Read, Think, Analyse and solve by applying linear equations.
1. Three numbers are in the ratio of 4:5:6. If the sum of the largest and the smallest equals to the sum of the third and 55. Find the numbers.​

The triangle is the essential geometric form in the construction and support of a geodesic dome.

        A geodesic dome is a spherical structure like a round tent that is formed by the simultaneous placements of triangular structures one along the other. The triangles are placed in such a way it seems that rhombuses are placed one after the other.

         They are lightweight, and a layer of canvas or transparent material is placed over the structure to make it water-proof.

          It was first created by the American designer Richard Buckminster Fuller in the 20th century.

          Although these homes save energy and give a perfect place to live in nature, they can also pose some issues like the placement of the chimney, creating rooms within the dome, leakage in the roof, and so on.

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We must have used at least 6 of one type of stamp.we get:

\(5n + 8m = 72\)

The amount of postage you make must be even, we can use the fact that 5 cents and 8 cents are both even. Let's say we use n 5-cent stamps and m 8-cent stamps.

Since both types of stamps are even, the sum n5 + m8 will be even only if both n and m are even.

(b) Suppose we made an even amount of postage, say 2k cents. If we used an odd number of both types of stamps, then the total number of stamps we used would be odd. Let's say we used n 5-cent stamps and m 8-cent stamps.

(c) Suppose we made exactly 72 cents of postage, say using n 5-cent stamps and m 8-cent stamps. Then, we have:

\(n5 + m8 = 72\)

we get:

\(5n5 + 5m8 = 360\)

Rearranging, we get:

\(25n + 40m = 360\)

we get:

\(5n + 8m = 72\)

Now, we know that n and m are both non-negative integers, so the only possible values for m are\(0, 1, 2, 3, 4,\) or\(5\). But if m is less than 6, then 5n + 8m is less than 40, which means we cannot make exactly 72 cents of postage. Therefore, we must have used at least \(6\)of one type of stamp.

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Answer:

it is basic and .........

The solution to the systems of equations graphically is (2, 4)

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

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Answer:

12015

Step-by-step explanation:

use a g o o g l e calculator bro.

Answer:

(3. 5) (0,2)

Step-by-step explanation:

You just let x2-4x +2 =x+2

Then count x

X got 2 answer 0 and 3

Then put the answer in the equation y=x+2

Then find the y

Answer:

D (bottom right answer)

Step-by-step explanation:

The denominator of an exponent is the index of the root.

For example, x^1/2 means √2.

x^1/5 means the 5th root of x.

You have 3x^1/5.

3 is not in the root, so you need an answer that has a plain 3.

That eliminates the two answers on the top line.

Then you have x^1/5 which means the 5th root of x.

The correct answer must be 3 × 5th root of x

Answer: D

Answer

D. 3•5√x

Step-by-step explanation:

the law of indices

√x = x^1/2

i.e 3*x^1/5

for the first one,it will be

3x^5*1/2

for the second one

(3x)^1/5

i.e 3^1/5 * x^1/5

the third one will be

3*x^5*1/2

Answer:

8:1

Step-by-step explanation:

Mathematical literacy refers to a person's ability to understand and use mathematical concepts and skills to solve real-world problems in a variety of contexts. It involves the ability to reason quantitatively and use mathematical tools effectively.

Mathematical literacy is essential in various aspects of daily life. For instance, it is required to manage personal finances, make purchasing decisions, calculate taxes, and understand financial statements.

In the workplace, it is necessary to analyze data, make predictions, and optimize systems. In fields such as medicine, engineering, and science, mathematical literacy is essential to make accurate measurements, analyze experimental results, and model complex systems.

Thus, mathematical literacy is required in various social and political contexts to analyze statistical data, understand probabilities, and make informed decisions.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

What is Mathematical Literacy​?

Answer:

A if not then D

Answer:

569,75

Step-by-step explanation:

Answer:

volume of cuboids having size 4cm 3cm and 3cm is 36cm^3 because the formula to calculate volume of cuboids is length × breathe × height.

other question I didn't understand.

