petroleum pollution in oceans stimulates the growth of certain bacteria. an assessment of this growth has been made by counting the bacteria in each of randomly chosen specimens of ocean water (of a fixed size). the counts obtained were as follows.

The phrases that can be represented by the algebraic expression 2x + 1 are;

A: two times a number plus 1

E: double a number added to 1

Algebraic expressions are simply the idea of expressing numbers using letters or alphabets without specifying their actual values.

The algebraic expression is given as;

2x + 1

Where x is the variable

Thus, it means two times a number plus 1 or double a number added to 1

Thus, options A and E are correct.

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Answer:

A and E

Step-by-step explanation:

Let the length of the leg be \(x\). Since the right triangle is isosceles, the length of each leg is \(x\), and thus, by the Pythagorean theorem, the hypotenuse has a length equal to the square root of the sum of the squares of the lengths of the legs, or \(\sqrt{x^2+x^2}=x\sqrt{2}\).

Using this result, we see that to find the length of the hypotenuse, we multiply the length of the leg by \(\sqrt{2}\).

The vat percent is 10%.

Given that s.p.=Rs 450 and s.p with vat =Rs  495.

We want to find Amount of VAT that is how much value added tax is imposed in the selling price.

firstly, we will find Amount of VAT by taking Selling Price (S.P) and subtract it from Selling Price with VAT.

Amount of VAT = (S.P + VAT )- S.P

Amount of VAT = Rs 495 - Rs 450

Amount if VAT = Rs 45

Now, we will find the vat percent by dividing amount of VAT with selling price and multiply with 100, we get

VAT Percent = (Amount of VAT /Selling Price)×100

VAT Percent =(45/450)×100

VAT Percent=10%

Hence, the VAT percentage is 10% when the selling price is Rs. 450 with the VAT selling price Rs 495.

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Answer:

x = 2√58

Step-by-step explanation:

Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs and c is the hypotenuse of a right triangle)

Find the height of the triangle by using the base and hypotenuse of the smaller interior triangle and Pythagoras' Theorem:

   a² + b² = c²

⇒ a² + 6² = (6√2)²

⇒ a² = (6√2)² - 6²

⇒ a² = 36

⇒ a = 6

Now we have the base and height of the larger interior triangle, we can calculate x:

    a² + b² = c²

⇒ 6² + 14² = x²

⇒ x² = 232

⇒ x = √232

⇒ x = 2√58

\(\\ \rm\Rrightarrow \dfrac{6\sqrt{2}}{6}=\dfrac{x}{14}\)

\(\\ \rm\Rrightarrow 6x=84\sqrt{2}\)

\(\\ \rm\Rrightarrow x=14\sqrt{2}\)

Answer:

12p x (15 x 25) I might not be correct :')

Answer:

12p+15x0.25

Step-by-step explanation:

The molecular geometry of o=c=o is linear.

The molecular geometry of o=c=o is linear because it contains two atoms of similar electronegativity (the two oxygen atoms) and one atom of lower electronegativity (the carbon atom).

This means the two oxygen atoms will pull the electrons of the carbon atom towards themselves, creating a linear geometry. The Molecular Geometry Chart can be used to confirm this.

The chart shows that when there are two atoms of similar electronegativity and one atom of lower electronegativity, the molecular geometry is linear.

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The interquartile range of the number of jumps of the 10 students during the competition is 38.

The interquartile range is the difference between the third quartile and the first quartile. The interquartile range is used to determine the variation of a data set.

Th first step is to determine the median of the first half of the dataset. The median of the first half is the first quartile.

First half of the data set: 30, 36, 38, 45, 57

Median = first quartile =  38

The next step is to determine the median of the second half of the dataset. The median of the second half is the third quartile.

Second half of the data set: 60, 77, 86, 88, 88

Median : third quartile =  86

Interquartile range = third quartile - first quartile

86 - 38 = 48

hence ,  interquartile range of the number of jumps of the 10 students during the competition is 38.

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As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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Answer:

I think it's C, but i am not sure about my answer

The company has the total number of employees as 140.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that company has two offices - one in Portlee and one in Queentown.

The ratio of the number of employees at Portlee to the number at Queentown is given as;

3:4

Now we know that 20% of the employees at Portlee are part-time.

25% of the employees at Queentown are part-time.

Therefore, 3x of 20% are part- time

4x of 25%

Then we have 32 part-time employees.

0.6x + 1x = 32

1.6x = 32

x = 32/1.6

x = 20

Hence, the total number of employees the company has

3x + 4x = 7x

7(20) = 140

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Answer:

C.) $9

Step-by-step explanation:

Solution: six friends all use $2-off coupons to buy themselves movie tickets. They spend a total of $42. What is the price of one movie ticket without the coupon? = 7 + 2 = 9 dollars.

