Rationalise the denominator and simplify 6/√3​

Answer:

\(\frac{167}{500}\)

Step-by-step explanation:

Write 0.334 as   \(\frac{0.334}{1}\)

Multiply both numerator and denominator by 10 for every number after the decimal point

\(\frac{0.334 }{1}\) x 1000

\(\frac{334}{1000}\)

Reducing the fraction gives  \(\frac{167}{500}\)

Answer:

y = 1/2x+5

Step-by-step explanation:

You have two points so you can find the slope

m = (y2-y1)/(x2-x1)

m = (8-3)/(6 - -4)

   (8-3)/(6+4)

    5/10

 1/2

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 1/2 x+b

Substitute a point into the equation

8 = 1/2(6)+b

8 = 3+b

b=8-3 = 5

y = 1/2x+5

You would reject the null hypothesis for a p-value of 0.08 and 0.05. So, the correct answer for rejection is a) and c).

A significance level of 10% means that the probability of rejecting the null hypothesis when it is actually true is 10%. This probability is also known as the Type I error rate.

If the p-value is less than or equal to the significance level, then we reject the null hypothesis. In this case, the significance level is 10%, so we would reject the null hypothesis for p-values less than or equal to 0.1.

Therefore, we would reject the null hypothesis for the p-value of 0.08 and 0.05, as they are less than or equal to the significance level of 10%. However, we would not reject the null hypothesis for the p-value of 0.89 and 0.11, as they are greater than the significance level.

So, the option a) and c) are rejected.

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Answer:

3

Step-by-step explanation:

Remove the parenthesis: -3 + 6

Calculate: 3

Good luck :)

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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Some part of the regression can be estimated precisely, but it is difficult to predict the effect of individual regressors when there is multicollinearity in the data.Multiple regression models require that variables be independent of one another, otherwise, multicollinearity will occur.

Consider the multiple regression model with two regressors X1 and X2, where both variables are determinants of the dependent variable. You first regress Y on X1 only and find no relationship. However when regressing Y on X1 and X2, the slope coefficient changes by a large amount.

This suggests that your first regression suffers from omitted variable bias. Imperfect multicollinearity implies that it will be difficult to estimate precisely one or more of the partial effects using the data at hand. Imperfect multicollinearity means that there is a strong correlation between the regressors, but they are not perfectly correlated.

As a result, some part of the regression can be estimated precisely, but it is difficult to predict the effect of individual regressors when there is multicollinearity in the data.Multiple regression models require that variables be independent of one another, otherwise, multicollinearity will occur.

When there is multicollinearity in the data, it means that two or more of the variables are highly correlated with one another. In other words, the data may contain redundant information, which can make it difficult to estimate the regression coefficients or partial effects.The dummy variable trap refers to a situation in which one of the variables is a perfect linear combination of the other variables.

This results in the model being unsolvable, and the coefficients cannot be estimated. Heteroskedasticity is the term used to describe when the variance of the residuals is not constant across all values of the independent variables. This means that the predictions of the model may be biased, and the standard errors of the coefficients may be incorrect.

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Answer:

x=2

Step-by-step explanation:

2.5(6x-4)=10+4(1.5+0.5x)

Distribute

15x -10 = 10 + 6 +2x

Combine like terms

15x -10 =16+2x

Subtract 2x

13x -10 = 16

Add 10

13x= 16+10

13x = 26

Divide by 13

13x/13 = 26/13

x =2

Answer:

x=2

Step-by-step explanation:

2.5(6x-4)=10+4(1.5+0.5x)

Distribute.

2.5*6x-2.5*4=10+4*1.5+4*0.5x

15x-10=10+6+2x

Combine like terms.

15x-10=16+2x

Add 10 to both sides

15x-10+10=16+10+2x

15x=26+2x

Subtract 2x from both sides.

15x-2x=26+2x-2x

13x=26

Divide both sides by 13

x=2

Answer:

1) circle

2) rectangle

Step-by-step explanation:

1) circle - parallel to base

2) rectangle - perpendicular to base

When we subtract a velocity vector from another velocity vector, the result is B. another velocity.

When we subtract a velocity vector from another velocity vector, we are essentially finding the difference between the two velocities. This difference is also a velocity vector, but in a different direction and with a different magnitude. Therefore, the answer is another velocity, option B.

It is important to note that acceleration is a change in velocity, not the result of subtracting one velocity from another. Scalar refers to a quantity with only magnitude, whereas velocity is a vector quantity with both magnitude and direction. Displacement refers to the change in position of an object and is not directly related to subtracting velocity vectors.

