(a) A house costs 36% more today than when it
was built. If the cost of the house when it was
built was $333 000, what is the cost today?

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Answer:

The ratio of girls to total students is 12:30, which can be simplified to 2:5.

Step-by-step explanation:

You can express the ratio in different ways by using the same numbers, for example, you could say that for every 2 girls, there are 5 total students, or that for every 5 total students, 2 of them are girls.

Answer:

A;-6

B;-8

C;-2

D;-14

E;-1

F;2

G;5

H;0

The ordered pair (-5, -4) does not satisfy both equations simultaneously, it is not a solution to the system.

To check whether the ordered pair (-5, -4) is a solution of the system of equations:

1) 3x - y = -11

2) 2x - 2y = -3

We substitute x = -5 and y = -4 into both equations and check if the equations hold true.

For equation 1:

3(-5) - (-4) = -11

-15 + 4 = -11

-11 = -11

The equation is satisfied.

For equation 2:

2(-5) - 2(-4) = -3

-10 + 8 = -3

-2 = -3

The equation is not satisfied.

The ordered pair (-5, -4) does not satisfy both equations simultaneously, it is not a solution to the system.

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Given:

The function \(g(x)\) doubles the square of the input and then subtracts 13.

To find:

The value of \(g(3)\).

Solution:

Let \(x\) be the input value.

The square of the input is \(x^2\).

Doubles the square of the input \(2x^2\).

Doubles the square of the input and then subtracts 13, i.e., \(2x^2-13\).

So, the function is:

\(g(x)=2x^2-13\)

Putting \(x=3\) in the above function, we get

\(g(3)=2(3)^2-13\)

\(g(3)=2(9)-13\)

\(g(3)=18-13\)

\(g(3)=5\)

Therefore, the value of \(g(3)\) is 5.

In the given case, where data was collected for a city that indicates that crime increases as median income decreases, and the relationship was moderately strong, an appropriate value for the correlation is the Pearson correlation coefficient. Pearson's correlation coefficient is a measure of the strength of a linear relationship between two variables.

It is a statistical measure that quantifies the degree of association between two variables, in this case, crime and median income. The Pearson correlation coefficient is a number between -1 and 1, where -1 indicates a perfectly negative correlation, 0 indicates no correlation, and 1 indicates a perfectly positive correlation. In the given case, as the relationship was moderately strong, the appropriate value for the correlation would be close to -1.

To find the Pearson correlation coefficient between crime and median income, we use the following formula:

r = (NΣxy - (Σx)(Σy)) / sqrt((NΣx² - (Σx)²)(NΣy² - (Σy)²))

Where,r = Pearson correlation coefficient, N = Number of pairs of scores, x = Scores on the independent variable (Median Income), y = Scores on the dependent variable (Crime), Σ = Sum of the values in parentheses

The correlation coefficient will be between -1 and 1. The closer the value is to -1 or 1, the stronger the correlation. The closer the value is to 0, the weaker the correlation.

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Answer:

g(5) = -19

Step-by-step explanation:

Substitute 5 for x in the equation

Plug in 5 for the x's and get g(x)=-3(5)-4 and then -15-4 which is -19 so g(x)=-19

Answer:

h = -3y + 2x

Step-by-step explanation:

Add 4x to both sides of the equation.

2h = −6y + 4x

Divide each term in 2h = −6y + 4x by 2 and simplify.

Divide each term in 2h = −6y + 4x by 2.

