Solve for x.
8.4x - 5 = 20.2

The equation of the line that passes through (1,3) and which is perpendicular to y = 2x ₊ 3 is x ₊ 2y = 7.

Given the equation of the which passes through the point is (1,3)

the line is perpendicular to y = 2x ₊ 3

first we need to determine the slope of the equation.

line is perpendicular to y = 2x ₊ 3

perpendicular means slope (m) = ₋1

but given the in the line equation we have

y = mx ₊ c

m = 2

therefore ₋1 = 2

hence slope m = ₋1/2

Then the line passing through (1,3), substitute the coordinates of the point in the equation of the line:

y ₋ y₁ = m(x ₋ x₁)

take (1,3) as (x₁,y₁)

y ₋ 3 = ₋1/2 (x ₋ 1)

y ₋ 3 = ₋1x/2 ₊ 1/2

y ₋ 3 = ₋x ₊ 1/2

2y ₋ 6 = ₋x ₊ 1

2y ₊ x ₋ 6 ₋ 1 = 0

2y ₊ x ₋ 7 = 0

2y ₊ x = 7

x ₊ 2y = 7

which is in the form ax ₊ by = c

Hence we derived the equation of the line as x ₊ 2y = 7 which is in the form of ax ₊ by = c.

Learn more about Linear equations here:

brainly.com/question/1884491

#SPJ9

y-intercept= 0

asymptote =\(lim_{n}\)→-0 (8/x) = -∞

\(lim_{n}\)→+0 (8/x) = +∞

range = R : { x ∈ R / {0} }

What is Range ?

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

I think the formula is:

f(x) = 8/x

(You wrote 8x; since a linear function has no asymptotes and you wrote 8x, I'm assuming the true function was 8/x.)

The amount that makes f(x) equal to 0 is the y-intercept.

Keep in mind that there is no value of x such that 8/x = 0 (because the quotient cannot be zero if the numerator is never zero).

Therefore, there is no y-intercept.

The asymmetry:

These are the four:

If the negative side of x tends to zero, then 8/x tends to negative infinity.

If x from the positive side approaches to zero, then 8/x tends to positive infinity.

These two asymptotes are expressed as follows:

\(lim_{n}\)→-0 (8/x) = -∞

\(lim_{n}\)→+0 (8/x) = +∞

Additionally, there are two cases where x tends to plus infinity (and 8/x goes to zero) and when x tends to minus infinity, where the function tends to zero once more. These two cases are denoted by the formulas:

\(lim_{n}\)→-∞ (8/x) = -∞

\(lim_{n}\)→∞ (8/x) = +∞

Lastly, the scope:

Only on limitations, y never reaches the following value:

y = 0

If so, the set of all real numbers excluding zero is the range, or

R : { x ∈ R / {0} }

Hence, y-intercept= 0

asymptote =\(lim_{n}\)→-0 (8/x) = -∞

\(lim_{n}\)→+0 (8/x) = +∞

range = R : { x ∈ R / {0} }

To learn more about Range click on the link

https://brainly.com/question/26098895

#SPJ13

Factor analysis and PCA (Principal Component Analysis) are statistical techniques used to reduce data dimensionality and identify underlying patterns.

Here's a general procedure for both methods:

1. Data collection: Gather a dataset with relevant variables for analysis.

2. Standardization: Standardize the data to ensure variables have equal weight and influence.

3. Covariance or correlation matrix: Calculate the covariance (for PCA) or correlation (for factor analysis) matrix to identify relationships between variables.

4. Eigenvalue decomposition: Perform eigenvalue decomposition on the matrix to obtain eigenvalues and eigenvectors, which represent the amount of variance explained and the direction of the principal components/factors, respectively.

5. Select principal components or factors: Choose the number of components/factors to retain based on the proportion of variance explained and the scree plot, which displays eigenvalues in descending order.

6. Rotation (for factor analysis): Apply a rotation method (e.g., varimax or promax) to the factor loading matrix to simplify interpretation and achieve a more meaningful structure.

7. Interpretation: Analyze and interpret the principal components or factors and their relationships with the original variables.

Remember that PCA and factor analysis have different assumptions and goals: PCA focuses on identifying orthogonal axes maximizing variance, while factor analysis aims to explain the correlation structure among variables using underlying latent factors.

To learn more about PCA (Principal Component Analysis) : brainly.com/question/30101604

#SPJ11

Answer:

(-2,0)

Step-by-step explanation:

Cause I took the quiz <3

Answer:

what you need help with

Step-by-step explanation:

Answer:

15x+28

Step-by-step explanation:

15x+10+18

15x+28

The number of possible combinations of three coins from the bag of 16 coins with different dates can be calculated using the formula for combinations, which is nCr = n! / r!(n-r)!, where n is the total number of objects, r is the number of objects to be chosen, and ! denotes factorial (the product of all positive integers up to the given number).