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Answer:

Debit Salaries Expense $480 and credit Salaries Payable $480

Step-by-step explanation:

Firstly, we will need to calculate the salary expense of the company on these two employees.

Mathematically, that would be

2 employees * 2 days * 120/employee/day = 2 * 2 * 120 = $480

Thus, the month-end adjusting entry to record the salaries earned but unpaid is that salaries expense will be debited $480 and salaries payable will be credited $480

Answer:

The expression that represents the number of materials being distributed this situation is;

Explanation:

Let P and G represent the number of coloured pencils and glue sticks to be distributed;

For 6 tables we have;

Given;

So, we have;

The expression that represents the number of materials being distributed this situation is;

The number of questions on the CUNY Math Assessment Test can vary depending on the specific version of the test administered. However, typically, the CUNY Math Assessment Test consists of multiple-choice questions covering a range of math topics such as algebra, geometry, and trigonometry.

While the exact number of questions can vary, it is common for the CUNY Math Assessment Test to have around 40 to 50 questions. These questions are designed to assess your mathematical knowledge and skills in order to determine your readiness for college-level math courses.

The test is typically timed, and you will have a set amount of time to complete all the questions. It is important to manage your time effectively and pace yourself throughout the test to ensure you have enough time to answer each question.

In order to prepare for the CUNY Math Assessment Test, it is recommended to review and practice a variety of math topics, including algebraic equations, functions, graphs, geometry, and basic trigonometry concepts. Familiarizing yourself with these topics and practicing similar questions can help you become more comfortable with the content and format of the test.

Remember, it's always a good idea to consult official CUNY resources or speak with an academic advisor to get the most up-to-date and accurate information regarding the specific version of the CUNY Math Assessment Test you will be taking.

Overall, the number of questions on the CUNY Math Assessment Test can vary, but typically it consists of around 40 to 50 multiple-choice questions covering various math topics.

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Answer:

1x113= 113, nothing else can equal to 113 unless you estimate ig

Step-by-step explanation:

The solution to the initial value problem is:

y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)

To solve a second-order linear homogeneous differential equation the equation is y′′ 2y′-8y = 0.

Given initial conditions: y(102) = 3 and y′(102) = -12.

To solve this differential equation, we can use the characteristic equation: r^2 + 2r - 8 = 0

Factoring this equation, we get: (r + 4)(r - 2) = 0

So the roots of the characteristic equation are r = -4 and r = 2.

The general solution to the differential equation is:

y(t) = c1 * e^-4t + c2 * e^2t

To find the values of c1 and c2, we can use the initial conditions.

We know that y(102) = 3, so we can substitute t = 2 into the general solution:

3 = c1 * e^-8 + c2 * e^4

We also know that y′(102) = -12, so we can take the derivative of the general solution and substitute t = 2:

y′(t) = -4c1 * e^-4t + 2c2 * e^2t

y′(102) = -4c1 * e^-8 + 2c2 * e^4 = -12

Solving for c1, we get:

c1 = (-3/4) * e^4 + (3/4) * e^-8

Solving for c2, we get:

c2 = (3/8) * e^8 - (3/8) * e^-4

Therefore, the solution to the initial value problem is:

y(t) = (-3/4) * e^(-4t+4) + (3/8) * e^(2t+8)

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ASA Criterion means that the triangles are congruent if the corresponding Angle-Side-Angle is also congruent.

From the the Triangle ABC :

corresponds with ASA.

Likewise from the Triangle DEF :

Since the given figure already states that :

and BC = FE

The other item that will complete the ASA will be :

SAS criterion means that the triangle are congruent if the corresponding Side-Angle-Side are also congruent.

The following corresponds with SAS :

From the triangle ABC :

From the triangle DEF

Here in the given diagram all the sides are equal and the diagonals are perpendicular. So the given parallelogram is a rhombus.

Here the data given are

ABCD is a parallelogram

∠BOC = 90°

So AOB = 180 - ∠BOC ( angle of a straight line is 180°)

∠ AOB = 180-90 = 90°

Also ∠ COD = ∠DOA = 90°

OA = OC, OB= OB ( Diagonals of a parallelogram bisect each other)

So the triangles are congruent. So AB = BC

Similarly ΔBOC and ΔCOD are congruent, BC= CD

Similarly ΔCOD and ΔDOA are congruent, CD= AD

So, AB = BC = CD= DA

Since all sides are equal and diagonals are perpendicular, the given parallelogram is a rhombus.

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The complete question is given as the image below.

Answer:

32.9811320755

Step-by-step explanation:

Written out it is 32.9811320755 but the way i thing that your test or question will take is is 32.98

Answer: \(38.7^{\circ}\)

Step-by-step explanation:

Use a calculator.

