Downtown Mathville is laid out as a 6 x 6 square grid of streets (see diagram below). Your apartment is located at the southwest corner of downtown Mathville (see point H). Your math classroom is located at the northwest corner of downtown Mathville (see point M). You know that it is a 12-block walk to math class and that there is no shorter path. Your curious roommate (we’ll call her Curious Georgia) asks how many different paths (of length 12 blocks – you don’t want to back track or go out of your way) could you take to get from your apartment to the math class. It should also be clear that no shorter path exists. Can you solve Curious Georgia’s math problem?

Answer:

i cant see it

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

Its impossible tto calculate x there.

But i can simply the expression for you...

42x²-13x+1

Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

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Answer:

5,-3

Step-by-step explanation:

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

A. down

Step-by-step explanation:

The parent graph is

f(x)=x

If this graph is transformed to obtain

g(x)=f(x)−4

The subtracttion means the graph will shift downward vertically

The graph of g(x) is obtained by shifting f(x) down by 4 unit.

Therefore the direction is down.

Mark this as brainliest please.

Answer:  \((x, y) \to (x+ 8, y-6)\)

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

Explanation:

Point Q has x coordinate -9

Point Q' has x coordinate -1

The horizontal movement from Q to Q' is "shift 8 units to the right". So we have x update to x+8

At the same time, we're shifting 6 units down since we go from y = 5 to y = -1. So we'll subtract 6 from the y coordinates.

The translation rule is therefore \((x, y) \to (x+ 8, y-6)\) to shift 8 units right and 6 units down.

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

Let's apply this rule to point R to see it in action.

\((x, y) \to (x+ 8, y-6)\\\\(-6, 3) \to (-6+ 8, 3-6)\\\\(-6, 3) \to (2, -3)\)

We have R(-6, 3) arrive at R ' (2, -3) which is what the graph shows. This confirms the translation rule works for point R.

I'll let you confirm this rule with points P and Q.

Answer:

92

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define

2a² + 5b²

a = -6

b = 2

Step 2: Evaluate

Answer:

∠E = tan

∠D = tan

Step-by-step explanation:

Common sense, only perpendicular and base is present.

Answer:

7mins

Step-by-step explanation:

Answer:

It will take her 7.5 minutes.

Step-by-step explanation:

600 divided by 80 = 7.5

+add unit

The probability of rolling a sum from 2 to 12 on 2 dices is 100%

Given the data,

The two dice should be rolled.

Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).

The resultant 36 results are as follows:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6

2-1, 2-2, 2-3, 2-4, 2-5, 2-6

3-1, 3-2, 3-3, 3-4, 3-5, 3-6

4-1, 4-2, 4-3, 4-4, 4-5, 4-6

5-1, 5-2, 5-3, 5-4, 5-5, 5-6

6-1, 6-2, 6-3, 6-4, 6-5, 6-6

When using two dice, there are a total of 36 possibilities that might occur.

As a result, the results' total ranges from 2 to 12.

Hence , the probability is 100 %

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The Amy has 42 books, Betty has 36 books, and Carol has 18 books.

Let's set up equations to represent the given information:

Let A represent the number of books Amy has.

Let B represent the number of books Betty has.

Let C represent the number of books Carol has.

Let's say Amy has x books.

Betty has 6 books less than Amy, so Betty has (x - 6) books.

Carol has half as many books as Betty, so Carol has (x - 6)/2 books.

According to the problem, the total number of books they have is 96.

So, we can write the equation:

x + (x - 6) + (x - 6)/2 = 96

To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:

2x + 2(x - 6) + (x - 6) = 192

2x + 2x - 12 + x - 6 = 192

5x - 18 = 192

5x = 210

x = 42

Amy has 42 books.

Betty has (42 - 6) = 36 books.

Carol has (36)/2 = 18 books.

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Answer:

x=-2 and y=-5

Step-by-step explanation:

y=5x+5

3x-6y=24

3x-6(5x+5)=24

3x-30x-30=24

           +30   +30

-27x=54

x=-2

y=5(-2)+5

y=-10+5

y=-5

Answer:

a) 16.6

b) The 95% confidence level of the mean of the time playing video games is between 15.7 and 17.5 hours.

c) The 99% confidence level of the mean of the time playing video games is between 15.4 and 17.8 hours.

d) The margin of error increases as the confidence level increases, due to the value of z, which means that the 99% confidence interval is larger.