In this case, we have n = 16 (the total number of coins in the bag) and r = 3 (the number of coins to be chosen for each combination). Using the formula for combinations, we can calculate the number of possible combinations as follows:

nCr = 16! / 3!(16-3)!
nCr = (16 x 15 x 14) / (3 x 2 x 1)
nCr = 560

Therefore, 560 possible combinations of three coins can be chosen from the bag of 16 coins with different dates. These combinations could represent different historical events, significant dates, or other symbolic meanings depending on the dates inscribed on the coins. The calculation of combinations is an important concept in combinatorics and probability theory, and it has many real-world applications in fields such as statistics, economics, and computer science.

To learn more about Probability, visit:

https://brainly.com/question/13604758

#SPJ11

Answer:

Step-by-step explanation:

The purple car looks lit but kinda smaller than the black one. (are you really going to buy one if you are only in high school?)

Answer: both of you have a lead yet but you can get it right away if I can see you guys again in a developer way but I have a game pass

Step-by-step explanation: yes

Answer:

The firs one is 1/2

Step-by-step explanation:

Is a half

The probability of a premature baby girl being born at this hospital is 5%.

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.

If the likelihood of boys being born is 56%, then the complement of that is the likelihood of girls being born which is 100% - 56% = 44%.

Since we are given that of the baby girls born, 12% are premature, the probability of a premature baby girl  being born is:

(0.44)(0.12) = 0.0528 or 5.28%

The closest answer is the 5%.

The probability of a premature baby girl being born at this hospital is 5%.

Find out more information about probability here

https://brainly.com/question/28146099

#SPJ4

The area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To solve this problem, we can use the formula for the volume of a hexagonal prism:

V = (3√3/2) * a^2 * h

where V is the volume, a is the length of one side of the hexagonal base, and h is the height of the prism.

We are given that the height of the prism is 4 units and the volume is 98 units^3. Plugging these values into the formula, we can solve for the length of one side of the base:

98 = (3√3/2) * a^2 * 4
a^2 = 98 / (12√3)
a ≈ 2.95

Now that we know the length of one side of the base, we can find the area of the hexagon by using the formula:

A = (3√3/2) * a^2

where A is the area of one of the bases. Plugging in the value we found for a, we get:

A = (3√3/2) * (2.95)^2
A ≈ 7.39

Therefore, the area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To know more about hexagonal prism visit:

https://brainly.com/question/10726499

#SPJ11

The (posterior) probability that the selected individual has the disease, given two positive test results, is approximately 66.04%.

To determine the posterior probability that the individual has the disease, we can use Bayes' theorem. Let's denote the following probabilities:

- P(D) as the probability of the disease (0.05 in this case),

- P(D') as the probability of not having the disease (1 - P(D)),

- P(Pos|D) as the probability of testing positive given that the individual has the disease (0.98),

- P(Neg|D) as the probability of testing negative given that the individual has the disease (1 - P(Pos|D)),

- P(Pos|D') as the probability of testing positive given that the individual does not have the disease (1 - specificity, which is 1 - 0.99 = 0.01),

- P(Neg|D') as the probability of testing negative given that the individual does not have the disease (specificity, which is 0.99).

To calculate the posterior probability, P(D|Pos1, Pos2), applying Bayes' theorem:

P(D|Pos1, Pos2) = (P(Pos1, Pos2|D) * P(D)) / P(Pos1, Pos2),

where P(Pos1, Pos2|D) is the probability of observing two positive test results given the individual has the disease.

Since the two test results are independent, we can calculate P(Pos1, Pos2|D) as the product of the individual probabilities: P(Pos|D) * P(Pos|D) = 0.98 * 0.98 = 0.9604.

Now, we need to calculate the denominator, P(Pos1, Pos2), which represents the probability of observing two positive test results, regardless of whether the individual has the disease or not.

P(Pos1, Pos2) = P(Pos1, Pos2|D) * P(D) + P(Pos1, Pos2|D') * P(D').

Since the two tests are independent, we can calculate P(Pos1, Pos2|D') as the product of the individual probabilities: P(Pos|D') * P(Pos|D') = 0.01 * 0.01 = 0.0001.

Using these values, we can calculate the denominator as:

P(Pos1, Pos2) = (0.9604 * 0.05) + (0.0001 * 0.95) = 0.04802 + 0.000095 = 0.048115.

Finally, substituting the values into the Bayes' theorem equation:

P(D|Pos1, Pos2) = (0.9604 * 0.05) / 0.048115 ≈ 0.6604.

