6 Evaluate: 2 (V125a%b3 o 5a²6 0 25a-6 25a263 Оба?3

Answer:

y=4

Step-by-step explanation:

42/30 = (y+24)/20

Cross multiplying,

30*(y+24) = 42*20

30y + 30*24 = 840

30y + 720 = 840

Subtract 720,

30y + 720 - 720 = 840 - 720

30y = 120

Divide by 30,

y = 120/30 = 4

Answer:

3.6million

Step-by-step explanation:

See image for explanation (gotten from Chegg tutor)

Answer:

3.6 million

             _______

            /  (o)   (o)  \

          /      -___-     \

          -------------------

Answer:

Nothing is hard if you put your mind to it.

Step-by-step explanation:

The length of the loan in months is 151. 33 months

The formula for determining simple interest is expressed as;

I = PRT/100

Where;

From the information given, we have that;

Principal interest = $600

Simple interest = $681

Rate = 9%

Substitute the values into the formula

$681 = $600 × 9 × T/100

Multiply the numerators

$681 = 5400T/100

cross multiply

68100 = 5400T

Divide both sides by 5400

T = 68100/5400

T = 12. 61 years

Convert the years to months

T = 12.61(12)

T = 151. 33 months

Hence, the value is 151. 33 months

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

Answer:

x > 5

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

8x - 6(x + 1) < 4(2x - 9)

Step 2: Distribute parenthesis

8x - 6x - 6 < 8x - 36

Step 3: Combine like terms

2x - 6 < 8x - 36

Step 4: Subtract 2x on both sides

-6 < 6x - 36

Step 5: Add 36 on both sides

30 < 6x

Step 6: Divide both sides by 6

5 < x

Step 7: Rewrite

x > 5

The line of best fit for the set of data in this problem is given as follows:

y = 0.613x + 4.142.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) of the data-set in the calculator.

The points for this problem are given as follows:

(-2, 2.9), (-3.5, 2), (1.4, 4.8), (-4.2, 1.5), (0,4), (2.8, 6), (-1.5, 3.5).

Inserting these points into a calculator, the line of best fit is given as follows:

y = 0.613x + 4.142.

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Answer:10−45

Step-by-step explanation: if you actually saw it then you will get that answer

the solution is: \(w < -5\) . Since all real numbers are either less than or greater than  \(-5\) , the solution set for this inequality is "All reals".

To solve for w in  \(w + 19 < 14\)  , we need to isolate w on one side of the inequality.

This means that any value of w that is less than   \(-5\) would make the inequality true.

For example,    \(w = -6\) is a solution because   \(-6 + 19 < 14.\) Likewise, any value of w that is greater than or equal to -5 would make the inequality false. For example,   \(w = -5\) is not a solution because  \(-5 + 19 = 14\)  .

Subtracting 19 from both sides of the inequality, we get:

\(w + 19 - 19 < 14 - 19\)

\(w < -5\)

Therefore, the solution is:  \(w < -5\) . Since all real numbers are either less than or greater than   \(-5\) , the solution set for this inequality is "All reals".

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The Boolean expression A >= B is equivalent to  !(A < B) (option A)

To simplify a Boolean expression, use De Morgan's Law.

De Morgan's Law is used to simplify or find the equivalent of a negation of compound expressions.

The principle is:

NOT (A AND B) is equivalent to (NOT A) OR (NOT B)

NOT (A OR B) is equivalent to (NOT A) AND (NOT B)

When the expression involves >, <, = signs, then to simplify the expression, move the not and flip the sign.

! is the symbol of negation or NOT.

Hence,

! (>) becomes <=

! (<) becomes >=

Here are some examples:

!(A > B) is equivalent to (A <= B)

!(A <= B) is equivalent to (A > B)

!(A >= B) is equivalent to (A < B)

!(A == B) is equivalent to (A != B)

!(A != B) is equivalent to (A == B)

!(A < B) is equivalent to (A >= B)

From the above list we can conclude that A >= B is equivalent to !(A < B) (option A)

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Type I error: Reject the null hypothesis H₀, when H₀ is true.

Failure to reject the null hypothesis H₀, when H₀  is untrue is a Type II mistake.

A hypothesis is a proposed explanation or prediction for a phenomenon or observed phenomenon. It is a statement that suggests an explanation for an observed fact or set of facts and provides a basis for further investigation or experimentation.

 Given Information

Determine the hypothesis:

Hₐ: p₁>p₂

Type I error: Reject the null hypothesis H₀, when H₀ is true.

Although being ineffectual, the adjustment gives the impression of being effective.

As a result, more vehicles than anticipated have brake problems, which might result in additional expenses for the company.

Failure to reject the null hypothesis H₀, when H₀  is untrue is a Type II mistake.

Interpretation: The adjustment is successful even though it appears to be ineffective.

As a consequence, fewer automobiles than anticipated have brake issues, which might result in financial savings for the corporation.

