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The cost of building a house with the area 5,425 square feet is $763,125.

The given function is C(x)=85,000+125x.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, x represents the area of a house is 5,425 square feet.

Put x=5425 in the given function, that is

The total cost = C(5425)=85,000+125 × 5425

= $763,125

Therefore, the cost of building a house with the area 5,425 square feet is $763,125.

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It is not true that whenever  we add two irrational numbers we get an irrational number.

Since we know a rational number is a number in the form, p/q, where q ≠ 0. Let  take two numbers : 2 + √3 & 2 - √3

The sum of the two numbers be :

= 2 + √3 + 2 - √3

= 4

Here the number is rational, taking another irrational numbers :  2 + √5 & 2 - √3

= 2 + √5 + 2 - √3

= 4 + √5 - √3,  where it is an irrational number.

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Answer:

9:12

Step-by-step explanation:

you take 3 x 3 = 9

then you take 4 x 3= 12

so the ratio would be 9:12

The ratio which describes ratio of teaspoons of sugar to salt is 9:12.

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is. A ratio divides two quantities in order to compare them.

As per the information given in the question,

The recipe requires 3 teaspoons of sugar and 4 teaspoons of salt, then the ratio will be ⇒ 3:4

Then, the mixture gets tripled,

Now the ratio will be,

(3 × 3) : (4 × 3) = (9 : 12)

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Answer:

8x^2-7x-4

Step-by-step explanation:

Answer:

8x^2 - 7x -4

Step-by-step explanation:

Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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Answer:

b

Step-by-step explanation:

cause u are using 3 gallons which is taking away

Answer:

the answer is only 3

Step-by-step explanation:

you read all of them and you make it an equation and if it is negative or subtraction that would be your answer

Frequency = 14

Probability = 0.28

The sample size is given to be 50

Frequency must sum to 50

Let the missing frequency be x

6 + x + 22 + 8 = 50

x + 36 = 50

x = 50 - 36 = 14

The corresponding probability for the frequency above is:

14/50 = 0.28

Frequency = 14

Probability = 0.28

The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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-1 (false)
The subspace of even polynomials of degree at most n consists of polynomials that satisfy the property f(-x) = f(x) for all x. The subspace of odd polynomials of degree at most n consists of polynomials that satisfy the property f(-x) = -f(x) for all x.

To determine if Pn(R) is the direct sum of these two subspaces, we need to check if their intersection is only the zero polynomial. However, their intersection is not just the zero polynomial; it includes all constant polynomials. Therefore, Pn(R) is not the direct sum of these two subspaces.

Therefore, the answer is -1 (false).

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The point of intersection of the two lines is at (1,-1)

The given system of expression is shown below

x - 2y = 3

5x + 3y = 2

The solution to the system of equation is the point of intersection

From equation 1

x = 3 + 2y

Substitute into 2

5(3+2y) + 3y = 2

15 +10y + 3y = 2

13y = -13

y = -1

Substitute y = -1 into 3

x = 3 + 2y

x = 3+(-2)

x = 1

Hence the point of intersection of the two lines is at (1,-1)

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Answer:

3(z+3) = 3z + 9 if thats what your asking

Step-by-step explanation:

The fractional equivalent of the repeating decimal 0.2 is 2/9

From the question, we have the following parameters that can be used in our computation:

Repeating decimal = 0.2

Represent properly

So, we have

Repeating decimal = 0.2222

Express as fraction

So, we have

Fraction = 2/(10 - n)

In this case

n = 1

So, we have

Fraction = 2/(10 - 1)

Evaluate

Fraction = 2/9

Hence, the fractional equivalent is 2/9

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When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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Answer:

11/16

I hope this helps ^^

In this case, the first two components are multiples \((4 = -2 * -2, 6 = -3 * -2)\), so if h is \(-16 (8 * -2),\) the vectors are scalar multiples, and thus linearly dependent. For all other values of h, the vectors are linearly independent.

To find the transpose of a matrix, interchange its rows and columns. The standard matrix of a linear transformation T, which rotates points through 3/4 pi radians counterclockwise, can be given as:

\([cos(3/4 pi) -sin(3/4 pi)][sin(3/4 pi)  cos(3/4 pi)]\)

To find the matrix product AB, first check if the dimensions are compatible. If not, AB is undefined.

To find the inverse of a matrix, check if it is invertible. If not, the matrix does not have an inverse.

To determine if columns of a matrix form a linearly independent set, analyze the solutions of Ax = 0. If it has only the trivial solution, the columns are linearly independent. If it has more than one solution, they are not linearly independent.

For the vectors [-2 -3 8] and [4 6 h] to be linearly independent, they must not be scalar multiples of each other.

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Answer:

b

Step-by-step explanation:

Answer:

Chloe will earn $100 outright plus $7 dollars for every lap she swims for her school.

Step-by-step explanation:

We can write 2 equations from the information given.

Let the amount invested in CD be "x" and the amount invested in bond be "y".

The total amount invested is $600,000. Thus, we can write,

The CD pays 2% (0.02) and the bond pays 8.5% (0.085). Total interest needed is $27,000. Thus, we can craft another equation,

Solving the first equation for "x", we can substitute it into the second equation and solve for "y" first. The steps are shown below:

Now, we can find "x",

Rounded to the nearest dollar, we write our answer >>>

The perimeter of the rectangle is (29.5t+7)feet

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.

To find the perimeter of the rectangle we add a the sides together i.e

p = l+l+w+w

p = 2(l+w)

p =2 ( 8.25t - 6.5+ 6.5t + 10)

p = 2( 14.75t + 3.5)

p = (29.5t + 7) feet

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Answer:

19 - R = C

7

Step-by-step explanation:

Let R = the number of cars rented

Let C = the number of cars left

19 - R = C

19 - 12 = 7

The slope of the regression line predicting y from x is 0.30.