Answer:fixed ratio

Step-by-step explanation: :)

This is an illustration of a fixed ratio reinforcement schedule: after a predetermined number of responses, Frances is given a reward (in this case, $1). (every pound of worms).

An example of a reinforcement plan utilized in the behavioral psychology concept of operant conditioning is a fixed ratio reinforcement schedule. A reward or reinforcement is delivered according to this schedule after a predetermined number of actions or responses. As an illustration, a rat might receive a food pellet after every 10 lever presses.

Fixed ratio schedules work well for encouraging high response rates since the subject is driven to keep up the activity in order to earn the reward. Yet, if the reinforcement is stopped, the behavior can become less frequent or cease entirely.

Fixed ratio schedules can also cause behaviors to become rigid or stereotyped because the subject may start concentrating only on the number of responses required to earn the reward and stop considering other options or actions.

Overall, fixed ratio reinforcement regimens can be helpful in teaching both humans and animals to carry out particular tasks, but they should be utilized with caution and consideration for any unexpected consequences.

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Answer:

x ≈ 25.1

Step-by-step explanation:

Using the cosine ratio in the right triangle, that is

cos64° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{11}{x}\) ( multiply both sides by x )

x × cos64° = 11 ( divide both sides by cos64° )

x = \(\frac{11}{cos64}\) ≈ 25.1 (  to the nearest tenth )

Answer:

Divide

Step-by-step explanation:

Using PEMDAS, the first would be parenthesis, but there are none, so we do not use P. Next is E which is exponents, which would be the first thing completed. Then is M and D which is multiplication and division. The division is used which is "dividend by two" as it's the second thing completed.

Hope this helped.

Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

Answer:

If you are finding the equation using two points then the answer is

y = −2 x + 1

If this does not help, just ignore honestly.

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is 0.653, which is equivalent to 65.3%.

It is important to note that this value is based on a random sample of respondents and may not necessarily represent the true proportion of the entire population of Vermont who exercise regularly.

To find the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week, follow these steps:

1. Convert the given percentage (65.3%) to a decimal by dividing by 100: 65.3 / 100 = 0.653
2. Multiply the decimal by the number of participants in the random sample (100 respondents): 0.653 * 100 = 65.3
3. Round the result to the nearest whole number to find the number of participants who exercised: 65.3 ≈ 65
4. Divide the number of participants who exercised (65) by the total number of participants in the random sample (100): 65 / 100 = 0.65

This means that out of the 100 participants sampled from Vermont, 65.3 of them answered "yes" to the question of whether they had exercised for more than 30 minutes a day for three days out of the week.

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.65 or 65%.

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

We can use the following formulas to find the variance of X:

Var(X) = E[X^2] - (E[X])^2

E[X] = p1 + 2p2 + 3p3

E[X^2] = p1 + 4p2 + 9p3

Substituting these expressions into the formula for the variance, we get:

Var(X) = p1 + 4p2 + 9p3 - (p1 + 2p2 + 3p3)^2

Simplifying this expression, we get:

Var(X) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\)

To maximize Var(X), we want to maximize this expression subject to the constraint p1 + p2 + p3 = 1. We can use Lagrange multipliers to find the maximum. Let:

L(p1, p2, p3, λ) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3 + λ(1 - p1 - p2 - p3)\)

Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 2/7, p2 = 3/7, p3 = 2/7, λ = 4/7

Therefore, the values of p1, p2, p3 that maximize Var(X) are p1 = 2/7, p2 = 3/7, and p3 = 2/7.

To minimize Var(X), we want to minimize the expression \(-(p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\) subject to the constraint p1 + p2 + p3 = 1. We can use the same Lagrange multiplier method to find the minimum. Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 0, p2 = 1/3, p3 = 2/3, λ = 2/3

Therefore, the values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

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The original price of the chair was £636.

To calculate the original price of the chair, we can use the formula:

where the discount rate is expressed as a decimal. In this case, the sale price is £540.60 and the discount rate is 15%, or 0.15 as a decimal.

So, plugging in the numbers we get:

Therefore, the original price of the chair was £636.

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Answer:

No

Step-by-step explanation:

3/10 = 6/20 not 2/15

Answer:

14<36

Step-by-step explanation:

5(y=2)^2-2x < (x=3)^2

5(2)^2 < (3)^2

5*2 = 10

10^2 = 20

-----------------------------------------

2(x=3)

2(3)=6

______________________

Put the first part together

20-6 = 14

Other side

3*2 = 6

______________________

Put all of it together

14<6+1 or any number lower than 7