased or inaccurate data.

2. Respondents might consider the survey to be junk mail: If the survey is distributed via mail or email, some recipients may disregard it as unwanted communication. This can result in a lower response rate and a less representative sample of the population.

3. Respondents do not have enough time to consider their answers: If the survey has a tight deadline or contains complex questions, respondents may feel rushed and not have adequate time to reflect on their responses. This can lead to hasty or incomplete answers that do not accurately capture their opinions or experiences.

4. Respondents may not represent an accurate population sample: If the survey's sample is not representative of the target population, the results may be biased and not generalizable to the broader population. It is crucial to ensure that the sample selection process is unbiased and reaches a diverse range of participants.

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Answer: $2400.00 without 8% tax $2592.00 with 8% tax

Step-by-step explanation:

2x12x100

(X1.08 for tax)

Answer:

-1

Step-by-step explanation:

if the input is 4 you just go through the cycles

4 then subtract 7

4-7

-3

Then divide by 3

-3/3

-1

Hopes this helps please mark brainliest

Answer: it would take her 15 hours to read 400 pages

Step-by-step explanation: 400 devided by 80 is 5 and 5 x 3 = 15 hours

Answer: 15 hours to read 400 pages

Answer: Step 4: (x² + 2xy + y²) - (x² - 2xy + y²) = x² + 2xy + y² - x² + 2xy - y²

Step-by-step explanation:

The solution is : C. Combining like terms

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

here, we have,

we are given that

Darlene wrote this proof of the identity (x + y)2 - (x - y)2 = 4xy.

we have been asked to find

Which of the following is a justification for Step 3 of her proof?

Step 3 of her proof is

Step 3: (x² + xy + xy + y²) - (x² - xy - xy + y²) = (x² + 2xy + y²) - (x² - 2xy + y²)

As we can observe inside each of the paranthesis only like terms have been added. It mean the required justification is

C. Combining like terms

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To determine whether Tanisha's calculation of lifting over 2000 pounds while lifting 17 rocks averaging 8 pounds each is reasonable, we can compare the calculated weight to the actual weight.

Tanisha lifted 17 rocks, and each rock averaged 8 pounds. Therefore, the total weight she calculated would be:

Total weight = 17 rocks * 8 pounds/rock = 136 pounds

However, Tanisha stated that she lifted over 2000 pounds in all, which is significantly higher than the calculated weight of 136 pounds. This suggests that there may have been an error in either Tanisha's calculation or her statement.

Given this discrepancy, it is reasonable to agree with Tanisha's father and conclude that Tanisha's calculation of lifting over 2000 pounds seems unreasonable or incorrect based on the information provided.

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The amount that is closest to Nathan's total costs after the 15% discount and including 6% sales tax, assuming tax is applied after the discount is applied would be $624. That is option A.

The discount on sales is the amount of money that is being deducted from the original price of an item by a seller to their customers.

The original price for labor= $299.88

The original price for parts = $ 307.54

The original price for others = $ 74.71

The total original price = $682.13

The discount of on the total price = 15%.

That is;

= 15/100 × 682.13

= 10,232.95/100

= $102.32

When discount is removed from the original price;

= 682.13 - 102.32

= $579.81

When the tax is acted on the discount total sales;

= 6/100 × 579.81

= $3,478.86/100

= $34.79.

The total cost after discount and tax would be;

= 579.81 + 34.79

= $614.59

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Answer:

7

Step-by-step explanation:

total cost/total yards=cost per yard. $24.50/3.5=7

The area of the drawing as required to be determined in the task content is; 71.25 m².

It follows from the task content that the area of the drawing is to be determined according to the given parameters.

Since the actual rectangular shape has dimensions 95m by 75m. Upon drawing using a scale of 1m to 10m.

It follows that the dimensions of the drawing becomes; 95/10 by 75/10.

Hence, since the dimension of the drawing by evaluation is; 9.5 by 7.5;

The area of the rectangle (A = l × b) is; 9.5 × 7.5 = 71.25 m².

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To calculate the moment of inertia about the x-axis, the moment of inertia about the y-axis, and the polar moment of inertia passing through point O, we need to determine the geometric properties of the given figure, such as the shape and dimensions.

To calculate the moment of inertia about the x-axis, we need to determine the area of the figure and the distance of each element from the x-axis. The moment of inertia about the x-axis, denoted as Ix, is given by the sum of the individual moments of inertia of each element about the x-axis.

Similarly, to calculate the moment of inertia about the y-axis (Iy), we need to determine the area of the figure and the distance of each element from the y-axis. The moment of inertia about the y-axis is given by the sum of the individual moments of inertia of each element about the y-axis.

The polar moment of inertia passing through point O (J) represents the resistance of the entire figure to torsional or rotational deformation. It is the sum of the moments of inertia about the x-axis and y-axis, denoted as Ix and Iy, respectively.

