a school community had planned to reduced the number of grade 9 students per class room by constructing additional class rooms. how ever ,they constructed 4 less rooms than they planned.as the result the number of students per class was 10 more than they planned. if there are 1200 grade 9 students in the school,determine the current number of class rooms and the number of students per class​

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Answer:

(5z +2) (z+1)

Step-by-step explanation:

5z^2 +7z +2

(5z +2) (z+1)

The first term when multiplied out is 5z^2  The last term is 2

The middle term is 2z+5z = 7z so this is the correct factorization

Answer:

y=150x

Step-by-step explanation:

y=mx+b

150 would be the slope (m)

0 would be the y intercept(b)

If x represents minutes the equation would be y=150x

The particular solution for the differential equation r(x) = 6x\(e^{(3x)}\) can be expressed as (A\(x^{2}\) + Bx + C)\(e^{(3x)}\), where A, B, and C are constants to be determined.

In the particular solution, we assume the form of the solution to be a polynomial multiplied by the exponential term \(e^{(3x)}\). Since the right-hand side of the equation is a product of x and \(e^{(3x)}\), we consider a second-degree polynomial A\(x^{2}\) + Bx + C to capture these terms. The constants A, B, and C are determined by substituting the assumed solution into the original differential equation and solving for the coefficients.

By differentiating the particular solution twice, we obtain the derivatives (2A + 6Ax + 3B\(x^{2}\) + 3B + 6C\(x^{2}\) + 6C)\(e^{(3x)}\). Setting this equal to the given function 6x\(e^{(3x)}\), we can equate the coefficients of like terms on both sides to determine the values of A, B, and C. Once we have these constants, we can write the particular solution in the desired form: (A\(x^{2}\) + Bx + C)\(e^{(3x)}\).

Note that the particular solution represents a specific solution that satisfies the given differential equation. It is obtained by adding the complementary solution (the solution to the homogeneous equation) to the particular solution.

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Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

2×2=1

3×2=6

4/6-1/6= 3/6 = 1/2

Answer:

The anwer is 1/6

Step-by-step explanation:

if you multiply the 3 by 2 it is 6 and then take away 1 from 2 and the anwer is 1/6

Answer: A

Step-by-step explanation:

\(m\angle ABC=59^{\circ}\) by the inscribed angle theorem.

Therefore, the value of the line integral is approximately 21.898.

In mathematics, an integral is a mathematical concept that expresses the area or accumulated quantity of a function plotted along an axis. It is a fundamental concept in calculus, which is a branch of mathematics that deals with the study of continuous change. An integral is represented by the symbol ∫, and it can be used to calculate various quantities, such as area, volume, and the center of mass. Integrals are used in many areas of mathematics, physics, and engineering to solve a wide range of problems, including optimization, differential equations, and probability theory.

Here,

First, we need to parameterize the curve C. Since C is the parabola y = x² between (0,0) and (4,16), we can let x = t and y = t² for t between 0 and 4.

Then, dx/dt = 1 and dy/dt = 2t.

Substituting into the line integral, we get:

∫C -y sin(x) dx + cos(x) dy = ∫0⁴ -t² sin(t) dt + cos(t) (2t) dt

Using integration by parts on the first term, we get:

=-∫0⁴ (-t² cos(t) dt + 2t sin(t) dt) + cos(4) (2(4)) - cos(0) (2(0))

Simplifying and evaluating, we get:

=-12 cos(4) - 8 sin(4) + 8

=21.898

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Answer:

the second one ( - 3, -6)

Step-by-step explanation:

I used the method of substitution

Answer:

(-3, -6)

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Use order of operations (PEMDAS) to simplify and solve algebraic equations:

P - Parentheses: Simplify all parentheses in the equation first.
E - Exponents: Evaluate all exponential expressions in the equation next.
M/D - Multiplication/Division: After P and E, Multiplication in the equation comes next. These are interchangeable, so if these are the only operations left, calculate in the direction left to right.
A/S - Addition/Subtraction: After everything else has been done, move on to Addition/Subtraction.  These two are also interchangeable, so you must also calculate in the direction left to right.