The sample size increases, the probability of obtaining a sample mean less than 3500 decreases. The mean of the sample mean distribution is equal to the population mean, which is 7500.

a) The probability that, on a single test, x is less than 3500 can be calculated using the standard normal distribution. We need to standardize the value using the z-score formula: z = (x - μ) / σ. Substituting the given values, we get z = (3500 - 7500) / 1750 ≈ -2.286.

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -2.286. The probability is approximately 0.0116, or 1.16%. Therefore, there is a 1.16% chance that a single test result will be less than 3500, indicating leukopenia.

(b) When the doctor uses the average x (sample mean) for two tests taken about a week apart, the probability distribution of x (sample mean) follows a normal distribution. The mean of the sample mean distribution is equal to the population mean, which is 7500. The standard deviation of the sample mean distribution is equal to the population standard deviation divided by the square root of the sample size. In this case, the sample size is 2.

The probability distribution of x (sample mean) < 3500 can be calculated by standardizing the value using the z-score formula and then finding the corresponding probability from the standard normal distribution table or a calculator. With two tests, the probability distribution will be narrower compared to a single test. The exact probability depends on the specific value of the sample mean and the standard deviation of the sample mean distribution.

(c) When considering three tests taken a week apart, the process is similar to part (b). The mean of the sample mean distribution remains the same at 7500, but the standard deviation of the sample mean distribution is now divided by the square root of 3, since the sample size is 3. As the sample size increases, the standard deviation of the sample mean distribution decreases, resulting in a narrower distribution.

The probability distribution of x (sample mean) < 3500 can be calculated using the z-score formula and finding the corresponding probability from the standard normal distribution table or a calculator. With three tests, the probability distribution will be even narrower compared to two tests.

In summary, as the sample size increases, the probability of obtaining a sample mean less than 3500 decreases. With more tests, we can have greater confidence in the accuracy of the sample mean and draw stronger conclusions about the individual's condition. If a person had a sample mean less than 3500 based on three tests, it would indicate a higher level of certainty about the presence of leukopenia, potentially leading to further investigation or treatment options.

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Answer:

-8/5

Step-by-step explanation:

hope it helps!

Answer:

The solution of the system is:

(x, y) = (-1, -6)

Step-by-step explanation:

Given the system of equations

-6x – 3y = 24

4x – 2y = 8

solving the system of equations

\(\begin{bmatrix}-6x-3y=24\\ 4x-2y=8\end{bmatrix}\)

\(\mathrm{Multiply\:}-6x-3y=24\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-12x-6y=48\)

\(\mathrm{Multiply\:}4x-2y=8\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x-6y=24\)

so

\(\begin{bmatrix}-12x-6y=48\\ 12x-6y=24\end{bmatrix}\)

adding the equations

\(12x-6y=24\)

\(+\)

\(\underline{-12x-6y=48}\)

\(-12y=72\)

so the system of equations becomes

\(\begin{bmatrix}-12x-6y=48\\ -12y=72\end{bmatrix}\)

solve -5y=72 for y

\(-12y=72\)

Divide both sides by -12

\(\frac{-12y}{-12}=\frac{72}{-12}\)

Simplify

\(y=-6\)

\(\mathrm{For\:}-12x-6y=48\mathrm{\:plug\:in\:}y=-6\)

solving

\(-12x-6\left(-6\right)=48\)

\(-12x+6\cdot \:6=48\)

\(-12x+36=48\)

subtract 36 from both sides

\(-12x+36-36=48-36\)

Simplify

\(-12x=12\)

Divide both sides by -12

\(\frac{-12x}{-12}=\frac{12}{-12}\)

\(x=-1\)

Therefore, the solution of the system is:

(x, y) = (-1, -6)

Answer:

Increase of 9.3%

Step-by-step explanation:

Hence, the percent increase in salary did Jerry receive is \(4.68\)%.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Here given that,

Jerry’s monthly salary was $\(3,050\) last year. This year his monthly salary is $\(3,350\).

His monthly salary in last year is $ \(3050\).

