the least common multiple of 9 and 42 through prime factorization?

a) The linear equation is x - y = 15 and

the quadratic equation is x^2 - 20y = 300.

b) The numbers are x = 0, y = -15 and x = 20, y = 5

c) The two numbers that Simon is thinking of is x = 20, y = 5.

In this question,

Let the first number be x and

The second number be y

Part a:

The first number minus the second number is 15, then the linear equation is

⇒ x - y = 15 ------ (1)

The square of the first number minus 20 times the second number is equal to 300, then the quadratic equation is

⇒ x^2 - 20y = 300 ------- (2)

Part b:

Solve the system of equations

From (1) ⇒ y = x - 15 ------- (3)

Then, equation 2 becomes

⇒ x^2 - 20(x-15) = 300

⇒ x^2 - 20x + 300 = 300

⇒ x^2 - 20x = 300 - 300

⇒ x^2 - 20x = 0

⇒ x(x-20) = 0

⇒ x = 0 or x = 20

When x = 0, y = -15 and

When x = 20, y = 5

Part c:

The two numbers that Simon is thinking of is

The value of x and y are positive.

So, x = 20 and y = 5.

Hence we can conclude that

a) The linear equation is x - y = 15 and

the quadratic equation is x^2 - 20y = 300.

b) The values are x = 0, y = -15 and x = 20, y = 5

c) The two numbers that Simon is thinking of is x = 20, y = 5.

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Answer:

$1,500

Step-by-step explanation:

Divide 126 by 8.4% (.084)

Your answer is 1500

Answer:

The two angles of ΔABC are equal to the two respective angles of ΔFED. Also, the sum of all interior angles of a triangle is 180º. Therefore, third angle of both triangles will also be equal in measure.

Answer: skewed to the right, possible outlier at 12, median at 5

Answer:

40   mark Brainliest please

Step-by-step explanation:

15/40

Let the missing number be x .

Then :-

\( \frac{3}{8} = \frac{15}{x} \)

\( 3 \times x = 8 \times 15\)

\(3x = 120\)

\(x = \frac{120}{3} \)

\(x = 40\)

The missing number is 40 .

Let us check it by doing cross multiplication :-

\(3 \times 40 = 15 \times 8\)

\(120 = 120\)

Hence proved the missing number is 40 .

\(therefore \: , \frac{3}{8} = \frac{15}{40} \)

That day the number of adults was 95 and the number of children was 38

Let's define the variables:

x = number of adults.

y = number of children.

We know that 133 people used the public swimming pool. then we can write:

x + y = 133

We also know that the receipts for admission totaled 270.75, then we can write other equation as:

2.25x + 1.5y = 270.75

Then the system of equations is:

x + y = 133

2.25x + 1.5y = 270.75

In the first equation we can isolate x to get:

y = 133 - x

Now replace that in the other equation to get:

2.25x + 1.5*(133 - x) = 270.75

0.75x + 199.5 = 270.75

0.75x = 270.75 - 199.5

x = 71.25/0.75 = 95

Then the value of y is:

y = 133 - 95 = 38

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To forecast using data that has seasonality, one commonly used method is seasonal decomposition of time series (STL). This method separates the time series data into three components: trend, seasonality, and residuals. By isolating the seasonal component, you can forecast future values by extrapolating the pattern observed in previous seasons.

Another approach is the use of seasonal autoregressive integrated moving average (SARIMA) models. SARIMA models are an extension of ARIMA models that incorporate seasonal patterns. These models capture both the trend and seasonality in the data and can be used to make forecasts.

To control volatility in various time series models, a common technique is to use a volatility model, such as the generalized autoregressive conditional heteroskedasticity (GARCH) model. This model estimates the volatility of the time series by incorporating past volatility and squared residuals. By modeling and forecasting the volatility, you can better understand and manage the potential fluctuations in the time series data.

A simple moving average method is a technique used to smooth out fluctuations and identify trends in time series data. It involves calculating the average of a fixed number of data points, often referred to as the window size or period. As new data becomes available, the oldest data point in the window is dropped, and the newest data point is included in the calculation. This process is repeated for each subsequent data point. The resulting moving average values can provide insights into the overall trend of the data, helping to identify patterns or changes over time.

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Answer:

A

Step-by-step explanation:

the cost and weight are directly proportional, so decreasing one decreases the other at the same rate.

ratio is cost : weight, which is 15:10. the simplest ratio is 3:2, on the graph find where the cost is 3 and weight is 2. only graph A satisfy the condition

The possible outcomes of all the situations are found using the given tree diagram.

What is a tree diagram?