First, implement the order of operations to simplify the equation:

2²(x + 3) + 9 - 5 = 32 --- Evaluate the exponent.

4(x + 3) + 9 - 5 = 32 --- Use the Distributive Property to multiply.

4x + 12 + 9 - 5 = 32 --- Add/Subtract (Combine like terms).

4x + 16 = 32

Next, isolate the variable x to solve for its value:

4x + 16 = 32 --- Subtract 16 from both sides of the equation.

4x = 16 --- Divide both sides of the equation by 4 to get the value of x.

x = 4

To confirm that x = 4, you can substitute x for 4 in the original equation and see if both sides of the equation are equal:

2²[(4) + 3] + 9 - 5 = 32 --- Simplify the parentheses.

2²(7) + 9 - 5 = 32 --- Evaluate the exponent.

4(7) + 9 - 5 = 32 --- Multiply.

28 + 9 - 5 = 32 --- Simplify the equation using Addition/Subtraction.

32 = 32

After using substitution, we can confirm that x = 4.

To solve for the x-variable in a linear equation, we will need to isolate it on one side of the equation. If the x-variable is inside a parenthesis, we will need to open the parenthesis first, then isolate the variable. To solve/simplify the equation, we will need to use PEMDAS. It is a common method used to simplify equations and inequalities through priorities.

The word "PEMDAS" is a shortened word of "Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction". We follow this order (left-right) to simplify algebraic terms. Since parenthesis is the first priority, we would simplify the expression inside the parentheses. There are two exceptions to this priority in PEMDAS. (1) One of the terms in the expression is a variable, so the expression cannot be simplified, or (2) if there was no parenthesis in the first place. The next priority is "Exponents". This priority is used if there are any exponents used in the equation. The only exception to this priority is when there are no exponents used in the equation. The next priority is "Multiplication". This means that you have to simplify any products "multiplying terms" first. The only exception to this is when there are no terms being multiplied. The next priority is "Division". This priority tells that we need to simplify any division occurring the equation next. There is only one exception to this priority. Only possible if there is no division occurring in the equation. Then, we have "addition" as our 5th priority. This priority states that simplifying any expression that is being added next. The only exception to this priority is when there are no terms being added. The last and final priority is subtraction. This priority states that simplify any expression that is being subtracted. There is no exception to this priority.

Simplifying the equation using PEMDAS:

We have the following equation: 2²(x + 3) + 9 - 5 = 32

Let us simplify using our first priority. Unfortunately, there is a variable inside the parenthesis. Therefore, we can't simplify the expression inside the parenthesis. Let us now simplify using out second priority. We can see a term outside the parenthesis "2²". Since that term has an exponent, let us simplify that term! Eventually, the term will simplify to 4.

Before we move onto the next priority, let us open the parenthesis as we need to isolate the x-variable. This basically means that we need to simplify the distributive property. To simplify the distributive property, we need to multiply the term outside the parenthesis to all the terms inside the parenthesis. So, we have the following simplified equation:

Our next priority is multiplication. So, let us simplify any products occurring in the equation. We can see 4 being multiplied to 3. Therefore, let us simplify that term! Simplifying that term basically gives us 12. So:

Now, our next priority is division. However, we do not see any division occurring in the equation. Therefore, this follows the exception of the division priority in PEMDAS. So, let us move on to the next priority.

The next priority is addition. We can see 12 being added to 9. Therefore, let us simplify the expression. Simplifying that expression gives us 21. So:

The last and final priority is subtraction. We can see 5 being subtracted from 21. Therefore, let us simplify the expression, which gives us 16. So:

Solving for the x-variable by isolating it:

Now, let us isolate the x-variable to determine its value. This can be done by subtracting 16 on both sides of the equation. Then, we can divide 4 both sides to cancel out the coefficient of x.

Therefore, the value of x in the equation is 4.

