f(x) = x/4 - 3
g(x) = 6x - 7
h(x) = 2^x


work out the value of x when h(x) = f(13)

Answer:

x = 6

Step-by-step explanation:

\(\frac{-2}{3}x+9=\frac{4}{3} x-3\)

-2x = -12

x = 6

Answer:

x = 6

Step-by-step explanation:

The most likely marble to be chosen will be red.

Given  that,

Number of red marbles = 1/2

Number of blue marbles = 1/4

Number of green marbles = 1/6

Number of yellow marbles = 1/12

To compare the probabilities, we need to find a common denominator. The common denominator for 2, 4, 6, and 12 is 12.

Therefore,

Probability of choosing a red marble = 6/12

Probability of choosing a blue marble = 3/12

Probability of choosing a green marble = 2/12

Probability of choosing a yellow marble = 1/12

Since the highest probability is for red marble, it is most likely to be chosen.

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Answer:

When the solution is negative

Step-by-step explanation:

One example, let's say you are buying pens and each pen cost 3 dollars and you cannot spend more than 15 dollars, how many pens can you buy?

The inequality would be 3x < 15, so any negative solution is not reasonable because you cannot buy negative pens. The same goes for most real-world problems dealing with time, money, or distance.  

Answer:

B. 54 square meters

Step-by-step explanation:

by similarity;

\(\frac{|AB|}{|DE|}=\frac{|BC|}{|EF|} \\ \\\frac{12}{4}=\frac{|BC|}{3} \\\\|BC|=9\\\)

Area of ABC equal to 12.9/2=54

If you don't understand, you can ask me :)

Answer:

co- ordinates of points:-

F = ( 1 , -2 )

G = ( 3 , 1 )

H = ( 5 , -2)

J = (3 , -5)

Answer:

Your first equation y=1/2(1+0.3)^t is going to be growth

Your second equation y=0.3(0.95)^t is going to be decay

Your third equation y=((1+0.03)^1/2)^2t is going to be growth

your fourth equation y=200(0.73)^t is going to be decay

your last equation y=4(1/4)^t is going to be decay

Step-by-step explanation:

You can find this by graphing each of you equations on desmos

Answer:

Step-by-step explanation:

See attachment

Answer:

Step-by-step explanation:

10 nails x 3 choices = 3 ^ 10 = 30,000,000,000

A. The probability that exactly 5 adults meet the criteria for hypertension is approximately 0.0916 or 9.16%.

B. The probability that none of the adults meet the criteria for hypertension is approximately 0.0255 or 2.55%.

C.  The probability that less than or equal to 7 adults meet the criteria for hypertension is approximately 0.9999 or 99.99%.

To calculate the probabilities,

Use the binomial probability formula.

The binomial probability formula is,

P(X = k) = C (n ,k) × \(p^k\) × \((1 - p)^{(n - k)\)

Where,

P(X = k) is the probability of exactly k successes

n is the number of trials

k is the number of successes

p is the probability of success in a single trial

(1 - p) is the probability of failure in a single trial

C(n, k) represents the binomial coefficient,

which can be calculated as n! / (k! × (n - k)!)

A. To calculate the probability that exactly 5 adults meet the criteria for hypertension,

n = 15 (number of adults assessed)

k = 5 (number of adults meeting the criteria)

p = 0.30 (probability of meeting the criteria)

A. Probability that exactly 5 adults meet the criteria for hypertension,

n = 15

k = 5

p = 0.30

P(X = 5) = C( 15, 5) × 0.30⁵ × (1 - 0.30)¹⁵⁻⁵

Using the binomial coefficient formula C (n ,k) = n! / (k! × (n - k)!), we have,

(¹⁵C₅) = 15! / (5! × (15 - 5)!) = 3003

P(X = 5) = 3003 × 0.30⁵ × 0.70¹⁰

Calculating the probability,

P(X = 5) = 0.0916 (approximately)

B. Probability that none of the adults meet the criteria for hypertension,

n = 15

k = 0

p = 0.30

P(X = 0) = (¹⁵C₀) × 0.30⁰× (1 - 0.30)¹⁵⁻⁰

(¹⁵C₀) = 1 (since choosing 0 from any set results in 1)

P(X = 0) = 1 × 0.30⁰ × 0.70¹⁵

Calculating the probability,

P(X = 0) = 0.0255 (approximately)

C. Probability that less than or equal to 7 adults meet the criteria for hypertension,

n = 15

k = 0, 1, 2, 3, 4, 5, 6, 7

p = 0.30

P(X ≤7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

Calculate each individual probability using the binomial probability formula and sum them up.

