The perimeter of a rectangular field is 298m. If the width of the field is 64m, what is it’s length?

The equation for money collected m for h boxes of chocolate bars sold is m = 30h.

We are given that the band is selling every bar of chocolate for $1.50

Now, they have boxes of chocolate, with every box containing 20 bars of chocolate in them.

Hence if we are going to calculate the amount of money collected on selling one box it will be

20 X $1.5

= $30

We need to find the equation for the amount of money collected based on the number of boxes of chocolate bars sold.

We have been given that money collected should be represented b m while the number of chocolate boxes sold should be represented by h

Now we know that

Money collected = price per box X no.of boxes sold

we have already calculated the price per box hence we get

m = 30h

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Answer:

60 square units

Step-by-step explanation:

Area = (b*h)/2

Half the base: 5 (triangle: 5, h, 13)

a^2 + b^2 = c^2

5^2 + h^2 = 13^2

25 + h^2 = 169

h^2 = 169 - 25

h = sqrt 144

Height = 12

Area = (10*12)/2

Area = 60 square units

The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.

The probability of renting exactly three apartments in a week is given by the Poisson probability function:

\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)

Substituting the values, we get:

\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)

P(X = 3) = (0.09963 * 12.167) / 6

P(X = 3) = 0.2018

Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

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Answer:

2 Less than or equal to x

The inequality is x ≥ 2.

The correct option is B: 2 Less-than-or-equal-to x.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

We have a graph of an inequality in the number line.

In the number line,

2 is at the closed dotted circle.

x = 2

And increasing from 2.

So, the inequality is

x ≥ 2.

Therefore, x ≥ 2 is an inequality.

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Answer:

x<-6

Step-by-step explanation:

-3x>18

Divide by -3, flip the sign since dividing by a negative.

x<-6

Answer:

x < -6

Step-by-step explanation:

The researcher is assessing item equivalence, If a study is in parallel forms of the measurement instrument to the same person. The correct option is C).

When a study introduces parallel forms, the researcher is assessing item equivalence. Item equivalence refers to the extent to which the different forms of the measurement instrument produce similar results for the same individual.

This assessment is crucial in research because it allows researchers to evaluate the consistency and reliability of the measurement instrument across different versions. By administering parallel forms to the same person, any differences in responses can be attributed to individual factors rather than variations in the instrument.

This helps ensure that the instrument is measuring the intended construct consistently and accurately. The correct option is C).

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Answer:

1. 24a + 40

2. 24 - 8d or -8d + 24

3. 18x - 63y

Step-by-step explanation:

1.

multiply the 8 by 3a then by 5

8(3a + 5)

24a + 40

2. multiply the 4 by the 6 and -2d

4(6 - 2d)

24 - 8d or -8d + 24

3. multiply the 9 by the 2x and -7y

9(2x-7y)

18x - 63y

A statistical technique that would allow a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is called factor analysis.

Statistical techniques are methods and procedures used in the collection, analysis, interpretation, and presentation of data. These techniques involve the use of mathematical and statistical models to draw meaningful insights and conclusions from data.

Some common statistical techniques include:

Descriptive statistics: These techniques are used to summarize and describe the key features of a dataset, such as central tendency, variability, and distribution.

Inferential statistics: These techniques are used to make inferences about a larger population based on a sample of data. This involves using probability theory to estimate population parameters and test hypotheses.

Regression analysis: This technique is used to model the relationship between one or more independent variables and a dependent variable.

Hypothesis testing: This technique is used to test the validity of a hypothesis or claim about a population using sample data.

Time series analysis: This technique is used to analyze data that varies over time, such as stock prices or weather patterns.

Cluster analysis: This technique is used to group similar observations together based on their characteristics.

Data mining: This technique involves the use of automated methods to discover patterns and relationships in large datasets.

Statistical techniques are widely used in many fields, including business, economics, social sciences, medicine, and engineering. They are used to make informed decisions, identify trends and patterns, and to understand complex systems.