Therefore, the (posterior) probability that the selected individual has the disease, given two positive test results, is approximately 66.04%.

To learn more about denominator click here: brainly.com/question/32621096

#SPJ11

Answer: I think is A

Step-by-step explanation:

the volume of the solid generated by revolving the region bounded by the graph of y = 3sin(x^2) and the x-axis for 0 ≤ x ≤ √π around the y-axis is 0.

To find the volume, we can use the formula for the volume of a solid of revolution using cylindrical shells:

V = ∫[a, b] 2πx(f(x)) dx,

where a and b are the limits of integration, f(x) is the function defining the curve, and x represents the axis of revolution (in this case, the y-axis).

In this problem, the function is y = 3sin(x^2), and the limits of integration are from 0 to √π.

To calculate the volume, we need to express the function in terms of x. Since we are revolving around the y-axis, we need to solve the equation for x:

x = √(y/3) and x = -√(y/3).

Next, we need to find the limits of integration in terms of y. Since y = 3sin(x^2), we have:

0 ≤ x ≤ √π  becomes 0 ≤ y ≤ 3sin((√π)^2) = 3sin(π) = 0.

Now we can set up the integral:

V = ∫[0, 0] 2πx(3sin(x^2)) dx.

Since the lower and upper limits of integration are the same (0), the integral evaluates to 0.

Therefore, the volume of the solid generated by revolving the region bounded by the graph of y = 3sin(x^2) and the x-axis for 0 ≤ x ≤ √π around the y-axis is 0.

Learn more about volume here:

https://brainly.com/question/28058531

#SPJ11

Answer: 8

Step-by-step explanation: If we can define $ as k$, this would mean /frac32 would be K+($6). So, the answer is 8

SOLUTION:

Step 1:

In this question, we are given the following:

Write 3 x 3 x 3 x 3 x 3 as an exponential expression.

Type a number for the base and a number for the exponent.

Step 2:

The details of the solution are as follows:

3 x 3 x 3 x 3 x 3 =

where 3 is the base and 5 is the exponent.

The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.

An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.

Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).

The given interval is [1, 2]

The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'

The given statement is 'false'.

This is beacuse, an interval consists set of all the real values in between the two values given.

So, according to the definition, there are not only the end values but also many real values in between them.

Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.

Learn more about interval notation here:

https://brainly.com/question/10878781

#SPJ4

The measurement of angle DBC is equal to 33°, here we have to know the meaning of angle.

Angle is the measurement distance between two straight line or ray when they meet and it can also say that their one part is opening and other part is joint.

We have given that, ∠ABD = 4x, ∠DBC = 3x and measure of angle ABC is equal to 77°.

So ∠ABD + ∠DBC = ∠ ABC

⇒  4x + 3x = 77°

⇒ 7x = 77°

⇒ x = 11°

So, ∠ ABD = 4x = 4 * 11 = 44°

and, ∠DBC = 3x = 3 * 11 = 33°

Therefore, angle DBC is equal to 33°.

To Learn more about Angle, visit:

https://brainly.com/question/1309590

#SPJ1

Complete Question:

What is the measure of angle DBC if the measure of angle ABD is represented by 4x, the measure of angle DBC is represented by 3x and the measure of angle ABC is 77° ?

The rule of inference used to arrive at the statements s(y) and c(y) from the statement s(y) ∧ c(y) is called Simplification. Simplification allows us to extract individual components of a conjunction by asserting each component separately.

The rule of inference used in this scenario is Simplification. Simplification states that if we have a conjunction (an "and" statement), we can extract each individual component by asserting them separately. In this case, the conjunction s(y) ∧ c(y) represents the statement "y is a movie produced by Sayles and y is a movie about coal miners."

By applying Simplification, we can separate the conjunction into its individual components: s(y) (y is a movie produced by Sayles) and c(y) (y is a movie about coal miners). This allows us to conclude that there is a movie produced by Sayles (s(y)) and there is a movie about coal miners (c(y)).

Using the Simplification rule of inference enables us to break down complex statements and work with their individual components. It allows us to extract information from conjunctions, making it a useful tool in logical reasoning and deduction.

Learn more about logical reasoning here:

https://brainly.com/question/32269377

#SPJ11

Answer

x-19=27

Step-by-step explanation:

3^(-2) = 1/(3^2) = 1/(3*3) = 1/9

The rule used here is x^(-y) = 1/(x^y) to make the exponent positive.

3^2 turns into 3*3 because the exponent 2 tells us how many copies of the base '3' to multiply out.