Step-by-step explanation:

a. Find the best point of estimate of the population mean

The best estimate for the population mean is the sample mean, which is 16.6

b. Find the 95% confidence level of the mean of the time playing video games

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.96\frac{2.8}{\sqrt{35}} = 0.9\)

The lower end of the interval is the sample mean subtracted by M. So it is 16.6 - 0.9 = 15.7 hours

The upper end of the interval is the sample mean added to M. So it is 16.6 - 0.9 = 17.5 hours

The 95% confidence level of the mean of the time playing video games is between 15.7 and 17.5 hours.

c. Find the 99% confidence interval of the mean time playing video games

Following the same logic as above, we have that \(Z = 2.575\). So

\(M = 2.575\frac{2.8}{\sqrt{35}} = 0.9\)

The lower end of the interval is the sample mean subtracted by M. So it is 16.6 - 1.2 = 15.4 hours.

The upper end of the interval is the sample mean added to M. So it is 16.6 + 1.2 = 17.8 hours.

The 99% confidence level of the mean of the time playing video games is between 15.4 and 17.8 hours.

d. Which is larger? Explain why.

The margin of error increases as the confidence level increases, due to the value of z, which means that the 99% confidence interval is larger.

The mean is 16.6, 95% confidence interval is between 15.68 to 17.52, the 99% confidence interval is between 15.39 to 17.81, and the 99% confidence interval is larger.

It is given that the in recent study of 35 ninth-grade students the mean number of hours per week is 16.6 with standard deviation of the population was 2.8.

It is required to find the best point of estimate of the population mean, 95% confidence interval, and 99% confidence interval.

It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.

We have confidence level = 95% = 0.95

We know:

\(\alpha = \frac{1-0.95}{2}\)  = 0.025

\(\rm Z_1 _-_\alpha = Z_{0.975} = 1.96\)  (from the Z table)

The sample size n = 35

We know the Margin of error formula:

\(\rm M =Z\frac{\sigma}{\sqrt[]{n} }\)  ( \(\rm \sigma\\\) = 2.8 )

\(\rm M =1.96\frac{2.8}{\sqrt[]{35} }\)  

M = 0.92

The 95% interval will be:

= X - M ⇒ 16.6 - 0.92 ⇒15.68

= X+ M ⇒ 16.6+0.92 ⇒ 17.52

For 99% confidence level:

\(\alpha = \frac{1-0.90}{2} = 0.005\)

\(\rm Z_1 _-_\alpha = Z_{0.005} = 2.575\)  (from Z table)

\(\rm M =2.575\frac{2.8}{\sqrt[]{35} }\)

M = 1.21

The 99% interval will be:

=16.6 - 1.21 ⇒  15.39

= 16.6+ 1.21 = 17.81

As the value of M increases the confidence value increases due to the value of Z that means 99% confidence interval is larger.

Thus, the mean is 16.6, 95% confidence interval is between 15.68 to 17.52, the 99% confidence interval is between 15.39 to 17.81, and the 99% confidence interval is larger.

Learn more about the confidence interval here:

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Answer:

Joff-tchoff-tchoffo-tchoffo-tchoff!

Tchoff-tchoff-tchoffo-tchoffo-tchoff!

Joff-tchoff-tchoffo-tchoffo-tchoff!

Step-by-step explanation:

Answer:

"Joff-tchoff-tchoffo-tchoffo-tchoff!

Tchoff-tchoff-tchoffo-tchoffo-tchoff!

Joff-tchoff-tchoffo-tchoffo-tchoff!"

Answer: −3a^3−3a^2+a+8

Step-by-step explanation:  (3a^3-7a^2+a)-(6a^3-4a^2-8)

3a^3+−7a^2+a+−1(6a^3)+−1(−4a^2)+(−1)(−8)

3a^3+−7a^2+a+−6a^3+4a^2+8

(3a^3+−6a^3)+(−7a^2+4a^2)+(a)+(8)

−3a^3+−3a^2+a+8

Answer:

x = 4

Step-by-step explanation:

3x -5 = -2 + 9

-2 + 9 = 7 so now its 3x - 5 = 7

add 5 to the -5 so it cancels itself out. then add the 5 to 7 so it become 12. the you have 3x = 12

divide 12 ÷ 3 = 4

x = 4

Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

(c) To determine the modes of the data set, identify the values that appear most frequently.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.