Given that,

x              y

29          215

62          225

75          173

99         129

108        111

So, the coordinate points are (29, 215) and (62, 225)

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope = (225-215)/62-29)

= 10/33

= 0.30

Therefore, the slope of the regression line predicting y from x is 0.30.

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==========================================================

Explanation:

Refer to the diagram below. I've added the variables x, y and z. The goal is to find x. For now, let's find y.

Focus on the larger triangle. The three angles of any triangle must add to 180.

46+64+y = 180

110+y = 180

y = 180-110

y = 70

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

Next, we'll find the angle z

The three angles y = 70, 49, and z all form a straight angle of 180 degrees.

y+49+z = 180

70+49+z = 180

119+z = 180

z = 180-119

z = 61

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

Now we can find angle x. Focus on the smaller triangle

z+52+x = 180

61+52+x = 180

113+x = 180

x = 180-113

x = 67 which points us to choice C as the final answer.

Step 1

Given; A frequency table that shows the number of hours of sleep that each staff member of Tia's Toy store got.

Required; To find how many employees work at Tia's Toy store.

Step 2

To find how many employees work at Tia's Toy store we sum the column of the number of employees

Therefore, the number of employees that work at Tia's Toy store is 9

Answer = 9 employees

Answer:

9 Employees

Step-by-step explanation:

So, all we have to do to solve this problem is, add the number of employees up, to get our total and answer.

1 + 0 + 4 + 2 + 1 + 1 = 9

Therefore, 9 employees work at Tia's toy store.

Happy Holidays!

Answer:

Step-by-step explanation:

12,787

a. ^p^ represents the proportion of adults who chose chocolate pie, ^q^ represents the proportion of adults who did not choose chocolate pie, n represents the sample size, E represents the margin of error, and p represents the population proportion.

b. The value of α for a 99.99% confidence level is 0.0001.

a. ^p^ represents the sample proportion of adults who chose chocolate pie, ^q^ represents the proportion of adults who did not choose chocolate pie (1 - ^p^), n represents the sample size of 1500, E represents the margin of error of ±3 percentage points (0.03), and p represents the population proportion of adults who choose chocolate pie.

b. To find the value of α for a 99.99% confidence level, we need to subtract the confidence level from 100% to get the level of significance, which is 0.0001. This means that there is a 0.0001 probability of rejecting the null hypothesis when it is actually true.

The level of significance (α) is used to determine the critical value for the test statistic, which is then used to determine whether or not to reject the null hypothesis.

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Applying the linear pair theorem and the sum of interior angles of hexagon, we have:

Angle 7 = 92°

Angle 1 = 107°

According to the linear pair theorem/postulate, when two angles lie on a straight line, the sum of their measures equals 180 degrees.

Angle 7 lie on a straight line with 88°, therefore, applying the linear pair theorem, we have:

Angle 7 + 88 = 180

Subtract both sides by 88

Angle 7 + 88 - 88 = 180 - 88

Angle 7 = 92°

Also, using the linear pair theorem, we have:

Angle 5 = 180 - 64

Angle 5 = 116°

Angle 3 = 180 - 57

Angle 3 = 123°

Sum of interior angles of hexagon equals 720°, therefore:

Angle 1 + angle 3 + angle 5 + angle 7 + 118 + 164 = 720°

Plug in the known values

Angle 1 + 123 + 116 + 92 + 118 + 164 = 720

Angle 1 + 613 = 720

Subtract both sides by 613

Angle 1 + 613 - 613 = 720 - 613

Angle 1 = 107°

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The marginal profit for producing x units is given by the derivative of the profit function, which is -1.1x + 3000.

The given profit function is P = -0.55x^2 + 3000x - 1150000. To find the marginal profit, we need to take the derivative of the profit function with respect to x, which gives us dP/dx = -1.1x + 3000.

This derivative represents the rate of change of profit with respect to the number of units produced.

The coefficient of x (-1.1) represents the decrease in profit as the number of units increases, and the constant term (3000) represents the additional profit generated for each unit produced.

Therefore, the marginal profit for producing x units is given by -1.1x + 3000 dollars per unit.

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Answer:

\(A = 15\)   \(B = 20\)   \(C = 25\)

\(D = 30\)   \(E = 40\)   \(F = 50\)

\(D = 3\)    \(E = 4\)     \(F = 5\)

Step-by-step explanation:

Given

Similar Triangles: ABC and DEF

\(A = 15\)

\(B = 20\)

\(C = 25\)

Required

Determine the sides of DEF

No options were given, so I will solve on a general terms.

Since both triangles are similar, then the following relationship exists.

DEF = ABC * n

i.e.

\(D = A * n\)    \(E = B * n\)     \(F = C * n\)

Where

\(n = Scale\ Factor\)

Assume n = 2.

So, we have:

\(D = A * n\)    

\(D =15 *2\)

\(D = 30\)

\(E = B * n\)    

\(E = 20 * 2\)

\(E = 40\)

\(F = C * n\)

\(F = 25 * 2\)

\(F = 50\)

Assume \(n = \frac{1}{5}.\)

So, we have:

\(D = A * n\)    

\(D =15 *\frac{1}{5}\)

\(D = 3\)

\(E = B * n\)    

\(E = 20 * \frac{1}{5}\)

\(E = 4\)

\(F = C * n\)

\(F = 25 * \frac{1}{5}\)

\(F = 5\)

So, the possible sides are:

\(A = 15\)   \(B = 20\)   \(C = 25\)

\(D = 30\)   \(E = 40\)   \(F = 50\)

\(D = 3\)    \(E = 4\)     \(F = 5\)