find the constant of proportionality (r) in the equation y=rx

Answer:

Therefore, the measure of ∠x is 33 degrees.

Step-by-step explanation:

As angle ∠S is a right angle and angles ∠R and ∠x are complementary, we have:

∠R + ∠x = 90 degrees

Substituting the given values, we get:

57 + ∠x = 90

∠x = 90 - 57

∠x = 33 degrees

Answer: x = 32°

Step-by-step explanation: triangle of ABC = 58°, 90° & x°

                                              x = 180°-148° = 32°

(x° is equal to the unknown° where C is, as well as 58° where A is)

Answer     2x and 7y

Step-by-step explanation:

Question:

Find 4 possible solutions in the context of the problem.

The 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)

Given the equation that models the situation expressed as:

4x + 6y = 48

We are to find 4 possible solutions for x and y. Note that the values of x and y must be integers.

If there are no cars i.e. at when x = 0

4(0) + 6y = 48

0 + 6y = 48

6y = 48

y = 48/6

y = 8

One of the solution is (0, 8)

If there are 3 cars, i.e. at when x = 0

4(3) + 6y = 48

12 + 6y = 48

6y = 48 - 12

y = 36/6

y = 6

The second solution will be (3, 6)

If there are 6 cars, i.e. at when x = 6

4(6) + 6y = 48

24 + 6y = 48

6y = 48 - 24

y = 24/6

y = 4

The third solution will be (6, 3)

If there are 9 cars, i.e. at when x = 9

4(9) + 6y = 48

36 + 6y = 48

6y = 48 - 36

y = 12/6

y = 2

The fourth solution will be (9, 2)

Hence the 4 possible solutions in the context of the problem are (0, 8), (3, 6), (6, 3), and (9, 2)

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Answer:

The next step is: 14x - 6 = 9. The answer to this equation would be: x = 15/14.

Step-by-step explanation:

To solve this equation first you expand:

14x - 6 = 9

Then solve from there:

14x = 15

x = 15/14

Hey there!

Use the distributive property and distribute 2:

2(7x-3)=9

14x-6=9

Now, add 6 to both sides (remember the golden rule of algebra)

14x=15

divide both sides by 14

x=15/14 (improper fraction)

x=1+1/14 (mixed number)

Hope everything is clear.

Let me know if you have any questions!

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:-)

Answer:

32

Step-by-step explanation:

\(g(13) = 16 \\ f(16) = 32\)

6.78 is the probability of selecting a person at random having an IQ between 100 and 120 when iq scores are normally distributed with a mean of 100 and a standard deviation of 15.

The given data is as follows:

z = (x-μ)/σ

μ is the population mean = 100

σ is the population standard deviation = 15

For x = 100

z = 101 - 100/15

z = 0.053

Probability value from Z-Table:

P(x = 100) = 0.502

For x = 120

z = 120 - 100/15

z = 1.33

Probability value from Z-Table:

P(x= 120) = 0.0678

Therefore,  6.78 is the probability of selecting a person at random having an IQ between 100 and 120.

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The trigonometry equation to solve for x is tan(37) = x/12

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

The triangle

Where, we have

Opposite of 37 = x

Adjacent of 37 = 12

using the above as a guide, we have the following:

tan(37) = Opposite/Adjacent

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

tan(37) = x/12

Hence, the equation is tan(37) = x/12

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Answer:

164.67 cm

Step-by-step explanation:

The arithmetic mean of height of 5 pupils is 164cm . Let the sum of heights of 5 pupils be x . Then , according to the question ,

\(\sf\longrightarrow \dfrac{x}{5}= 164cm \)

On solving ,

\(\sf\longrightarrow x = 5*164cm =\bf{820cm}\)

When a student of height 168cm is added ,

\(\sf\longrightarrow Mean = \dfrac{820cm+168cm}{6}\\\)

\(\sf\longrightarrow Mean = \dfrac{988}{6}\\ \)

\(\sf\longrightarrow \boxed{\pink{\sf Mean = 164.66 \approx 164.67 cm }}\)

Answer:

a = 1 and b = 2

Step-by-step explanation:

Input the counterexample into the formula.