2h/2 = -6y/2 + 4x/2

Simplify the left side.

h = −6y/2 + 4x/2

Simplify the right side.
Simplify each term.
Cancel the common factor of −6 and 2.

h = -3y+2(2x)/2

Cancel the common factors.
Factor 2 out of 2.

h = -3y+2(2x)/2(1)
Cancel the common factor

h = -3y+2(2x)/2(1)
Rewrite the expression
h = -3y + 2x/1

Divide 2x by 1.
h = -3y + 2x

hopefully its right LOLZ

Answer:

x=9

Step-by-step explanation:

7x = 4x + 27

subtract 4x on both sides

3x=27

divide 3 on both sides

x=9

plug in

7(9)=63

4(9)+27=63

63=63

Answer:

7x= 4x+27

X = 9....9 is ur answer

Answer:

Use pythagoras theorem

Therefore, the largest region on which the function is defined is option 1: All points not on the cylinder \(x^2 + z^2 = 2.\)

From the given function, we can see that the denominator of the fraction should be nonzero, i.e., \((x^2 + z^2 - 2) = 0\), in order to avoid division by zero.

All points not on the cylinder \(x^2 + z^2 = 2\): The function is defined for all points in 3D space except for those lying on the cylinder \(x^2 + z^2 = 2.\) This region includes all points outside the cylinder.

All points on the cylinder \(x^2 + z^2 = 2\): The function is not defined for any points lying on the cylinder \(x^2 + z^2 = 2\) because it would result in a division by zero.

All points on the plane z = 2: The function is defined for all points lying on the plane z = 2 since it does not violate the condition \((x^2 + z^2 - 2) =0.\)

All points not on the plane z = 2: The function is defined for all points not lying on the plane z = 2.

All points not on the planes x = ±√2 and z = ±√2: The function is defined for all points except those lying on the planes x = ±√2 and z = ±√2 since they would result in division by zero.

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The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

Answer:

Step-by-step explanation:

I see three equations that represents the first step. All the others (I think) have flaws of one kind or another.

Third

The third one divides both sides of the equation by 3. All that remains on the left is what is inside the brackets. 24/3 becomes 8 which what equation 3 says.

x + 6 = 24/3

x + 6 = 8

Fourth

Shows how the distributive property is performed. It does this with great care. The right side is not affected.

3*x + 6*3 = 24       is what is the result. It is a good first step.

Five

This one is a little iffy. It is more like the second step. You have taken the fourth choice and removed the brackets.  If you can do this in your head, I think it counts.  I'm not sure how to answer what you should do. You're darned if you do and darned if you don't. My opinion is that it is perfectly OK but your marker may not agree.

Answer:

Step-by-step explanation:

45 degrees. See inset photo of a right 90 degree isosceles triangle

The probability that their first child will have kidney disease is 1/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

Both parents must be heterozygous to have a 1/4 chance of having an

affected child. Parent 2 is heterozygous (her father was homozygous recessive, but she has unaffected).

For the child to have the disease, both Parent 1 and Parent 2 would need to be heterozygous

There is a 50% chance of this for Parent 1 and a 100% chance of this for Parent 2 and then, there is a 25% chance that their first child will be affected:

50%× 100% × 25% = 12.5%

1/2 × 1/4 = 1/8

Hence, the probability that their first child will have kidney disease is 1/8.

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The 85% confidence interval for the mean time at lunch is (31.84, 39.36) minutes.

In a random sample of fourteen people, the mean time at lunch was 35.6 minutes.

Standard deviation of 8.2 minutes.

A common method to calculate the confidence interval for the mean of a normal distribution is to use the Z-score. For a 85% confidence interval, the Z-score is 1.44. Therefore, the confidence interval can be calculated as:

The confidence interval formula in statistics is used to describe the amount of uncertainty associated with a sample estimate of a population parameter.

Where,

n= Number of terms

\($\overline{\mathrm{x}}\)= Sample Mean

\($\sigma\)=Standard Deviation

\($z_{\alpha / 2}\)= Value corresponding to a2 in z table

\($t_{\alpha / 2}\)= Value corresponding to a2 in t table

\($\alpha\)=(1 - Confidence Level /100)

So for the given data, the confidence interval would be:

35.6 ± 1.44 * 8.2 / √14

35.6 ± 1.44 * 8.2 / 3.74

35.6 ± 3.76

Therefore, the 85% confidence interval for the mean time at lunch is (31.84, 39.36) minutes.