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\(5\sqrt{3x+1} = 10\\\\\implies \sqrt{3x+1} = \dfrac{10}5 \\\\\implies \sqrt{3x+1} = 2 \\\\\implies 3x +1 = 4\\\\\implies 3x = 4-1 \\\\\implies 3x = 3\\\\\implies x =1\)

Answer:

x = 1

Step-by-step explanation:

Given equation:

\(\dfrac{5(3x+1)^1}{2} =10\)

If a term has "1" as it's exponent, it means that it's the number itself. Therefore, we can remove the "exponent".

\(:\implies\dfrac{5(3x+1)}{2} =10\)

Simplify the distributive property:

\(:\implies\dfrac{15x+5}{2} =10\)

Using cross multiplication:

\(:\implies15x+5} =10 \times 2\)

Simplify the R.H.S:

\(:\implies15x+5} =20\)

Subtract 5 both sides:

\(:\implies15x+5 - 5} =20 - 5\)

Simplify both sides:

\(:\implies15x} =15\)

Divide 15 both sides:

\(:\implies\dfrac{15x}{15} } =\dfrac{15}{15}\)

Simplify both sides:

\(:\implies x= 1\)

Answer:

Find the minimum and maximum values of the objective function subject to the given constrants. Objective function: C= 2x + 3y

Constraints:

x>0

y>0

Comment: These two conditions tell you the answers are in the 1st Quadrant.

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

x +y < 9

Graph the boundary line: y = -x+9

Solutions points are below the boundary line and in the 1st Quadrant.

Answer:

12, sq root of 147, sq root of 210, 15

Step-by-step explanation:

\(\sqrt{147}\) = 12.12

\(\sqrt{210}\) = 14.49

Answer:

12, 147 sq root, 210 square root, 15

Step-by-step explanation:

starts with 12 for being the lowest next is 147, square rooted is 12.12 than 210 square rooted is 14.49, and now we just have 15.

(f.g)(x) = (4x + 6)(-5x) = -20x^2 -30x

ok done. Thank to me :>

Answer:

Step-by-step explanation:

let the money in her purse be $x

1/3 of the money is 1/3x

Since his father gave him $5 and the total amount became $12

the expression for the total amount would be

12= 1/3x+5

We can now solve for x

12-5= 1/3x

1/3x= 7

cross multiply we have

x= 7*3

x= $21

Therefore the money in joes mother's purse is $21

Answer:

5/2

Step-by-step explanation:

alternative = 2 1/2 , 2.5

The solution for the equation given would be x = 2 and x = -1.

To solve the equation 2[x² + 2x + 1] - x² - 4x + 4 = x² - 3x, we can simplify and rearrange the terms as follows:

2x² + 4x + 2 - x² - 4x + 4 = x² - 3x

x² - 3x + 6 = x² - 3x

2x² - 2x - 6 = 0

Dividing both sides by 2, we get:

x² - x - 3 = 0

We can then solve for x by factoring or using the quadratic formula. Factoring gives:

(x - 2)(x + 1) = 0

So, the solutions are x = 2 and x = -1.

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The given sum can be simplified to Σ 3(k+2)2 -7k + 116 where k is an integer running from n2 to n+1-4k+1. To solve this, we can use the summation formula, Sn = (n/2)(a1 + an).

In this case, a1 = 3(n2+2)2 - 7n2 + 116, and an = 3(n+1-4k+1+2)2 - 7(n+1-4k+1) + 116.

Substituting these values into the summation formula gives us: Sn = (n/2)[3(n2+2)2 - 7n2 + 116 + 3(n+1-4k+1+2)2 - 7(n+1-4k+1) + 116]

We can simplify this further to obtain the result: Sn = 3n3+36n2-72n-24k2+128k+276

This is the result for the sum of the given expression. In order to justify each step, it is important to note that we used the summation formula, which can be derived from the definition of the sum. By substituting the values of the first and last terms of the sequence, we obtained the final result.

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The rate of change of f(x, y) = 3xy y2 at the point (1, 3) in the direction v = 2 i − j is (9/√5 i^ + 9/√5 j^).

The rate of change of any function is given by its gradient.

i.e.

∇f(x,y) = df(x,y)/dx i^ +df(x,y)/dy j^ +df(x,y)/dz k^

Here,

f(x,y) is given as 3xy + y²

so,

∇f(x,y) = d{3xy + y²}/dx i^ +d{3xy + y²}/dy j^ +d{3xy + y²}/dz k^

Since, the function has no z components, the k^ component will be 0.