In this year his salary is $\(3350\).

So, the increase in salary is

\(3350-3050=300\)

And the overal salary is $ \(3050+3350=6400\)

So, the percent increase in salary did Jerry receive is

\(\frac{300}{6400}\) × \(100=4.68\)

Hence, the percent increase in salary did Jerry receive is \(4.68\)%.

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The real solutions of the cubic equation x^3 + 56 = 3x^2 + 36x are:

x1 = -2.084

x2 = 2.333

The third root of the cubic is complex and not a real solution.

To solve the cubic equation x^3 + 56 = 3x^2 + 36x, we first need to depress the cubic by substituting x = y - b/3, where b is the coefficient of the quadratic term (in this case, b = -3). This gives:

(y - b/3)^3 + 56 = 3(y - b/3)^2 + 36(y - b/3)

Expanding the left-hand side and simplifying, we get:

y^3 - 9y^2 + 12y - 227 = 0

Next, we can use CARDANO's formula to solve this depressed cubic. CARDANO's formula expresses the roots of the cubic equation in terms of the coefficients of the cubic:

y = u + v

where u and v are given by:

u = (q + (q^2 + r^3)^1/2)^(1/3)

v = (q - (q^2 + r^3)^1/2)^(1/3)

with q and r defined as:

q = (3b - a^2) / 9

r = (9ab - 27c - 2a^3) / 54

where a, b, and c are the coefficients of the depressed cubic.

Substituting the coefficients of the depressed cubic into these formulas, we get:

q = (3(-9) - 0^2) / 9 = -3

r = (9(0)(-227) - 27(1) - 2(0)^3) / 54 = -227/18

Substituting q and r into the formulas for u and v, we get:

u = (-3 + (-3)^2 - (227/18)^3)^(1/3) = -5.567

v = (-3 - (-3)^2 - (227/18)^3)^(1/3) = 2.483

Therefore, the three roots of the depressed cubic are:

y1 = u + v = -3.084

y2 = -(u +v)/2 + I(u-v)√3/2 = 1.333 - 3.296i

y3 = -(u +v)/2 - I(u-v)√3/2 = 1.333 + 3.296i

Finally, we can find the roots of the original cubic equation by adding back b/3 = 1 to each root:

x1 = y1 + 1 = -2.084

x2 = y2 + 1 = 2.333 - 3.296i

x3 = y3 + 1 = 2.333 + 3.296i

Therefore, the real solutions of the cubic equation x^3 + 56 = 3x^2 + 36x are:

x1 = -2.084

x2 = 2.333

The third root of the cubic is complex and not a real solution.

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The speed of the particle at time t = 0 is 5 units per unit of time.

To find the speed of the particle at time t = 0, we need to calculate the magnitude of the velocity vector of the particle at that instant.

The velocity vector of the particle is the derivative of the position vector with respect to time:

v(t) = c'(t) = (-4sin(4t), 4cos(4t), 3)

Substituting t = 0 into the velocity vector, we get:

v(0) = (-4sin(0), 4cos(0), 3)

= (0, 4, 3)

Now, to find the speed of the particle at t = 0, we calculate the magnitude of the velocity vector:

|v(0)| = √(0^2 + 4^2 + 3^2)

= √(0 + 16 + 9)

= √25

= 5

The speed of a particle measures the rate at which it is moving along its path, regardless of the direction. In this case, the speed of the particle at t = 0 is 5 units per unit of time, indicating that it is moving with a constant speed along the helix.

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Step-by-step explanation:

oi1i1iiiii1i1¹111111¹1o1ooooooo

The number of permutations is:

39,916,800

To find this, we need to take the quotient between the the factorial of the total number of elements (11 in this case) and the difference between the total and the number we are selectingh (10)

Then the number is:

11p10 = 11!/(11 - 10)! = 11! = 39,916,800

So that is the number of permutations that we can do with 10 elements out of a set of 11 elements.