Answer:

C, or $9

Step-by-step explanation:

You multiply 6 friends by $2 to get the amount they saved. $12+$42= $54. That is the amount of money they would have spent without the coupons. Dividing $54 by 6 friends to get the price per ticket, you get $9. Each ticket costed $9.

An algebraic expression to represent the situation is y = 32 / x.

An algebraic expression is a set of numbers or variables combined using the operations +, –, × or ÷. Arithmetic expression is an expression which contains only numbers and mathematical operators; and, algebraic expression is an expression which contains variables, numbers and mathematical operators.

In this case, given information are:

Some students equally share 2 baskets of peaches.

Each basket has 16 peaches.

Let the number of students be x.

And, the number of peach each one gets be y.

Then, further information given that there are 16 peaches in each basket.

So, in 2 baskets there will be:

= 16 x 2

= 32 peaches

These 32 peaches are to be shared between x students; thus, each student will get:

y = 32 / x

Hence, the algebraic expression to represent the situation is y = 32 / x.

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Answer:

T/(kV) = P

Step-by-step explanation:

Step 1: Write equation

T = kPV

Step 2: Solve for p

Answer:

  P = T/(kV)

Step-by-step explanation:

Divide by the coefficient of P.

  \(T=kPV\\\\\dfrac{T}{kV}=\dfrac{kPV}{kV}\\\\\dfrac{T}{kV}=P\\\\\boxed{P=\dfrac{T}{kV}}\)

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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Answer:

B 4 is the correct answer

Step-by-step explanation:

b - 12 = - 8

b = 12 - 8

b = 4

The following statement which are true are Kayla's opportunity cost to go to the movie is $9.50 and Tara's total cost of attending the movie is $50.5, option B, D.

Tara earns $8.50 per hour

She is scheduled to work for 4 hours

Total earnings=$8.50 × 4

=$34

Tara's opportunity cost of attending the movie instead of working is $34

Since, a ticket cost $9.50

And she always spend about $7 on snacks

Tara's total cost of going to the movies = opportunity cost of attending the movie + cost of tickets + cost of snacks

=$34 + $9.50 + $7

=$50.5

Opportunity cost refers to the cost of satisfying a want at the expense of another want. It can also be called REAL COST or TRUE COST.

Therefore,

2. Kayla's opportunity cost to go to the movie is $9.50

4. Tara's total cost of attending the movie is $50.5

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Complete question:

Tara earns $8.50 an hour (after taxes) at the pizza place. She is scheduled to work four hours this afternoon. However, her friend Kayla called and asked her if she wants to go to the movie. A ticket to the movie costs $9.50. In addition, she always spends about $7 on snacks.

Which of the following statement are true? Select all that apply.

1. Tara's opportunity cost if she goes to work instead of the movie is $34.

2. Kayla's opportunity cost to go to the movie is $9.50.

3. There is no opportunity cost for Tara to go to the movie.

4. Tara's total cost of attending the movie is $50.5

5. Tara's opportunity cost if she goes to the movie instead of working is $34

Explanation

We are given a right-angled triangle with the following:

We are required to determine the missing side (i.e. the value of x).

We can achieve this by using the Pythagorean theorem as follows:

Hence, the answer is:

The true statement on the absolute values are:

When we make use of absolute value to compare numbers, we are essentially comparing their sizes or quantities, regardless of any negative signs that may be present. Irrespective of their positivity or negativity, the magnitude or quantity of something is what matters. The reason behind this is that the positive and negative counterparts of a number have equal absolute values.

In the case of -14 ° and -8 °, we know that with temperature, the lower the number, the colder it is. This is why -14 ° is colder than -8 °.

When it comes to debt, the larger negative number is more than the smaller negative so - $45 is a greater debt than -$38.

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Answer:

Explanation:

Given the expression:

This can be written as a difference of two squares. But before that, we can rewrite the expression as:

So, as a different of two squares, we write:

The probability that one or more machine failures occur in a given day, given that the company experienced ten failures in the past 100 days, is option c) 0.095.

To calculate the probability of one or more machine failures occurring in a given day, we can use the concept of the complement rule. The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

Given that the company experienced ten failures in the past 100 days, we can calculate the probability of no failures occurring in a day by dividing the number of failure-free days by the total number of days:

No. of failure-free days = Total days - No. of failures = 100 - 10 = 90

Now, the probability of no failures in a day is calculated by dividing the number of failure-free days by the total number of days:

Probability of no failures = No. of failure-free days / Total days = 90 / 100 = 0.9

Finally, to find the probability of one or more failures occurring in a day, we use the complement rule:

Probability of one or more failures = 1 - Probability of no failures = 1 - 0.9 = 0.1

Therefore, the probability that one or more machine failures occur in a given day is 0.1, which corresponds to option c).