(a + b)² = a² + b²

(1 + 2)² = 1² + 2²

(3)² = 1 + 4

9 ≠ 5

This proves that the statement is false.

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

On Thursday, it would be -7°

I hope this helped♡

The integer showing temperature on Thursday is -7° C

An integer is a number with no decimal or fractional part, and it includes negative and positive numbers, including zero.

Given that, On Wednesday, the temperature was 27° above zero. On Thursday, it was 7° below zero.

Since, below zero, it starts negative numbers,

And, the temperature on Thursday was 7° below zero.

Therefore, the temperature on Thursday was -7° C

Hence, the integer showing temperature on Thursday is -7° C

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Answer:

The probability of drawing a purple marble is 3/10

The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

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Answer:

12

Step-by-step explanation: Ryan played 12 songs because 9+3=12

Answer:

Y'(-5, 5)

Step-by-step explanation:

To find the coordinates of Y' after the translation, we apply the given rule to the coordinates of point Y(-3, 4).

Using the translation rule (x, y) → (x - 2, y + 1), we can substitute the coordinates of Y(-3, 4) into the rule:

x' = x - 2 = -3 - 2 = -5

y' = y + 1 = 4 + 1 = 5

Therefore, the coordinates of Y' are (-5, 5).

Answer: A: (-2,5). B: (6,3). C: (-3,-7). D: (2,-5). E: (0,-3). F: (-7,0). G: (6,0). H: (0,6).

Step-by-step explanation:

Since the quadrants go as 1, 2, 3, and 4 in a counterclockwise motion starting from the top right, we already know all the point's quadrants. now it's a matter of looking at the points. Hope this helps!

To collapse worksheet rows to display only subtotals and the grand total, and then display individual records for the Appliances subcategory, follow these steps:

Step:1. Select the range of data in your worksheet that you want to collapse, including the headers, subcategory rows, and subtotal rows.
Step:2. Go to the Data tab in the Excel toolbar.
Step:3. Click on the Group button (located in the Outline section) and choose the Group option from the drop-down menu.
Step:4. Excel will create row level buttons with minus (-) symbols to the left of your data. Click on the row level button with the number "2" to collapse the rows and display only the subtotals and grand total.
Step:5. Locate the subtotal row for the Appliances subcategory. To the left of this row, you should see a show details button with a plus (+) symbol.
Step:6. Click on the show details button to display individual records for the Appliances subcategory.
By following these steps, you have successfully collapsed the worksheet rows to display only subtotals and the grand total, and then used the show details button to display individual records for the Appliances subcategory.

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4*10^6 = 4,000,000

1*10^4= 10,000

ANSWER: 400

Answer:

3/10

Step-by-step explanation:

When we measure a ECG waveform the large boxes represents 0.2 seconds.

To determine the measurements of the big box on ECG paper, we need to consider the standard calibration of ECG paper.

In most ECG papers, the standard calibration is as follows:

These measurements allow for accurate interpretation of the ECG waveform and analysis of heart activity.

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The sum of the two number is 23.

Let's call the two numbers x and y. We know that:

x^2 + y^2 = 327

xy = 101

We want to find x + y.

We can start by squaring the equation x + y:

(x + y)^2 = x^2 + 2xy + y^2

Substituting in the values we know:

(x + y)^2 = x^2 + y^2 + 2xy

(x + y)^2 = 327 + 2(101)

(x + y)^2 = 529

Taking the square root of both sides:

x + y = ±23

Since both x and y are non-negative, we know that x + y must be positive. Therefore:

x + y = 23

So the sum of the two numbers is 23.

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Congress decides to allocate funds for a new road system, resulting in reduced spending on education and defense for the next two years. This prioritization reflects a trade-off between infrastructure development and investments in other critical sectors.