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Jane makes sure that the (B) coffee is brewed simultaneously in each pot as part of her experimental study.

Experimental investigations involve introducing an intervention and observing its results.

Typically, volunteers in experimental research are grouped randomly, or by chance.

In experimental research, the dependent and independent variables are compared to examine how they relate to one another.

A link between a certain feature of an item and the variable under investigation is either accepted or denied following the conclusion of an experimental research study.

Laboratory experiments are the most fundamental type of experimental study, albeit they can take on several forms depending on the research topic.

Laboratory experiments are the most fundamental type of experimental study, albeit they can take on several forms depending on the research topic.

So, in the given situation, Jeane makes sure that the coffee is brewed simultaneously in all of the pots.

Therefore, Jane makes sure that (B) coffee is brewed simultaneously in each pot as part of her experimental study.

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Complete question;
Jenae noticed that many of her co-workers would opt for the coffee that appeared to be most recently brewed, regardless of the flavor of the coffee offered. This leads her to believe that what she was witnessing was not really representative of everyone's true flavor preferences. She adapted her experimental study accordingly. Select one control in Jenae's experimental study:

a. Jeane places condiments at random places throughout the kitchen.

b. Jeane makes sure that the coffee in different pots is brewed at the same time.

c. Jeane uses different locations in the kitchen for the coffee pots.

d. Jeane monitors the habit of co-workers who do not drink coffee.

Methods used that summarize or describe characteristics of data are called Descriptive statistics

Descriptive statistic is defined as the method fro summarizing data and information to partition them into a section of meaningful data.It contains descriptive coefficients that defined the meaningfulness of the data .

Variability and central tendency are the part of descriptive statistics that describe the spread and central point of the data respectively.

Other options are incorrect because overall statistics measure complete components ,average statistics take mean of complete statistic data and inferential statistic is based on random data sample.

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Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer: $1725

Step-by-step explanation:

The absolute maximum and minimum values of the function f(x, y) = x^2 + y^2 - 2y on the set R = {(x, y): x^2 + y^2 ≤ 9} can be found by analyzing the critical points and the boundary of the region R.

To find the critical points, we take the partial derivatives of f(x, y) with respect to x and y, and set them equal to zero. Solving these equations, we find that the critical point occurs at (0, 1).

Next, we evaluate the function f(x, y) at the boundary of the region R, which is the circle with radius 3 centered at the origin. This means that we need to find the maximum and minimum values of f(x, y) when x^2 + y^2 = 9. By substituting y = 9 - x^2 into the function, we obtain f(x) = x^2 + (9 - x^2) - 2(9 - x^2) = 18 - 3x^2.

Now, we can find the maximum and minimum values of f(x) by considering the critical points, which occur at x = -√2 and x = √2. Evaluating f(x) at these points, we get f(-√2) = 18 - 3(-√2)^2 = 18 - 6 = 12 and f(√2) = 18 - 3(√2)^2 = 18 - 6 = 12.

Therefore, the absolute maximum value of f(x, y) is 12, which occurs at (0, 1), and the absolute minimum value is also 12, which occurs at the points (-√2, 2) and (√2, 2).

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Hey there!

The answer is D

We solve this by multiplying the exponents, and we get 15:

3 x 5 = 15

So, the answer is 2^15

Hope it helps and have a great day!

Answer:

I hope this will help!

Step-by-step explanation:

Answer:

119 per km

Step-by-step explanation:

France population is equivalent to 0.84% of the total world population

Answer:

7*3=21

8-5=3

21+3-24

Step-by-step explanation:

To evaluate the integral ∫ x^3 (7x^4)^4 dx using the substitution u = 7x^4, the answer: (1/28)(1/5)(7x^4)^5 + c. Simplifying further, we obtain (1/140)x^20 + c, where c represents the constant of integration.