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Answer:

\( \sqrt{30} \)

Step-by-step explanation:

altitude rule

10 / x = x / 3

x^2 = 30

x = sqrt(30)

The statement is true. If a sequence {an} satisfies the condition an > 0 and lim n→∞ (an + 1)/an < 1, then the limit of the sequence as n approaches infinity, lim n→∞ an, is equal to 0.

To prove the statement, we use the limit comparison test. Let's assume that lim n→∞ (an + 1)/an = L, where L < 1. Since L < 1, we can choose a positive number ε such that 0 < ε < 1 - L. Now, there exists a positive integer N such that for all n ≥ N, we have (an + 1)/an < L + ε. Rearranging the inequality, we get an + 1 < (L + ε)an.

Now, let's consider the inequality for n ≥ N:

an + 1 < (L + ε)an < an.

Dividing both sides by an, we get (an + 1)/an < 1, which contradicts the given condition. Hence, our assumption that lim n→∞ (an + 1)/an = L is incorrect. Therefore, the only possible limit for the sequence {an} as n approaches infinity is 0, and hence the statement is true.

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The correct answer is (b) divide the sum of the cross-products of Z scores by the sample size.

When calculating the correlation coefficient, also known as Pearson's correlation coefficient, the last step involves dividing the sum of the cross-products of Z scores by the sample size. The correlation coefficient measures the strength and direction of the linear relationship between two variables.

To calculate the correlation coefficient, we follow these steps:

Standardize the variables: Convert the raw scores of each variable into Z-scores. The Z-score represents the number of standard deviations a particular score is from the mean. This step is done to put both variables on the same scale and make them comparable.

Calculate the cross-products: Multiply the Z-scores of the corresponding pairs of observations. This step gives us the cross-products of Z-scores for each pair of observations.

Sum the cross-products: Add up all the cross-products of Z-scores.

Divide by the sample size: Divide the sum of the cross-products of Z-scores by the sample size. The sample size represents the number of paired observations used in the analysis.

By dividing the sum of the cross-products by the sample size, we obtain the covariance of the variables. The covariance measures the extent to which the variables vary together. However, the covariance itself is not sufficient to determine the strength and direction of the relationship.

The final step involves dividing the covariance by the product of the standard deviations of the variables. This step normalizes the covariance and results in the correlation coefficient, which is a value between -1 and 1. The correlation coefficient indicates the strength and direction of the linear relationship between the variables. A positive correlation coefficient indicates a positive linear relationship, a negative correlation coefficient indicates a negative linear relationship, and a correlation coefficient close to zero indicates a weak or no linear relationship.

Therefore, the last step in calculating the correlation coefficient is to divide the sum of the cross-products of Z-scores by the sample size.

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Answer:

0.000093

Step-by-step explanation:

Answer:

0.000093

Step-by-step explanation:

Answer: Adding integers means adding integers with the same signs, while subtracting integers means adding the integers of opposite signs.

Step-by-step explanation:

Answer:

it is 100

Step-by-step explanation:

The correct answer for the first question is D. The data are discrete because the data can take on any value in an interval.

Quiz scores from a college level statistics course are analyzed to determine student progress. This is not a voluntary response sample because the students taking the quiz are required to participate, and their scores are collected for the purpose of analyzing their progress.

For the second question, the data described, which is the number of donations a charity receives each month, is discrete. Discrete data can only take on specific values and cannot be divided into smaller, meaningful intervals. In this case, the number of donations can only be whole numbers, such as 0, 1, 2, and so on. It cannot take on any value in an interval or be represented by fractions or decimals. Therefore, the data is discrete.

It is important to distinguish between discrete and continuous data when analyzing and interpreting data, as different statistical methods and techniques are used for each type. Discrete data is usually counted or measured in whole numbers, while continuous data can take on any value within a given range or interval.

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Answer:

-4

Step-by-step explanation:

Slope (m) =  

ΔY

ΔX

=  

-4

1

= -4

θ =  

arctan( ΔY ) + 360°

ΔX

= 284.03624346793°

ΔX = 5 – 2 = 3

ΔY = -8 – 4 = -12

Distance (d) = √ΔX2 + ΔY2 = √153 = 12.369316876853