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Answer:

5.2

Step-by-step explanation:

adding all the numbers together and dividing it by 10.

Answer:

mean = 5.2

Step-by-step explanation:

The mean (or average) of a group of numbers is defined as the value calculated by adding all the given numbers together and then dividing the result by the number of numbers given.

Therefore,

\(\boxed{\mathrm{mean = \frac{sum \ of \ the \ numbers}{number \ of \ numbers}}}\).

In the question, the numbers given are: 3, 7, 2, 4, 7, 5, 7, 1, 8, and 8.

Therefore,

sum = 3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8

       = 52

There are 10 numbers given in the question. Therefore, using the formula given above, we can calculate the mean:

\(\mathrm{mean = \frac{52}{10}}\)

            \(= \bf 5.2\)

Hence, the mean of the given numbers is 5.2.

Answer:

Definition – What is a cubed root? The cubed root of a number is the number that, when multiplied by itself three times (number x number x number), gives the original number. For example, the cubed root of 27 is 3, as 3 x 3 x 3 = 27. The cubed root of 125 is 5, as 5 x 5 x 5 = 125.

Step-by-step explanation:

Answer:

And so, in fact, we can perform a series of similarity transformations that map to . And so, the answer is yes, triangle would need to be dilated by a scale factor of three, rotated, and then reflected.

Step-by-step explanation:

1) The difference between Einstein's IQ and the mean is 60.

2) Einstein's IQ is 3.75 standard deviations from the mean.

3) Einstein's IQ has a z-score of 3.75.

4) Einstein's z-score is 3.75, which is outside the range of -2 and 2, his IQ is considered unusual.

1) The difference between Einstein's IQ and the mean is calculated as follows:

Einstein's IQ (160) - mean IQ (100) = 60.

So, the difference between Einstein's IQ and the mean is 60.

2) To find how many standard deviations Einstein's IQ is from the mean, divide the difference (60) by the standard

deviation (16): 60 / 16 = 3.75.

Einstein's IQ is 3.75 standard deviations from the mean.

3) To convert Einstein's IQ score to a z-score, use the formula:

z = (x - μ) / σ.

In this case, x = 160 (Einstein's IQ),

μ = 100 (mean), and

σ = 16 (standard deviation).

Plug in the values: z = (160 - 100) / 16 = 60 / 16 = 3.75.

Einstein's IQ has a z-score of 3.75.

4) Usual IQ scores convert to z-scores between -2 and 2.

Since Einstein's z-score is 3.75, which is outside the range of -2 and 2, his IQ is considered unusual.

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Answer:

V = 90π in³ or 282.7 in³

Step-by-step explanation:

The formula for the volume of a cylinder is V = hπr²

Since we are given height(h) and the radius(r), we simply plug these in and solve for the volume(V).

V = (10)π(3²)

V = (10)π(9)

V = 90π in³ or 282.7 in³

Answer:

-1/2

Step-by-step explanation:

1. First, let's take two points from the line.

2. Next, to find the slope, we use the formula \(\frac{y_2-y_1}{x_2-x_1}\) , plug in the values, and simplify.

Therefore, the slope is -1/2.

Answer:

1 Down and 2 Over

Step-by-step explanation:

You should be able to move down one and two times over if you calculate with your hands. This should lead to the following point, and so on. Hope it helps!

Answer:

-2, 4

-1, -2

0, 0

1, 2

2, 4

Step-by-step explanation:

X. Y

-2 = 4

-1 = 2

0 = 0

1 = -2

2 = -4

6x² - 31 x + 40, after factorization we get: (2x - 5) (3x - 8).

correct option: a

Expanding brackets is done in reverse when factorising. By eliminating the most common factors, an expression is fully factored when it is enclosed in brackets. The simplest method of factorization is to identify the term in the equation with the largest common factor. The Grouping technique, the Difference in Two Squares, the Sum or Difference in Cubes, and the Greatest Common Factors (GCF) are the four primary methods of factoring.

Similar to this, factoring is a very useful technique in algebra that is utilised at all levels. Additionally to, of course, simplifying complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.

= 6x² - 31 x+40

= 6x² - 15 x - 16 x +40

= 3x (2x - 5) - 8 (2x - 5)

= (2x - 5) (3x - 8)

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Answer:

B. 4

Step-by-step explanation:

\(7 \sqrt{7x} = \sqrt{49 \times 7x} \)

49 × 7x = 343x

14√7 = √(1372)

1372 ÷ 343 = 4 this is the vaule of x.