P(X ≤7) = (¹⁵C₀) × 0.30⁰ × 0.70¹⁵ + ¹⁵C₁× 0.30¹× 0.70¹⁴+ (¹⁵C₂) × 0.30²× 0.70¹³ + (¹⁵C₃) × 0.30³ × 0.70¹² + (¹⁵C₄) ×0.30⁴ × 0.70¹¹ + (¹⁵C₅) × 0.30⁵× 0.70¹⁰ + (¹⁵C₆) × 0.30⁶× 0.70⁹ + (¹⁵C₇) × 0.30⁷ ×0.70⁸

Calculating the probability,

P(X ≤ 7) ≈ 0.9999

Therefore, the probabilities for different conditions are,

A. For exactly 5 adults is 0.0916 or 9.16%.

B. For none of the adults is 0.0255 or 2.55%.

C. less than or equal to 7 adults is 0.9999 or 99.99%.

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To convert an area from inches to centimeters, conversion factor should be 15.24 square centimeters.

To convert an area from inches to centimeters, we use the conversion factor of 2.54 cm per inch.

This means that for every inch, there are 2.54 centimeters. In order to find the area in centimeters, we first need to find the area in inches, and then multiply it by 2.54.

To find the area, we use the formula
=> area = length x width.

Let's say the length of a rectangle is 2 inches and the width is 3 inches. The area of this rectangle would be 6 square inches

=> (2 x 3 = 6).

To convert this area to square centimeters, we multiply the area in inches by 2.54.

So,

=> 6 square inches x 2.54 = 15.24 square centimeters.

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Answer:

5/2

Step-by-step explanation:

Answer:

The slope of this line is - 5/2.

Step-by-step explanation:

In order to get from one red dot to another, you must go up 5 and to the left 2, because we are going left instead of right, the slope is negative. It doesn't matter which number you assign the negative sign. The entire formula for the line is y=- 5/2x - 3

Answer:

16/100 or simplified is 4/25

Step-by-step explanation:

The forecasted registrations for years 2 through 12 using exponential

smoothing, with a smoothing constant (α) of 0 and a starting forecast of 4.00 for year 1 are:

Year | Forecasted registrations

------- | --------

2 | 4.00

3 | 4.00

4 | 4.00

5 | 4.00

6 | 4.00

7 | 4.00

8 | 4.00

9 | 4.00

10 | 4.00

11 | 4.00

12 | 4.00

Exponential smoothing is a forecasting method that uses past data to predict future values. The smoothing constant (α) determines how much weight is given to the most recent data. In this case, we are using a smoothing constant of 0, which means that all of the weight is given to the most recent data. This means that the forecasted registrations for all years will be the same as the starting forecast of 4.00.

Here is the formula for exponential smoothing:

```

Forecasted registrations = α * most recent data + (1 - α) * previous forecast

```

In this case, α = 0, so the formula becomes:

```

Forecasted registrations = most recent data

```

Since the most recent data is always 4.00, the forecasted registrations will always be 4.00.

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Answer:

Step-by-step explanation:

Given expression

7.50h + 0.20s + 40

A)

Coefficients are 7.50 and 0.20

Variables are h and s

Constant=40

B) if Corinne works for 25 hours and selling $300 in magazine

Weekly earnings = 7.50h + 0.20s + 40

=7.50(25) + 0.20(300) + 40

= 187.5 + 60 + 40

=$287.5

C)

If Corinne starts earning $9 per hour.

Original expression

7.50h + 0.20s + 40

New expression

9h + 0.20s + 40

The coefficient of h will change because of the increase in earnings per hour

Coefficients are 9 and 0.20

Answer:

1:8

Step-by-step explanation:

since the base and sides are equal, I'll use 2 as a value for them. since all square sides are equal, we can find the area of the square. 2(2)=4. this means that in the situation the area of the triangle is 16.

16=1/2(2)h

32=2h

16=h

the height of the triangle is 16, while the side of the square is 2. the ratio is 2:16, or 1:8

Answer:

35°

Step-by-step explanation:

ABC is a equilateral triangle and that means all of its

interior angles have the same measure and = 60°

since angle ACB is 60° the complementary of it would be 120° this is alsıo the measure of angle ACD

The measure of angle CAD is given as 25°

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

So the missing angle ADC is 35°

The trend model that allows for one change in the direction of a series is:  A. linear trend model.

Here, we have,

The linear trend model is a commonly used technique in time series analysis, particularly when the data is expected to exhibit a consistent rate of growth or change over time.

First, Collect and organize your data, Before you can apply the linear trend model, you need to have a clear understanding of the data you're working with.

Then Plot your data on a graph, Once you have your data organized, the next step is to plot it on a graph. This will help you visualize any trends or patterns that may be present in the data.