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Answer: \(\sqrt[3]{a}\)

Step-by-step explanation:

Just as the square root is \(\sqrt[2]{a}\), the cube root is \(\sqrt[3]{a}\)

Hope it helps <3

Answer:

\(\sqrt[3]{a}\)

Step-by-step explanation:

a cube root of a number x is a number a such that a³ = x.

The additive inverse of the polynomial is +7y²-x²y+3xy+7x².

The additive inverse can be defined as when we add a number to some number and get result as zero.

Given polynomial:

-7y²+x²y-3xy-7x²

As, the value of additive inverse is same as of the number but the sign of the additive inverse is opposite.

So,

=  +7y²-x²y+3xy+7x²

Check:

-7y²+x²y-3xy-7x² + 7y²-x²y+3xy+7x²

= -7y²+  7y² +x²y -x²y -3xy +3xy -7x² +7x²

=0

Hence, the additive inverse of the polynomial is +7y²-x²y+3xy+7x².

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Answer:

here is the ratio  1 : 1.25   (sharks: dolphins)

Step-by-step explanation:

The ratio of sharks to dolphins is 4 : 5

Suppose the  real measurements were "a" and "b"

This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly cancelled from both the numerator and the denominator.

Thus, a = px, b = qx

Given Number of sharks = 4

Number of dolphins = 5

Therefore, the ratio of sharks to dolphins

= 4 : 5

Or  1 : 1.25

Number of animals = number of sharks + number of dolphins

Number of animals = 4 + 5 = 9

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The meer-kitty survey feedback tab has limitations in its data. The survey results must have at least 120 unique responses to be considered useful and aligned with the business objective. The current data, however, only has 40 total responses, with 11 of them coming from one user. This skews the results and makes it difficult to accurately analyze the feedback.

To address these limitations, it is recommended to remove the duplicates, in this case the 11 responses from one user, and focus on the remaining 29 unique responses. This will provide a clearer picture of the survey results and a more accurate representation of the feedback. By doing so, the analysis of the data will be better aligned with the original business objective and provide more valuable insights.

It is important to consider the limitations of the data when conducting any type of analysis, especially when it comes to surveys and feedback. By taking the necessary steps to ensure the data is as accurate and reliable as possible, the results of the analysis will be more meaningful and relevant to the business.

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Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that \(p = 0.09\)

41 people arrested for DUI in Illinois are selected at random.

This means that \(n = 41\)

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158\)

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

\(P(X = 0) + P(X \geq 1) = 1\)

We want \(P(X \geq 1)\).

Then

\(P(X \geq 1) = 1 - P(X = 0)\)

In which

\(P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209\)

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791\)

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

\(E(X) = np = 41*0.09 = 3.69\)

d. What is the standard deviation of the number of repeat offenders?

\(\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83\)

Answer: 2, 1.5 , -0.75

(b) \(4x-3y-10=0\)

Step-by-step explanation:

Given

line is \(3x+4y-6=0\)

Converting it into intercept form

\(\Rightarrow 3x+4y=6\\\\\Rightarrow \dfrac{3x}{6}+\dfrac{4y}{6}=\dfrac{6}{6}\\\\\Rightarrow \dfrac{x}{2}+\dfrac{y}{1.5}=1\)

So, the x-intercept is \(2\) and y-intercept is \(1.5\)

The slope is given by

\(-\dfrac{\frac{1}{2}}{\frac{1}{1.5}}=-0.75\)

(b) the line perpendicular to the above line and passing through \((1,-2)\)

The slope of the required line

\(m=-\dfrac{1}{-0.75}\\\\m=\dfrac{4}{3}\)

Equation of the line is given by

\(\Rightarrow \dfrac{y-(-2)}{x-1}=\dfrac{4}{3}\\\\\Rightarrow 3y+6=4x-4\\\Rightarrow 4x-3y-10=0\)

Answer:

The number of checks processed at a bank in a day is categorical data.

Step-by-step explanation:

In Mathematics, a categorical data can be defined as a statistical data type that is used to group informations having the same attributes or characteristics. Some examples of a categorical data are age, gender, race, religion etc.

A numerical data can be defined as a data set that is expressed in numbers only or a data set consisting of numbers rather than words. A numerical data is also known as a quantitative data.

Basically, numerical data are classified into two (2) main categories and these are;

1. Discrete data: a discrete data is a data set in which the number of possible values are either finite or countable. For instance, the value of a fair die, number of sweets in a jar, number of eggs in a crate etc.

2. Continuous data: a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable. Any quantity such as height, volume, weight, density, length, pressure, temperature, speed, distance, time are generally a continuous data.

Hence, the number of checks processed at a bank in a day is discrete data.

The pattern for the sequence 1.3, 8.3, 27.3, 64.3,… is f(n) = (n)³.3

The pattern in the question is given as

1.3, 8.3, 27.3, 64.3,…

In the above expressions and pattern, we can see that

From the above, we have the following

Current term = (n)³.3

Note that the decimal does not represent product

And also the pattern is a geometric sequence

Hence, the pattern for the sequence is f(n) = (n)³.3

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Hello !