Making the substitution u = 7x^4 simplifies the integral. We express the integral in terms of u and then differentiate u with respect to x to find du. Substituting u and du into the integral, we obtain ∫ (1/28)u^4 du. Evaluating this integral and substituting back for u, we finally arrive at the answer: (1/28)u^5 + c, where c represents the constant of integration. We start by substituting u = 7x^4 into the integral, which gives us ∫ x^3 (7x^4)^4 dx = ∫ x^3 u^4 dx. To proceed, we need to express dx in terms of du, so we differentiate u with respect to x: du/dx = d/dx (7x^4) = 28x^3. Rearranging, we have dx = du/(28x^3). Substituting dx and u into the integral, we obtain ∫ x^3 (7x^4)^4 dx = ∫ x^3 u^4 (1/(28x^3)) du. Simplifying, the x^3 and x^3 terms cancel out, leaving us with ∫ u^4/28 du. Integrating ∫ u^4/28 du gives us (1/28)∫ u^4 du. Applying the power rule of integration, we add 1 to the exponent and multiply by the reciprocal of the new exponent, resulting in (1/28)(1/5)u^5 + c. Finally, substituting back for u, we arrive at the answer: (1/28)(1/5)(7x^4)^5 + c. Simplifying further, we obtain (1/140)x^20 + c, where c represents the constant of integration.

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The Midpoint Rule evaluates the integrand at the midpoint of each subinterval. With n=3 subintervals on the interval [ -1,23], the subinterval width is (23-(-1))/3 = 8. The midpoints of the subintervals are:
-1 + (8/2) = -1 + 4 = 3
3 + (8/2) = 3 + 4 = 7
7 + (8/2) = 7 + 4 = 11

Therefore, the integrand is evaluated at x=3, x=7, and x=11.

When using the Midpoint Rule with n=3 subintervals on the interval [-1, 23], the x-coordinates at which the integrand is evaluated can be found by first calculating the width of each subinterval and then finding the midpoint of each subinterval.

The width of each subinterval is given by (b - a)/n, where a = -1, b = 23, and n = 3. In this case, the width (Δx) is (23 - (-1))/3 = 24/3 = 8.

Now, we can find the midpoints of each subinterval:

1. Midpoint of [-1, 7]: (-1 + 7)/2 = 6/2 = 3
2. Midpoint of [7, 15]: (7 + 15)/2 = 22/2 = 11
3. Midpoint of [15, 23]: (15 + 23)/2 = 38/2 = 19

So, the integrand is evaluated at x-coordinates x = 3, 11, and 19. Your answer: 3, 11, 19.

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Answer:

22-2.25x

Step-by-step explanation:

Answer:

(1, - 7 )

Step-by-step explanation:

using the midpoint formula

given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then

midpoint = ( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

here (x₁, y₁ ) = A (3, - 12 ) and (x₂, y₂ ) = B (- 1, - 2 )

midpoint = ( \(\frac{3-1}{2}\) , \(\frac{-12-2}{2}\) ) = ( \(\frac{2}{2}\) , \(\frac{-14}{2}\) ) = (1, - 7 )

Step-by-step explanation:

\( x_{m} , y_{m} \: = ( \frac{x _{1} + x_{2} }{2} ,\frac{y _{1} + y_{2} }{2}) \\ \)

x1 = 3, x2 = (-1)

y1 = (-12), y2 = (-2)

\( x_{m} , y_{m} \: = ( \frac{3+ ( - 1) }{2} ,\frac{( - 12)+ ( - 2) }{2}) \\ \)

\(x_{m} , y_{m} \: = ( \frac{3 - 1 }{2} ,\frac{( - 12) - 2 }{2}) \\ \)

\(x_{m} , y_{m} \: = ( \frac{2 }{2} ,\frac{- 14 }{2}) \\ \)

\(x_{m} , y_{m} \: = 1 ,( - 7)\)