While linear regression can be a useful tool for prediction, it is important to consider the quality of the data, assess the linearity assumption, and be cautious when extrapolating beyond the observed data range.

This is an example of using linear regression to predict the weight of a kitten at a specific time (10 weeks in this case) based on the given linear model ŷ = 1.7 + 1.48t.

Using linear regression to make predictions is a common practice and can provide reasonable estimates in many cases. However, whether it is considered a best practice for prediction depends on various factors. Here are a few considerations:

Data quality: The accuracy and reliability of the predictions heavily depend on the quality of the data used to build the linear model. If the data used for training the model is representative and accurately reflects the underlying relationship, the predictions are likely to be more reliable.

Linearity assumption: Linear regression assumes a linear relationship between the predictor variable (in this case, time) and the response variable (kitten weight). If the relationship is not truly linear, the predictions may be less accurate. It is important to assess the linearity assumption and consider alternative models if needed.

Extrapolation: When making predictions outside the range of the observed data (such as predicting the weight at 10 weeks when the data only goes up to 8 weeks), caution should be exercised. Extrapolating beyond the observed range can introduce more uncertainty and may lead to less accurate predictions.

In summary, while linear regression can be a useful tool for prediction, it is important to consider the quality of the data, assess the linearity assumption, and be cautious when extrapolating beyond the observed data range.

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Answer:

$1.51

Step-by-step explanation:

To find how much money Lisa has left, subtract the money she spent from how much money she started with.

\(4.26 - 2.75=1.51\)

Therefore, Lisa has $1.51 left.

Answer:

$16.22

Step-by-step explanation:

When 18 dollars is discounted by 15%, we first need to find what 15% of 18 is. 18 times .15 is 2.7, and 18-2.7 is 15.3.

Then, we need to find the sales tax, which applies to the discounted price. 15.3 times 0.06 is 0.918. Add that to 15.3 and you get 16.218, or about $16.22. Hope this helped! :D

Answer: 8¹⁰

Explanation: Since these two powers have the same base of 8, you can

multiply them together by simply adding their exponents to get 8¹⁰.

A common mistake in this problem would be to

multiply the bases together and give an answer of 64¹⁰.

It's important to understand however that the 8's can't be

multiplied together because they are not coefficients, they are bases.

When applying your exponent rules, your base will never change.

When the bill came, she would need to pay Millersburg sales tax of 8% and would want to leave a 15% tip on the original $300. Including tax and tip, Camilla's meal cost $369.

Given that,

Original Meal Cost: $300

Sales Tax: 8% of the original meal cost

Tip: 15% of the original meal cost

Total Cost: Sum of the original meal cost, sales tax, and tip

Original Meal Cost = $300

Sales Tax = 8% of $300 = 0.08 * $300 = $24

Tip = 15% of $300 = 0.15 * $300 = $45

Total Cost = Original Meal Cost + Sales Tax + Tip

Total Cost = $300 + $24 + $45 = $369

Including tax and tip, Camilla's meal cost $369.

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Answer:

sin Z = 9 / 15

cos Z = 12 / 15

tan Z = 9 / 12

Step-by-step explanation:

opposite of Z = 9

adjacent of Z = 12

hypotenuse = 15

sin = opp / hyp

so sin Z = 9 / 15

cos = adj / hyp

so cos Z = 12 / 15

tan = opp / adj

so tan Z = 9/12

Answer:

45°

Step-by-step explanation:

MA is the diameter of the circle.

\( \therefore m\widehat {MTA} =180\degree \)

\( m\widehat {TA} =m\widehat {MTA} -m\widehat {MT} \)

\( \therefore m\widehat {MT} =180\degree -45\degree \)

\( \therefore m\widehat {MT} =135\degree \)

\( m\angle S =\frac{1}{2} (135-45)\degree \)

\( m\angle S =\frac{1}{2} \times 90\degree \)

\( m\angle S =45\degree \)

Answer: There are a few different ways to approach this problem, but one common method is to use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we want to find the probability of at least one psychologist being chosen, which is the same as 1 minus the probability of no psychologists being chosen.