When Congress decides to prioritize funding for a new road system, it means that resources will be redirected from other areas, such as education and defense. This decision reflects a trade-off where the government chooses to invest in infrastructure development at the expense of reducing expenditures in education and defense sectors.

The impact of reduced education spending can have implications for schools, students, and educational programs. It may result in fewer resources for schools, leading to potential cuts in staff, curriculum, and extracurricular activities. Reduced funding for education can hinder educational opportunities and initiatives aimed at improving student outcomes and educational equity. Likewise, the reduction in defense spending can have consequences for national security and military capabilities. It may limit the resources available for military readiness, training, equipment modernization, and research and development. This reduction in defense spending could potentially impact the military's ability to respond effectively to security threats and maintain a strong defense posture.

Overall, the decision to fund a new road system at the expense of education and defense spending reflects a prioritization of infrastructure development. While investing in infrastructure is important, it is essential to carefully consider the potential consequences and seek a balanced approach that addresses the needs of various sectors for the overall well-being and progress of the country

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No triangles: angle 30°,85°,60° and sides 2,8,10

One triangle: sides 7,24,25

many triangles: angle 5°,15°,160° and angle 45°, 45°, 90°

A triangle is a geometric shape that is formed by connecting three points in a plane with straight lines. It has three sides, three angles, and three vertices (or corners). The sum of the angles in a triangle is always 180 degrees. Triangles are classified based on the lengths of their sides and the measures of their angles.

Sum of angles should not be equal to 180°

Sum of two sides of triangle is not always greater than third side.

30°+85°+60°=175°<180°

Hence, this angle do not form triangle

2+8=10

Hence, this sides do not form triangles.

Sum of two sides of triangle is always greater than third side.

7+24>25

Hence, this sides do not form triangles.

Sum of angles should be equal to 180°

5°+15°+160°=180°

Hence, this angle  form triangle

45°+45°+90°=180°

Hence, this angle  form triangle.

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The complete question is:

Image is attached below.

Answer:

EFG is 111 and the other one is 69.

Step-by-step explanation:

Answer:

55 degrees

Step-by-step explanation:

sum of all angles of a triangle equal 180

to find x we add them all and set them equal to 180

(57+x)+(72+x)+55=180

129+2x+55=180

184+2x=180

-184.    -184

2x= -4

/2.  /2

x=-2

now to find angle A

57+(-2)

55

hopes this helps

Answer:

A the first one

Step-by-step explanation:

because y increase as x increases

The process of measuring, analyzing, enhancing, and then controlling processes once they have been brought within the narrow Six Sigma quality tolerances or standards is referred to as the

Six Sigma process

The phrase "Six Sigma" refers to a collection of quality-control methods that organisations can utilise to get rid of flaws and enhance operations so as to increase productivity and revenues. A scientist created it in the 1980s while he was employed by Motorola.

A statistical and data-driven technique called Six Sigma examines small errors or flaws. It places a focus on cycle-time gains while lowering manufacturing faults to no more than 3.4 incidents per million units or events. The fact that only 3.4 out of a million events along a bell curve will deviate by more than six standard deviations indicates that an error usually occurs with an event that deviates by six standard deviations from the mean.

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Answer:

Step-by-step explanation:

A triangle has two angles that are 33 degrees and 54 degrees. What is the third angle?

the sum of the interior angles in a triangle is 180°

remove the known angles from 180 and find the unknown angle

180 - 33 - 54 = 93°

Answer:

93°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°

Two of the angle measures are stated as 54° and 33° in this specific triangle.

Now, to find the missing angle, we need to add these measures up and subtract it from 180:

33° + 54° + x = 180°

87° + x = 180°

x = 93°

Answer:

36

Step-by-step explanation:

(1/3)x - (1/4)x = 3

multiply by 12 to clear the fraction

4x - 3x = 36

x = 36