∇f(x,y) = 3y i^ + (3x + 2y) j^

putting the given points, i.e. (1,3) we get,

∇f(x,y) = 9 i^ + 9 j^

Now for calculating the slope in the given direction

we have to divide the magnitude of the direction that is,

∇f(x,y) = (9 i^ + 9 j^)/√(2²+(-1)²)

∇f(x,y) = (9/√5 i^ + 9/√5 j^)

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Answer:

2 candies to each friend

Step-by-step explanation:

This is a division problem. You would do:

10/5 as there are 10 candies to share and 5 friends to give them to. This would yield a result of 2 candies per friend.

The total cost of x number of keychains, K(x), can be expressed as the function K(x) = 750 + 12.50 * (x - 50).

To express the total cost K(x) of x number of keychains as a function of x, we can divide it into two parts: the cost for the first 50 keychains and the cost for the exceeded orders.

For the first 50 keychains, the store charges PHP 15.00 per keychain. So the cost for the first 50 keychains can be calculated as 15 * 50 = PHP 750.00.

For the exceeded orders, where x > 50, the store charges PHP 12.50 per keychain. The number of exceeded orders is x - 50, so the cost for the exceeded orders can be calculated as 12.50 * (x - 50).

To get the total cost K(x), we add the cost for the first 50 keychains and the cost for the exceeded orders:

K(x) = 750 + 12.50 * (x - 50)

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Answer:

65% of the orginal fee or $130.

Step-by-step explanation:

You didn't put the answer options so I am not sure how you want the question to be answered. There are three ways I would write it:

1:  100% = 10% + 25% + 65%

2:  200 = 20 + 50 + 130

3:  200 = (0.1 x 200) + (0.25 x 200) + (0.65 x 200)

All of them basically mean the same thing it is just a matter of how you need it written.

Based on the amount to be paid and the percentage paid in each installment, the expression for the third payment is 65% x 200.

Rodney has to pay $200 in three installments.

The third installment will be:

= Percentage in total - Percentages paid already

= 100% - 10% - 25%

= 65%

The third installment is therefore:

= Percentage to be paid x Amount

= 65% x 200

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Answer: A 3(5x-8)

Step-by-step explanation: 3 times 5x is 15x and 3 times -8 is -24

Below is the answer

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The probability of rolling a number less than 6 and then rolling a number less than 2 is 5/36.

The probability of rolling a number less than 6 on a 6-sided die is 5/6, and the probability of rolling a number less than 2 is 1/6. To find the probability of rolling a number less than 6 and then rolling a number less than 2, we can multiply the probabilities of each event:

P(roll less than 6 and roll less than 2) = P(roll less than 6) * P(roll less than 2)

P(roll less than 6 and roll less than 2) = (5/6) * (1/6)

P(roll less than 6 and roll less than 2) = 5/36

Therefore, the probability of rolling a number less than 6 and then rolling a number less than 2 is 5/36.

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Answer:

A

Step-by-step explanation:

I just took the quiz

Iota is an imaginary unit number that is denoted by i and the value of iota is \(i=\sqrt{-1}\)

Letter A represent \(z^{3}\)

Given that, z = 1 - i

Now finding  \(z^{3}\) ,

                    \(z^{3}=(1-i)(1-i)(1-i)\\\\=(1+i^{2-2i} )(1-i)\\\\=1+i^{2}-3i-i^{3}+2i^{2}\\\\=1-1-3i+i-2\\\\=-2-2i\)

In given diagram, it is observed that Point A is  \(-2-2i\).

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Answer:

about 45%

Step-by-step explanation:

it should be right

Answer:

<BAC = 80

Step-by-step explanation:

All triangle angles equal 180

<BAC = x

x + 50 + 50 = 180

x + 100 = 180

x = 180 - 100

x = 80

Answer:   h=12.8in

a Base edge 15   in

V Volume 960  in³

Using the formula

V=a2h

3

Solving for h

h=3V

a2=3·960

152=12.8in

Step-by-step explanation: