To get from the stone to the tree you must avoid walking through a pond. To avoid the pond, you must walk 34 yards north
and 41 yeards west. Approximately how many yards would be saved if it were possible to walk through the pond?
Explain step-by-step using the Pythagorean theorem

Answer:

7788987797998789878888878999999

Answer:

First, let's simplify both sums by combining like terms:

3x + 5y - 2 + 2x - 3y + 1 = 5x + 2y - 1

4x - 8y + 3 - 5x + 6y + 7 = -x - 2y + 10

Now we can subtract the second sum from the first:

(5x + 2y - 1) - (-x - 2y + 10) = 5x + 2y - 1 + x + 2y - 10

Simplifying this expression, we get: 6x + 4y - 11

a) We fail to reject the null hypothesis at the 5% level of significance. Therefore, the population mean is 8.75

b) We fail to reject the null hypothesis at the 5% level of significance. Therefore, the population mean is 8.75.

The claim about the population mean under the one-tailed alternative hypothesis and two-tailed alternative hypothesis are tested by the z-test statistic. The critical value approach is used to identify the true statement under the null and the alternative hypothesis at the 5% level of significance.

Sample size , n = 20

Sample mean, x(bar) = 9.5

Population standard deviation, σ = 3.5

a) Null hypothesis: \(H_0:\)μ = 8.75

Alternative hypothesis: \(H_a\) μ \(\neq\) 8.75 Two tailed

Level of significance, α = 0.05

Excel function for the critical value:

=NORMINV(0.05/2,0,1)

\(Z_0_._0_5_/_2\) = ± 1.96

The Z-test statistic is defined as:

Z = x(bar) - μ /  σ / \(\sqrt{n}\)

Z = 9.5 - 8.75 / 3.5/\(\sqrt{20}\)

Z = 0.958

The test statistic value is less than the critical value at the 5% level of significance. We fail to reject the null hypothesis at the 5% level of significance. Therefore, the population mean is 8.75.

b)  Null hypothesis: \(H_0:\)μ = 8.75

Alternative hypothesis: \(H_a\) μ \(>\) 8.75 Right tailed

Level of significance, α = 0.05

Excel function for the critical value:

=NORMINV(0.05,0,1)

\(Z_0_._0_5_/_2\)  = + 1.645

The Z-test statistic is defined as:

Z = x(bar) - μ /  σ / \(\sqrt{n}\)

Z = 9.5 - 8.75 / 3.5/\(\sqrt{20}\)

The test statistic value is less than the critical value at the 5% level of significance. We fail to reject the null hypothesis at the 5% level of significance. Therefore, the population mean is 8.75.

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Answer:

(x, y) = (-8, 19)

Step-by-step explanation:

9x + 3y = -15

-4x - 3y = -25

(9x + 3y) + ((-4x) - 3y) = -15 + (-25)

5x = -40

x = -8.

So,

9x + 3y = -15

9 * (-8) + 3y = -15

-72 + 3y = -15

3y = 57

y = 19

The solution to the linear system is unique solution which is  x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.

The correct answer is option  A.

To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:

[1  -4  5  |  23]

[2   1   1  |  10]

[-3  2  -3 |  -23]

We'll apply row operations to transform this matrix into echelon form:

1. Multiply Row 2 by -2 and add it to Row 1:

[1  -4   5   |  23]

[0   9   -9  |  -6]

[-3  2  -3  |  -23]

2. Multiply Row 3 by 3 and add it to Row 1:

[1  -4  5   |  23]

[0   9  -9  |  -6]

[0   -10 6  |  -68]

3. Multiply Row 2 by 10/9:

[1  -4  5    |  23]

[0   1   -1   |  -2/3]

[0   -10 6  |  -68]

4. Multiply Row 2 by 4 and add it to Row 1:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  -10 6  |  -68]

5. Multiply Row 2 by 10 and add it to Row 3:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  0   -4  |  -34/3]

Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:

From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.

From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.

From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.

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Answer:

I am not sure my guy

Step-by-step explanation:

sorry?

The probability of a single birth resulting in a girl if the probability of a single birth resulting in a boy is 51% is 49%

Probability is the measure of the likelihood of an event occurring. The probability of an event occurring ranges from 0 to 1. If an event is impossible, the probability of its occurrence is 0, and if the event is certain to occur, the probability is 1. The probabilities of the complement of an event equal one minus the probability of the event. For instance, the probability of the complement of an event A, denoted as A', is 1 - P(A). If the probability of an event A is P(A), then the probability of the complement of A is 1 - P(A).

Here, the probability of a single birth resulting in a boy is 51%. Therefore, the probability of a single birth resulting in a girl is the complement of this event, which is 49%. Hence, the main answer is that the probability of a single birth resulting in a girl if the probability of a single birth resulting in a boy is 51% is 49%.

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Answer:

ITS CORRECT

Step-by-step explanation:

THE ANSWER IS 0.02 OR 1/50

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

Reason:

For any triangle, the inside angles always add to 180 degrees.

(angle1)+(angle2)+(angle3) = 180

(6x+13)+(79)+(6x+4) = 180

(6x+6x)+(13+79+4) = 180

12x+96 = 180

12x = 180-96

12x = 84

x = 84/12

x = 7

Then use this to compute angle A.

A = 6x+13 = 6*7+13 = 42+13 = 55 degrees

If you wanted, you can compute the other angle as well

6x+4 = 6*7+4 = 42+4 = 46 degrees

Then as a check:

(angle1)+(angle2)+(angle3) = (55)+(79)+(46) = 180

which confirms the answer.

Answer:

provide a valid passport

Step-by-step explanation:

Answer:

be a us citizen

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

2x-3 = 5

2x = 8

x = 4

Hope this helps

I hope this helps you

in similar triangle sides are can be rate

ABC~EFD

AB/EF=BC/FD=AC/ED

5/2x-3=6/FD=4/9

9.5/4=2x-3

11.25+3=2x

2x=14.25

x=7.125

Answer:

\( \frac{2}{7} \\ \\ \frac{5}{16} \\ \\ \frac{7}{24} \)

Using Taylor series, the approximation P3(1.2) = 0.77083. Error R3(1.2) < 0.000235. Thus, P3(1.2) - |R3(1.2)| = 0.770599, within 0.001 of f(1.2).

In part C, we found the third-order Taylor polynomial for f about x=1 to be P3(x) = 1 - 1/2(x-1) + 1/8\((x-1)^2\)- 1/48\((x-1)^3\).

To show that this approximation is within 0.001 of the exact value of f(1.2), we need to estimate the error using the remainder term. The remainder term for the third-order Taylor polynomial is given by R3(x) = f(x) - P3(x) = (1/4!)\((x-1)^4\)f⁴(c), where c is some number between 1 and x.

Using the given formula for fⁿ(1), we can compute f⁴(c) = (-1)³(3!)/2⁴ = -3/16. Thus, we have R3(1.2) = (1/4!)\((0.2)^4\)(-3/16) = -0.000234375.

Since R3(1.2) is negative, we know that P3(1.2) > f(1.2), so our approximation is too high. Therefore, to ensure that our approximation is within 0.001 of the exact value of f(1.2), we need to subtract the error bound from our approximation. That is, we need to use P3(1.2) - |R3(1.2)| as our estimate. Substituting values, we get P3(1.2) - |R3(1.2)| = 0.770833333 - 0.000234375 = 0.770598958.

Since |f(1.2) - P3(1.2)| < |R3(1.2)|, we can conclude that our approximation is within 0.001 of the exact value of f(1.2).

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The equation for the graph of y = x translated 3 units downward is y = x - 3. The equation for the graph of y = x translated 3 units upward is y = x + 3. The equation for the graph of y = x vertically stretched by a factor of 3 is y = 3x. The equation for the graph of y = x vertically compressed by a factor of 3 is y = (1/3)x.

Translating the graph of y = x downward by 3 units means shifting all points on the graph downward by 3 units. This can be achieved by subtracting 3 from the y-coordinate of each point. So, the equation for the translated graph is y = x - 3.

Translating the graph of y = x upward by 3 units means shifting all points on the graph upward by 3 units. This can be achieved by adding 3 to the y-coordinate of each point. So, the equation for the translated graph is y = x + 3.

Vertically stretching the graph of y = x by a factor of 3 means multiplying the y-coordinate of each point by 3. This causes the graph to become steeper, as the y-values are increased. So, the equation for the vertically stretched graph is y = 3x.

Vertically compressing the graph of y = x by a factor of 3 means multiplying the y-coordinate of each point by (1/3). This causes the graph to become less steep, as the y-values are decreased. So, the equation for the vertically compressed graph is y = (1/3)x.

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Answer:

8.5 Yards

Step-by-step explanation:

Pythagorean Theorem: \(c = \sqrt{a^{2} +b^{2} }\)

a = 6

b = 6

Therefore: \(c = \sqrt{6^{2} +6^{2} }\) = 8.485

The path is 8.5 yards long

The utilization of the teller is approximately 53.33%.

To calculate the utilization of the teller, we need to compare the arrival rate and the service rate. The utilization represents the fraction of time the server (teller) is busy serving customers.

The arrival rate is given as 8 customers per hour, which means that, on average, 8 customers arrive at the teller's window in one hour. This follows a Poisson distribution.

The service rate is given as 15 customers per hour, indicating that, on average, the teller is able to serve 15 customers in one hour. The service times follow an exponential distribution.

Utilization is calculated as the ratio of the arrival rate to the service rate. In other words:

Utilization = Arrival rate / Service rate

Substituting the given values:

Utilization = 8 / 15 ≈ 0.5333

To express this as a percentage, we multiply the result by 100:

Utilization = 0.5333 * 100 ≈ 53.33%

Therefore, the utilization of the teller in this scenario is approximately 53.33%. This means that, on average, the teller is occupied serving customers about 53.33% of the time, and the remaining time is idle or available for serving new customers.

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(4,6) are the coordinates of the point on the directed line segment from (1,5) to(6, 10) that partitions the segment into a ratio of 3 to 2.

According to the midpoint theorem, the line segment drawn from the intersection of two triangle sides is parallel to and equal to half of the third side. To determine precise information about the lengths of triangle sides, one uses the Midpoint Theorem. According to the Midpoint Theorem, the segment connecting two triangle sides at their midpoints is parallel to the third side and is half its length.

Given

Points (1,5) (6.10)

Ratio 3 :2

Using mid point theorem,

( (mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n) )

3(6) + 2 (1)/ 3+2, 3(10) + 2(5)/ 2+3

18 + 2/5 , 20 + 10/5

20/5 , 30/5

4, 6

(4,6) are the coordinates of the point on the directed line segment from (1,5) to(6, 10) that partitions the segment into a ratio of 3 to 2.

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Answer:

whats up? whatja need help with

Step-by-step explanation:

Answer:

the answer is 45 please do you get it

The rate is his distance from second base decreasing when he is halfway to first base is -45ft

The rate is his distance from third base increasing at the same moment is 26ft

Let's call the batter's distance from second base "x" and his distance from third base "y". We want to find dx/dt (the rate at which x is changing) and dy/dt (the rate at which y is changing) when the batter is halfway to first base.

Since the baseball diamond is a square, we know that the distance from second base to first base is also 90 ft. Therefore, when the batter is halfway to first base, his distance from second base is:

x = 90 ft - 45 ft = 45 ft

Now we can find dx/dt by taking the derivative of x with respect to time:

dx/dt = -26 ft/s

The negative sign indicates that x is decreasing, as we expected.

Next, we need to find the rate at which the batter's distance from third base is increasing when he is halfway to first base. We know that the distance from third base to first base is also 90 ft, so the distance from the halfway point to third base is:

y = 90 ft - 45 ft - 90 ft = -45 ft

Well, in this case, it means that the batter is actually behind third base when he is halfway to first base. So, we need to flip the sign of y to make it positive:

y = -(-45 ft) = 45 ft

Now we can find dy/dt by taking the derivative of y with respect to time:

dy/dt = 26 ft/s

The positive sign indicates that y is increasing, as we expected.

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Complete Question:

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 26 ft/s.

At what rate is his distance from second base decreasing when he is halfway to first base?

At what rate is his distance from third base increasing at the same moment?

The simplified form of the expression 1/5 divied by 2 as a fraction is 1/10.

Given the expression in the question;

1/5 divied by 2

1/5 ÷ 2

To simplify, multiply 1/2 by the reciprocal of 2

1/5 ÷ 2

1/5 × 1/2

Simplify

( 1 × 1 ) / ( 5 × 2 )

( 1 ) / ( 5 × 2 )

Multiply 5 and 2

( 1 ) / ( 10 )

1/10

Therefore, the simplified form is 1/10.

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Answer:

30°,60°,90°

Step-by-step explanation:

Let :-

As we know :-

So that ,

Angles ,

Answer:

Let the angles be x and 2x.

We know that the sum of all interior angles of a triangle is 180°.

Therefore,

Angles,

The formula of the volume is given by;

Where:

s = 11 in

h = 11.5 in

So, we have:

Round to the nearest whole number is 464

Answer: 464 in^3

The salesman received a commission of $1,050 based on a 3.5% commission rate for the total sale of $30,000.

To find the amount of commission the salesman received, we can calculate 3.5% of his total sales.

The commission can be calculated using the formula:

Commission = (Percentage/100) * Total Sales

Given:

Percentage = 3.5%

Total Sales = $30,000

Plugging in the values, we have:

Commission = (3.5/100) * $30,000

To calculate this, we can convert the percentage to decimal form by dividing it by 100:

Commission = 0.035 * $30,000

Simplifying the multiplication:

Commission = $1,050

Therefore, the salesman received a commission of $1,050 based on a 3.5% commission rate for the total sale of $30,000.

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Answer:

What you need to do is to find a multiple of 20 and 16 in other words a number that can multiply into 20 and 16. You have 2 and you have 4. So now this is how it looks like.

Either:

4(5+4) Or

2(10+8)

Step-by-step explanation:

Answer: I'd say reflection

Answer:

It is a reflection

Step-by-step explanation:

In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

A recent college graduate is looking to begin saving for retirement. Option A is a savings account with 3.5% annual simple interest. Option B is a savings account with 3.5% annual interest compounded monthly. If the principal investment is the same for both options, the account which would have a larger balance after 10 years is  Option B because compound interest generates earnings from both principal and interest which is denoted as option C.

This is referred to as the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

Compound interest makes a sum of money grow at a faster rate than simple interest, because in addition to earning returns on the money you invest, you also earn returns on those returns or interest accrued at the end of every compounding period.

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Answer:

Option B will have the larger balance after 10 years because compound interest generates earnings from both principal and interest.

Answer:

2 real solutions

Step-by-step explanation:

\(y=x^2+3x-2\)

\(y=4x-1\)

\(x^2+3x-2=4x-1\)

\(x^2-x-2=-1\)

\(x^2-x-1=0\)

\(x=\frac{1 +-\sqrt{1-4*1*(-1)} }{2}\)

\(x=\frac{1+-\sqrt{5}}{2}\)

The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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