Next, Calculate the slope of the line, To determine the rate of change in your data, you'll need to calculate the slope of the line. This is done using a formula called the least squares regression line.

And then determine the intercept of the line, by using the intercept of the line represents the starting point for the data. In other words, it's the value of the data at the beginning of the time series.

Finally, use the linear trend model to make predictions, Once you've calculated the slope and intercept of the line, you can use the linear trend model to make predictions about future values of the data.

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Answer:

plant c is the answer to your question

Answer:

Given the mass of the object = 15g

Given the volume of the object = 3 mL

Density = ?

Step-by-step explanation:

We have two values of an object that is mass of the object and volume of the object. Now we are required to find the Density of the object. In order to find the density of the object, we have to divide the given mass with the given volume. Below is the calculation of the density.

Density = Mass / Volume

Density = 15g / 3 mL

Density = 5 g/ml

Answer:

Density = 5g/mL

Step-by-step explanation:

Given that the mass of the Object is

= 15g

Given that the volume accumulated is

= 3mL

We find,

Density =?

Theerefore, both the given mass of the object and its accumulated volume will be divided.

Mass ÷ Volume

15g ÷ 3mL

=5g/mL

Density = 5g/mL

Inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process.

Inverse distance weighting is a method used in geostatistics to estimate values at unsampled locations based on values at surrounding sample locations. It works by assigning weights to the sample points based on their proximity to the unsampled point. The closer a sample point is to the unsampled point, the higher its weight. The weights are then used to calculate a weighted average of the sample values, which is used as the estimate for the unsampled location.
The benefit of inverse distance weighting over a simple average is that it takes into account the spatial variability of the data. A simple average treats all sample points equally, regardless of their distance from the unsampled point. This can lead to inaccurate estimates if there is a high degree of spatial variability in the data. In contrast, inverse distance weighting gives more weight to sample points that are closer to the unsampled point, which is likely to provide a more accurate estimate.
Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process. For example, if there are two variables of interest (e.g., temperature and precipitation), inverse distance weighting can be used to estimate values for both variables simultaneously. This is not possible with a simple average.
Overall, inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Its ability to account for spatial variability and incorporate multiple variables makes it a powerful technique for analyzing spatial data.

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The two numbers are 3 and 12 when 15 is the result of sum two numbers. One to two are compared in a 4:1 ratio.

Given that,

15 is the result of adding two numbers. One to two are compared in a 4:1 ratio.

We have to find which two numbers are they.

We know that,

Let take x and y to denote the two numbers

We get

x + y = 15   ----->equation(1)

x = 4y        ----->equation(2)

Substitute the 4y in equation(1)

(4y) + y = 15

5y = 15

Divide both sides by 5

y = 3.

Substitute y=3 in equation(2)

x=4(3)

x = 12

Therefore, The two numbers are 3 and 12 when 15 is the result of adding two numbers. One to two are compared in a 4:1 ratio.

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Answer:

a

Step-by-step explanation:

Answer:

5/4

Step-by-step explanation:

Solve by plugging in the value to "a".

Solve:

3a + 3/6

3(1/4) + 3/6

Multiply the parenthesis.

3/4 + 3/6

Simplify 3/6

3/4 + 1/2

Find the common denominator, which is 4. Make the denominators the same.

3/4 + 2/4

Add the fractions.

5/4

Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

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Answer:

x=0

y= x + 8

Step-by-step explanation:

find the oblique asymptotes using long polynomial divison

The ladder can reach 78.40 feet.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

The formula for the Pythagoras theorem is written as c² = a² + b², where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, the Pythagoras equation can be used to any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.

Given:

Hypotenuse = 82 feet

Base = 24 feet

Using Pythagoras theorem

H²= P² + B²

82² = P²+ 24²

6724 = P²+ 576

P² = 6148

P= 78. 40 feet

Hence, the ladder can reach 78.40 feet.

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I'm so sorry if this is wrong but it might be 24.

Answer:

25 miles per gallon

Step-by-step explanation:

100 miles divided by 4 gallons

100/4 = 25 miles per gallon

Bar graphs can be used to display both discrete and continuous data, making them a versatile tool for visualizing a wide range of information.

The graphic presentation of data that displays its categories as rectangles of equal width with their height proportional to the frequency or percentage of the category is called a bar graph.

In a bar graph, the bars represent the categories being compared and are arranged along the horizontal axis, with the height of each bar representing the frequency or percentage of the category being displayed.

Bar graphs are a useful tool for presenting numerical data in a visually appealing way, making it easy for viewers to compare different categories and draw conclusions from the data.

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