The specific calculation method will depend on the shape and dimensions of the figure. For example, if the figure is a rectangle, the formulas for calculating the moments of inertia and the polar moment of inertia can be found in engineering mechanics or solid mechanics textbooks.

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The required number of breads based on given data in the question is 40

Probability is defined as the getting an random event out of total number of events.simply, it is the ratio of number of favorable outcomes to total number of outcomes.

We have given total number of breads are 50

It is said that jake has already recorded 16 blue and 4 green beads based on the result, take randomly pulls out a bead from the bag, records the color, and replaces it in the bag

Total recorded breads = 16 + 4 = 20

And, recorded blue breads = 16

probability = 16/20 = 0.8

Now number of blue breads = 50×0.8 = 40 breads.

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Answer:

Relative max : -4

Relative min: -4.5

Step-by-step explanation:

You have to look at the graph and identity the max as the highest point that is an actual point and identity the min as the lowest point that is an actual point.

Answer:

1. 20/3 or 6 2/3

2. 0.4

3. 11

4. 11

5. They are both similar

Hope this helps!

The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Based on your requirements, the appropriate test to determine whether DHA is a better treatment than control for treating eczema, considering that SCORAD is not normally distributed, is the Mann-Whitney U test (also known as the Wilcoxon rank-sum test).

The Mann-Whitney U test is a non-parametric statistical test that compares the distribution of two independent samples. In this case, the samples would be the DHA group and the control group.

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Answer: See explanation

Step-by-step explanation:

The value of the digit 3 in the number 63,297 is 3,000 while the value of the digit 3 in the number 60,325 is 300.

The difference between value of the digit 3 in the number 63,297 and the value of the digit 3 in the number 60,325 will be:

= 3000 - 300

= 2700

Given:

Total investments = $25000

She estimates the following:

Probability 0.2 of a $15,000 loss (-$15,000)

Probability 0.05 of a $20,000 loss (-$20000)

Probability 0.3 of a $35,000 profit (+35000)

Probability 0.45 of breaking even ($0)

Total probability = 0.2 + 0.05 + 0.3 + 0.45 = 1

Since the total probability is 1, to find the expected value of profit, we have:

Solving further:

Therefore, the expected value of the profit is $6,500

ANSWER:

a) $6,500

Answer:

Hope this helps

Step-by-step explanation:

a) x^2 + 3x = x(x+3)

b) 2x^2 - 8x = 2x(x - 4)

c) 6x + 9x^3 = 3x(2 + 3x^2)

d) 12x^3 - 4x^2 = 4x^2(3x - 1)

Answer:

The equation -x + 6y = -7 does not represent direct variation.

Step-by-step explanation:

Let us solve the question

∵ The equation is -x + 6y = -7

→ Substitute x by 0 to find the value of y-intercept

∵ x = 0

∴ 0 + 6y = -7

∴ 6y = -7

- Divide both sides by 6 to find y

∴ y = \(-\frac{7}{6}\)

∴ The y-intercept of the equation is (0, \(-\frac{7}{6}\) )

∵ The y-intercept of the direct variation is (0, 0)

∴ The equation -x + 6y = -7 does not represent direct variation.

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

To find the profit-maximizing conditions with third-degree price discrimination, we need to equate the marginal revenue (MR) to the marginal cost (MC) for each market segment.

Given the demand equations and the total cost function:

Market 1: Q1 = 160 - 10P1 or P1 = 16 - 0.1Q1

Market 2: Q2 = 200 - 20P2 or P2 = 10 - 0.05Q2

Total Cost: TC = 120 + 4Q

To find the profit-maximizing prices and quantities, we equate MR to MC for each market segment:

MR1 = MC:

16 - 0.2Q1 = 4

0.2Q1 = 12

Q1 = 60

MR2 = MC:

10 - 0.1Q2 = 4

0.1Q2 = 6

Q2 = 60

Substituting the quantities back into the demand equations, we find:

P1 = 16 - 0.1(60) = 10

P2 = 10 - 0.05(60) = 7

The total revenue (TR) can be calculated by multiplying the price by the quantity for each market segment:

TR = P1 * Q1 + P2 * Q2

TR = (10 * 60) + (7 * 60)

TR = 600 + 420

TR = 1020

The total cost (TC) is given by the total cost function:

TC = 120 + 4Q

TC = 120 + 4(60 + 60)

TC = 120 + 480

TC = 600

Finally, the profit (π) can be calculated by subtracting total cost from total revenue:

π = TR - TC

π = 1020 - 600

π = 420

In the absence of price discrimination, the profit-maximizing conditions would be different, and the resulting prices, quantities, total revenue, total cost, and profit would also be different.

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