\(\bold{\huge{\red{\underline{ Solution}}}}\)

\(\bold{\underline{ We \: have\: given :-}}\)

\(\sf{ 2x + 7y = 3 ...eq(1 ) }\)

\(\sf{ x = -4y ...eq(2) }\)

Here, we will use the substitution method for solving the above equations.

\(\bold{\underline{Subsitute \: eq(1)\:in \: eq(2)}}\)

\(\sf{ 2(-4y) + 7y = 3 }\)

\(\sf{ -8y + 7y = 3 }\)

\(\sf{ - y = 3 }\)

\(\sf{ y = - 3. ...eq( 3) }\)

\(\bold{\underline{Subsitute \: eq(3)\:in \: eq(2)}}\)

\(\sf{ x = -4(-3) }\)

\(\sf{ x = 12 }\)

\(\sf{\blue{ Hence, \: The \:value \:of \:x \:and \:y \:is\: 12\: and \:-3}}\)

Answer:

Step-by-step explanation:

Solving for x,

Now, we check the solutions to see which one is correct and which one isn't:

Therefore, we can conclude that the solution is:

Answer: These events are independent.

Step-by-step explanation:

Two events are considered independent if the outcome of one event does not affect the outcome of the other event. In this case, getting a 5 or 6 on a dice toss and getting at most 3 on a dice toss are independent events.

This is because the probability of getting a 5 or 6 is 2/6 or 1/3, which is completely unrelated to the probability of getting at most 3, which is 3/6 or 1/2. The outcome of getting a 5 or 6 does not affect the probability of getting at most 3, and vice versa. Therefore, these events are independent.

Answer:

4h

2d

Step-by-step explanation:

Answer:

57

Step-by-step explanation:

since angle 3 is 57 (180-123=57) and 3 and 7 are corresponding, and corresponding angles are congruent,angle 7=57

Answer:

angle 1 and angle 7=180°[co exterior angle]

123°+ <7=180°

<7=180°-123°

<7=57°

Regression equation correctly models the data is: y = -43.98x + 1,279.93

To determine the regression equation that correctly models the data, we can use the method of linear regression. The regression equation for a straight line is generally expressed as y = mx + b, where m is the slope and b is the y-intercept.

Using the given table, we can calculate the necessary values to determine the regression equation. Let's denote the sigma notation as Σ.

The slope (m) can be calculated using the formula:

\(m = (Σxy - (Σx)(Σy) / n(Σx^2) - (Σx)^2)\)

Plugging in the values from the table:

m =\((776,600 - (299)(12,400) / 6(18,109) - (299)^2)\)

m = (776,600 - 3,708,800 / 6(18,109) - 89,401)

m = (-2,932,200 / 66,654)

m ≈ -43.98

The y-intercept (b) can be calculated using the formula:

b = (Σy - m(Σx)) / n

Plugging in the values from the table:

b = (12,400 - (-43.98)(299)) / 6

b ≈ 1,279.93

The correct regression equation that models the data is:

y = -43.98x + 1,279.93

Out of the given options, the correct regression equation is:

y = -43.98x + 1,279.93

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Two lines are parallel to each other when they never intersect each other and their slopes are the same.

If the line is parallel to the line y=-1/4x+5, it must have the same slope, in this case -1/4x.

Let's find the line passing through the point (2,-1) using the next formula:

y- y1 = m(x - x1)

Where m= -1/4, x1 = 2 and y1 = -1.

Replace the values and solve for y:

y -(-1) = -1/4(x-2 )

y+1 = -1/4*x + (-1/4* -2)

y+1 = -1/4x + 1/2

y = -1/4x + 1/2 -1

y = -1/4x - 1/2

So y = -1/4x - 1/2 is the equation of the line parallel to the line y=-1/4x+5 and passing through the point (2,-1)

The product of :

We convert the mixed fractions to improper fractions and then multiply the two.

Thus, we have:

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

Answer:

it would be .742 or -2.85

Step-by-step explanation:

I did this not so long ago