Answer:

Joan has 78 Stickers left

Step-by-step explanation:

Joan gave 74 stickers to Sally: 263 - 74 = 189

Remaining Stickers: 189

Joan gave 51 stickers to her sister: 189 - 51 = 138

Remaining Stickers: 138

Joan gave 60 stickers to Jason: 138 - 60 = 78

Remaining Stickers: 78

A sequence of rigid motions and dialations that take square ABCD to square EFGH,

Dilation is a transformation that is used to change the size of an object. Dilation is used to enlarge or reduce objects. This transformation creates an image that is the same as the original shape. But the difference is in the size of the shape. Dilation should either stretch or shrink the original shape. This transformation is expressed by the term "scale factor". If the dilation creates a larger image, then it is called magnification.

Scale factor is defined as the ratio of the size of the new image to the size of the old image. The center of the dilation is a fixed point in plane.

We have , a square ABCD with rigid motion and dilation to come in shape square EFGH.

As, we see in above figure, the square ABCD is rotating as rigid motion of square . Also, the side of both square are not same that means square ABCD is dilated with a scalar factor. Now, we calculate scale factor for dilation,

Scale factor , k = new image size/ old image size

=> k = 2/7 < 1

Hence, The dilation of square ABCD by a scale factor 2/7.

To learn more about Dilation , refer:

https://brainly.com/question/3457976

#SPJ4

Answer:

16cm

Step-by-step explanation:

The area of a 2d figure is w x h. We know the area, a, is 80cm^2, the height, h, is 5, and the width, w, is 2x + 8.

Since we are solving for x, we want to isolate the variable.

5 x 2x + 8 = 80
80/5 = 2x + 8

We can now solve for x.

80/5 = 2x + 8
16 = 2x + 8
16 - 8 = 2x + 8 - 8
8 = 2x
8/2 = 2x/2
4 = x

We aren't done, we still need to solve for w, where we now know x = 4

w = 2x + 8
w = 2(4) + 8
w = 8 + 8
w = 16

The number of  ways that he can make the fruit salad if it must contain watermelon is 35.

Selection of the one object from the given samples with replacement or without replacement is called as the permutation. The selection of the items from the sample as they are different with each other.

The salad contains water melon, now we have to select 4 more fruits out of 7.

Using combination

\(^{n{C}_r\) = n! / r! (n-r)!

\(^{7}C_4\) = 7!/ 4! (7-4)!

      = 7*6*5*4! / 4! * 3*2

      = 35

Hence,  number of ways that he can make the fruit salad if it must contain watermelon is 35.

Learn more about Permutation and combination here:

brainly.com/question/11732255

#SPJ1

Answer: 35 on edge got it right

Step-by-step explanation:

The given sequence is:

To find the first 4 terms, we need to replace n=1,2,3,4 and solve for an, as follows:

The first four terms of the sequence are: -4 , -10 , -16 , -22

Assuming an annual appreciation rate of 5.4 percent, collection of 47 1952 silver dollars, purchased at face value, will be worth approximately $148.51 when you retire in 2057.

To calculate the future value of your collection, we can use the formula for compound interest: FV = PV * (1 + r)ⁿ, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. In this case, the present value is the face value of the silver dollars, which is equal to 47 * $1 = $47.

To find the future value in 2057, we need to calculate the number of years from the present to 2057, which is 2057 - current year. Assuming the current year is 2023, the number of years is 2057 - 2023 = 34.

Plugging in the values, we have

FV = $\(47 * (1 + 0.054)^{34\) = $\(47 * (1.054)^{34\) ≈ $148.51.

Therefore, your collection of 47 1952 silver dollars will be worth approximately $148.51 when you retire in 2057, assuming they appreciate at an annual rate of 5.4 percent.

Learn more about compound interest here: https://brainly.com/question/31217310

#SPJ11

Answer:

7

Step-by-step explanation:

Answer:

7 units

Step-by-step explanation:

To find the distance between two points, we use the distance formula:

\(d = \sqrt{(x_{2}-x_1)^2 + (y_2-y_1)^2 }\)

Plug in what you know.

\(d = \sqrt{(-5 - 2)^2 + (-2 - (-2))^2 }\)

Evaluate the double negative.

\(d = \sqrt{(-5 - 2)^2 + (-2 + 2)^2 }\)

Evaluate the parentheses.

\(d = \sqrt{(-7)^2 + (0)^2 }\)

Evaluate the exponents.

\(d = \sqrt{(49) + (0) }\)

Add.

\(d = \sqrt{(49)\)

Evaluate the radical.

d = ±7

Since distance cannot be negative, our answer is 7.

The distance between the two points is 7 units.

Hope this helps!

Answer:

exponetial growth; y-0.25

Answer:

the second option

Step-by-step explanation:

6(0.25)* 1 = 1.5 if x equals 1

6(0.25) * 2= 3 if x equals 2