A probability space can be represented by a tree diagram in probability theory. A series of independent events or conditional probabilities may be represented using a tree diagram. The diagram's nodes each represent an event and its respective probabilities. It is used to provide a visual representation of both the outcomes and probabilities of an event. The nodes and branches of a probability tree diagram make up its two components. An event is represented by a node. A branch is a visual representation of the relationship between an event and its result.

The complete question is given below.

Given,

First spinner: 2 sections:  A and B

Second spinner : 3 sections: 1, 2 and 3

Third spinner: 2 sections: Green and Pink

The possible outcomes are given using the tree diagram.

a) Total number of outcomes =  12

b) Number of outcomes landing on A and involving an odd number

= Outcomes with A and numbers 1 or 3 in the tree diagram

= (A,1, green), (A,1, pink),(A,3, green), (A,3, pink) = 4

c) Outcomes that do not involve pink = All outcomes with only green in it from the tree diagram = 6

Therefore the possible outcomes of all the situations are found using the given tree diagram.

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The coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point on the directed line segment that partitions it into a ratio of 1 to 3, we can use the concept of section formula.

The section formula states that if we have two points A(x₁, y₁) and B(x₂, y₂) dividing a line segment in the ratio of m₁ : m₂, then the coordinates of the dividing point P are given by:

Px = (m₁ * x₂ + m₂ * x₁) / (m₁ + m₂)

Py = (m₁ * y₂ + m₂ * y₁) / (m₁ + m₂)

In this case, the ratio is 1:3, which means m₁ = 1 and m₂ = 3. The given points are A(6, 2) and B(8, -10). Substituting these values into the formula, we can calculate the coordinates of the dividing point P:

Px = (1 * 8 + 3 * 6) / (1 + 3) = 7

Py = (1 * -10 + 3 * 2) / (1 + 3) = -2/2 = -1

Therefore, the coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point that divides the line segment between (6, 2) and (8, -10) in a 1:3 ratio, we can use the section formula. Applying the formula, where m₁ is 1 and m₂ is 3, the point P(x, y) can be determined.

By substituting the values into the formula, the x-coordinate is calculated as (1 * 8 + 3 * 6) / (1 + 3) = 7, and the y-coordinate is (1 * -10 + 3 * 2) / (1 + 3) = -1. Thus, the coordinates of the point that partitions the line segment into a ratio of 1 to 3 are (7, -1).

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The amount of money in the savings account depends on how much time has passed since the account was opened. Then, the amount of money is the depenent variable, and the amount of time is the independent variable.

Then, money is a function of time.

Answer: The cost of each game increases the price by $4.

Step-by-step explanation: More

Answer:

Step-by-step explanation:

R = 1.52

H = 2.2

π = 3.14

\(V=\frac13\pi R^2\cdot H\\\\V=\frac13\cdot3.14\cdot(1.52)^2\cdot2.2=5.3200810\overline6\approx5.32\)

Answer:

It's elevation at the surface is 0, and the elevation twenty feet below is -20.

Step-by-step explanation:

The surface level is 0, and diving 20 feet under means 0 - 20, which is negative 20, or -20.

\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

We know that, the sum of measures of supplementary angles is 180°

So, the Correct choice is :

because, 65° + 115° = 180°

The type of sampling used in this scenario is B. Stratified sampling. Stratified sampling involves dividing the population into distinct subgroups or strata and then selecting samples from each subgroup.

In this case, Miranda divides her day into three parts: morning, afternoon, and evening. Each part of the day represents a stratum or subgroup.  Miranda measures her breathing rate at 4 randomly selected times during each part of the day. This means she is taking samples from each of the three strata (morning, afternoon, and evening) and collecting data from within those subgroups.

By using stratified sampling, Miranda ensures that her samples represent the different parts of her day in a proportional and systematic manner, allowing her to capture potential variations in her breathing rate throughout the day.

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Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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The volume of the 1 sphere is 37.68 cubic cm, for 2 the volume is 47646.87 cubic cm, for 3 the volume is 8751.46 cubic cm, and for 4 the volume is 3889.5 cubic cm and the mean is 15081.38.

It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.

We know the volume of the sphere is the given by:

\(\rm V = \dfrac{4}{3}\pi r^2\)

For sphere 1 the radius r = 3 cm and π = 3.14

\(\rm V = \dfrac{4}{3} \times3.14 (3)^2\)

V = 37.68 cubic cm

For sphere 2: r = 42 in = 106.68 cm

\(\rm V = \dfrac{4}{3} \times3.14 (106.68)^2\)

V = 47646.87 cubic cm

For sphere 3: r = 18 in = 45.72 cm

V = 8751.46 cubic cm

For sphere 4: r = 1 ft = 30.48 cm

V = 3889.5 cubic cm

For the mean:

\(=\rm \dfrac{37.68 +47646.87 +8751.46+3889.5 }{4}\)

= 15081.3775 ≈ 15081.38

Thus, the volume of the 1 sphere is 37.68 cubic cm, for 2 the volume is 47646.87 cubic cm, for 3 the volume is 8751.46 cubic cm, and for 4 the volume is 3889.5 cubic cm and the mean is 15081.38.