68/17 = 4

=> yes for 68

84/17 = 4.941...

=> no for 84

357/17 = 21

=> yes for 357

1001/17 = 58.882...

=> no for 1001

Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).

Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It is expressed as a value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur.

To solve this problem, we can use the formula for the standard deviation of the sample mean:

Standard deviation of sample mean = standard deviation / √(sample size)

Plugging in the given values:

Standard deviation of sample mean = 7 / √(31)

Next, we can calculate the z-score, which is the number of standard deviations the sample mean is below the population mean:

z-score = (sample mean - population mean) / standard deviation of sample mean

Plugging in the given values:

z-score = (141.5 - 145) / (7 / √(31))

Using a calculator, we find that the z-score is approximately -2.22.

Finally, we can use a standard normal distribution table or a calculator to find the probability that a z-score is less than -2.22.

Using a standard normal distribution table, we find that the probability is approximately 0.0134 (rounded to four decimal places).

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The result is 16, which matches the information given in the problem. Thus, our solution is correct. Thao originally had 30 coins.

Let's solve this problem step by step.

Let's assume the number of coins Thao originally had is x.

According to the problem, Thao gives two fifths of her coins to her sister. Two fifths of x can be represented as (2/5)x.

After giving away two fifths of her coins, Thao receives 4 coins for her birthday. So, the number of coins she has now is (2/5)x + 4.

The problem states that she now has 16 coins. Therefore, we can set up the following equation:

(2/5)x + 4 = 16

To solve for x, we need to isolate x on one side of the equation. We can start by subtracting 4 from both sides:

(2/5)x = 16 - 4

(2/5)x = 12

To get rid of the fraction, we can multiply both sides of the equation by 5:

5 * (2/5)x = 5 * 12

2x = 60

Next, divide both sides of the equation by 2 to solve for x:

(2x)/2 = 60/2

x = 30

Therefore, Thao originally had 30 coins.

To verify our answer, we can substitute x = 30 back into the equation (2/5)x + 4 and see if it equals 16:

(2/5) * 30 + 4 = 12 + 4 = 16

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Answer:

A or -1/2, -rad2/2, -rad3/2

Step-by-step explanation:

Right on edge

Answer:

A

Step-by-step explanation:

correct on edge 202222222

The inverse of matrix A, if it exists, is:

A^(-1) = [7/43, 2/43; 10/43, 9/43]

To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.

Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:

det(A) = (9 * 7) - (-2 * -10)

= 63 - 20

= 43

Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.

The formula to calculate the inverse of a 2x2 matrix is:

A^(-1) = (1/det(A)) * [d, -b; -c, a]

Plugging in the values from matrix A and the determinant, we have:

A^(-1) = (1/43) * [7, 2; 10, 9]

Simplifying further, we get:

A^(-1) = [7/43, 2/43; 10/43, 9/43].

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The cumulative frequency for the class with a lower class limit of 27 is 4 + 7 + 7 = 18.

What is the cumulative frequency?

The cumulative frequency for a class is the total frequency of that class and all the classes before it.

In order to find the cumulative frequency for the class with a lower class limit of 27, you would need to add the frequency of that class with the frequencies of all the classes before it.

The cumulative frequency for a class with a lower class limit of 27 can be found by adding up the frequencies of all the classes that come before it.

In this case, the classes that come before the class with a lower class limit of 27 are "Ages 15-18", "Ages 19-22", and "Ages 23-26",

Hence, the cumulative frequency for the class with a lower class limit of 27 is 4 + 7 + 7 = 18.

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Complete Question:

Ages 15-18 19-22 23-26 27-30 31-34 35-38 Number of students 4 7 7 2 5 10 Based on the frequency distribution above, find the cumulative frequency for the class with a lower class limit 27?

The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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Answer:

The rule is to divide the weight of the bag by 4 to find the number of marbles.

Step-by-step explanation:

The rule is to divide the weight of the bag by 4 to find the number of marbles.

Answer:

x = 3

Step-by-step explanation:

If the same number is added to the numerator of 12/13 and subtract from the denominator, the new fraction is equal to 3/2. What is the number?

\(\frac{12+x}{13-x} =\frac{3}{2}\)

multiply both sides by 13-x:

\((13-x)\frac{12+x}{13-x} =\frac{3}{2}(13-x)\\\\12+x = \frac{3(13-x)}{2} \\\\12+x = \frac{39-3x}{2} \\\)

multiply both sides by 2:

\(2(12+x) = (\frac{39-3x}{2})\\\\24+2x = 39-3x\)

subtract 24 from both sides:

24 + 2x - 24 = 39 - 3x - 24

2x = 15 - 3x

add 3 x to both sides:

2x + 3x = 15 - 3x + 3x

5x = 15

divide both sides by 5:

5x/5 = 15/5

x = 3

check:

\(\frac{12+x}{13-x} =\frac{3}{2}\\\\\frac{12+3}{13-3} =\frac{3}{2}\\\\\frac{15}{10} =\frac{3}{2}\\\\\frac{3}{2} =\frac{3}{2}\)