To find the probability of no psychologists being chosen, we first need to calculate the total number of ways to choose 3 people from a group of 54, which is:

54 choose 3 = 54! / (3! * 51!) = 19,958

Then we need to find the number of ways to choose 3 psychiatrists from a group of 24, which is:

24 choose 3 = 24! / (3! * 21!) = 1,344

Now, we can use these values to calculate the probability of no psychologists being chosen:

P(no psychologists) = (24 choose 3) / (54 choose 3) = 1,344 / 19,958 = 0.067 or 6.7%

Finally, we can use the complement rule to find the probability of at least one psychologist being chosen:

P(at least one psychologist) = 1 - P(no psychologists) = 1 - 0.067 = 0.93 or 93%

So the probability that at least one psychologist is chosen from the conference is 93%

Step-by-step explanation:

Answer:

2x + (x + 2)

Step-by-step explanation:

Let the number = x

"twice a number" means 2x

"increased by the sum of the same number and five" means to add x + 5, so the expression is

2x + (x + 2)

Answer:

x=149

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

-2/3a + 5/6a - 1/6

-2/3a + 5/6a = 1/6

1/6 - 1/6 = 0

Another root is also irrational, and if a quadratic equation with integer coefficients and two distinct roots has one irrational root then another root is also irrational

If a quadratic equation with integer coefficients and two distinct roots has one irrational root then another root is also irrational.

Any equation of the ax² + bx + c = 0 form   where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation.

Let assume quadratic equation is:

ax² + bx + c = 0

Given that coefficients are integer and roots are distinct,

we know root of quadratic equation are,

x = -b±√b²-4ac/2a

As roots are distinct b²-4ac > 0

and one root is irrational so b²-4ac is not a perfect square,

Hence another root is also irrational, and if a quadratic equation with integer coefficients and two distinct roots has one irrational root then another root is also irrational.

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using Indices we can simplify the square root of 10,000,000 using powers of ten is: \(10^{7/2}\)

Indices in mathematics can be defined as a value that takes up in index form but still retain its magnitude.

It is writing big or complicated values in a simpler and smaller way.

Indices is so important for simplicity purposes.

in conclusion, using Indices we can simplify the square root of 10,000,000 using powers of ten is: \(10^{7/2}\)

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Answer:

B 1233 ft^2

Step-by-step explanation:

I hope this is right

ANSWER:

Loan A requires Bryce to pay less by $1,133.52

EXPLANATION:

For bank A, we're given;

Length of loan in years(t) = 6 years

Annual interest rate(r) = 8% = 8/100 = 0.08

Loan payment(PMT) = $497.94

Number of compounds per year(n) = 12

We can go ahead and determine the loan amount using the below formula as seen below;

So we can see that Bryce will pay back;

For bank B, we're given;

Length of loan in years(t) = 10 years

Annual interest rate(r) = 5.5% = 5.5/100 = 0.055

Loan payment(PMT) = $308.21

Number of compounds per year(n) = 12

We can go ahead and determine the loan amount using the below formula as seen below;

So we can see that Bryce will pay back;

We can see that Bryce will pay back $35,851.68 for Loan A and $36,985.20 for Loan B, so Loan A requires Bryce to pay less and by $1,133.52

Answer:

4

Step-by-step explanation:

46+4 = 50

50/5 = 10

Answer:

y = (1/6)x - 5/3

Step-by-step explanation:

Please find the attachment for detail

Answer:

7.84  ×  10 ^7

Step-by-step explanation:

The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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The solution to the system of equation is (-1, -6)

Given the system of equations

2x - 3y = 16

5x - 3y = 13

Subtract to have:

2x-5x = 16 - 13

-3x = 3

x = -3/3

x = -1

Substitute x = -1 into 1 to have:

2(-1) - 3y = 16

-2 - 3y = 16

-3y = 16 + 2

-3y = 18

y = -6

Hence the solution to the system of equation is (-1, -6)

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