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The sequence that shows a pattern where each term is 1.5 times the previous term is option D

Series of numbers can be in a sequence either in arithmetic or in geometric. In the above question, it is geometric because the sequence shows a pattern where each term is 1.5 times the previous term.

Let us test each option one by one.

Option A

1.5 x -4 = -6

But the next number in the series is 6

Option B

1.5 x 10 = 15

1.5 x 15 = 22.5

But the next number in the series is 25

Option C

1.5 x 98 = 147

But the next number in the series is 99.5

Option D

1.5 x -200 = -300

1.5 x -300 = -450

1.5 x -450 = -675

Therefore, the sequence that shows a pattern where each term is 1.5 times the previous term is option D

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Answer: D (-200,-300,-450,-675,...)

Step-by-step explanation:

Recognizing the pattern in a sequence is used to write the function that represents it.

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

1=27

2=34

Step-by-step explanation:

1)9y power 2÷3

or, y=9 power 2÷3

or, y=9×9÷3

or, y=81÷3

or, y=27

2) (8x power 2+4x)÷2

=(8x×8+4x)÷2

=(64x+4x)÷2

=68x÷2

or, x=68÷2

or, x=34

Step-by-step explanation:

in the 6 th process I've used natural logarithm ln and ln(e)=1.

if the answer is required in decimal u can substitute the value in calculator.

hope it helps

Rotating an image 90 degrees counterclockwise means turning the image so that it appears to be facing to the left. This can be done using various software programs, including image editors like Adobe Photoshop or online tools like PicMonkey.

In Adobe Photoshop, you can rotate an image 90 degrees counterclockwise by selecting the "Transform" option from the "Edit" menu. This will bring up a bounding box around the image, and you can then use the "Rotate" tool to turn the image counterclockwise.

If you are using an online tool, the process is similar. Simply upload the image you want to rotate, select the "Rotate" tool, and then choose the "90 degrees counterclockwise" option.

In conclusion, rotating an image 90 degrees counterclockwise is a straightforward process that can be done using various software programs and online tools. Whether you are editing photos for personal use or for a school project, understanding image manipulation is an important skill to have.

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The amount of tax refund that Lily can expect bac, given her federal total tax due and the amount on the Wage and Tax statement, is b. $ 890.50.

To find the tax refund due, you need to first calculate your total tax liability and then subtract any tax payments or credits you have made throughout the year.

The tax refund to Lily is therefore :

= Federal income tax withheld - Federal total tax due

= 1, 080. 50 - 190

= $ 890. 50

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The three equivalent ratios are 6/1 gallons/minute, 1/40 quarts/second and 360/1 gallons/hour.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, Tiffany can fill the pool at a rate of 1/10 gallons per second.

Equivalent ratios are the ratios that are the same when we compare them.

We know that, 60 seconds =1 minute

1/10 × 60 = 6 gallons/minute

1 gallon = 4 quarts

1/10 = 1/10×4 = 1/40 quarts/second

1 hour =60 minute

So, 6 gallons/minute =6×60

= 360 gallons/hour

Here, 6 gallons/minute = 1/40 quarts/second = 360 gallons/hour

Therefore, the three equivalent ratios are 6/1 gallons/minute, 1/40 quarts/second and 360/1 gallons/hour.

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Answer:

The initial height of the candle is H = 15cm

The rate at which the candle burns is 2.5 cm per hour

Then after one hour, the height of the candle is:

h = 15cm - 2.5cm = 12.5cm

after two hours is:

h = 15cm - 2*2.5cm = 10cm

then, after t hours, the height of the candle is:

h = 15cm - (2.5cm/h)*t

now, the domain of h (or the range of the function) is:

h ∈ [0cm, 15cm]

when t = 0, h(0h) = 15cm

and the maximum value of t will be such that the candle is totally consumed:

h(t) = 0 = 15 - 2.5*t

t = 15/2.5 = 6

Then the domain of the function is:

t ∈ [0h, 6h]

There are 22 girls and 32 boys in the class.

Given that,  there are 54 people in a class

and the ratio of girls to total people is \(2:5\)

Number of girls in the class is,

                                \(=\frac{2}{5}*54=21.6\)

In class, there are 22 girls.

Number of boys is, \(54-22=32\)

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