please help me with this math problem

Many people use relative location on a daily basis by using their mental maps of an area.

Relative location refers to the position of a place or object in relation to other landmarks or known locations. It involves understanding spatial relationships and navigating based on familiar references. Among the given choices, the best answer is "B. their mental maps of an area."

People often rely on their mental maps of an area to determine relative location. Mental maps are cognitive representations of familiar places, formed through personal experiences and observations. These mental maps help individuals navigate and understand the spatial relationships between different locations. By using their mental maps, people can estimate distances, find directions, and navigate based on familiar landmarks or known routes.

While the other options (coordinates on a GPS-enabled device, a location's exact address, and the Internet) can provide precise or specific location information, they do not capture the concept of relative location as directly as mental maps. Relative location is more about the spatial relationships between places and the ability to navigate based on one's understanding of the area, which is best represented by mental maps.

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Answer:

10 ways

Explanation:

The number of ways to select x elements from a group of n elements is calculated as

These ways are called combinations. In this case, we need to select 3 different extras from a group of 5 extras ( tomato, lettuce, bacon, onion, or cheese). So, the number of ways to make an order is

Therefore, the are 10 different ways to order a burger with three different extras.

Answer:

13/7

Step-by-step explanation:

Method 1 :

1/2*3/7-5/7*1/2+2​ = (3/14)- (5/14) + 2

                            = -2/14 + 2            

                            = -2/14 + 28/14

                            = 26/14

                            = 13/7

Method 2 :

1/2*3/7-5/7*1/2+2​ = (1/2) [3/7 - 5/7] + 2

                            = (1/2)(-2/7) + 2            

                            = (-1/7) + 14/7

                            = 13/7

The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

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Step-by-step explanation:

The equation will form a circle because it in the form of

\((x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} \)

First, let set the equation equal.

\((x - 7) {}^{2} + (y + 5) {}^{2} = 25\)

Here the center will be (7,-5), and the radius of 5. The boundary line will be dashed

Since this is in the inequalities, we must find the solution set.

Plug in 0,0 for x and y and see if it's true.

\((0 - 7) {}^{2} + (0 + 5) {}^{2} > 25\)

\(49 + 25 > 25\)

\(74 > 25\)

This is a true so we shade the region that includes 0,0

Since 0,0 has a greater distance from the center of the circle, 0,0 is outside of the circle, so our solution set will

be outside of circle.

Here a picture of graph,

Step-by-step explanation:

W^2 = 46.

We know that 6^2 = 36 and 7^2 = 49.

Therefore W should be between 6 and 7.

Answer:

We suppose that a is the old price in cents

the total cost of 9.20 $ equals 920 cents

so we have 20 liters bought with the old price (a) and 10 liters with the new price (a + 2). This is translated into this equation where a is the old price therefore our quest to be answered

20 xa + 10 x (a + 2) = 920 (cents)

20 xa + 10 xa + 20 = 920

30 xa + 20 = 920

30 xa = 920 - 20

30 xa = 900

a = 900: 30

a = 30 (cents)

therefore the old price for 1 liter of petrol is 30 cents

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Answer:

the equation is  

y= −5x + 23

Step-by-step explanation:

Math

Answer:

we need the graph in order to find the answer.

Step-by-step explanation:

The statement "nm = x" and the statement "nm = lm = tan(45°) = 1" are true regarding triangle LMN.

In triangle LMN, "nm = x" implies that the length of side NM is equal to the value of x. This suggests that the length of side NM is determined by the specific value of x.

The statement "nm = lm = tan(45°) = 1" is also true. This means that the lengths of sides NM and LM are equal, and they are both equal to 1. Additionally, the tangent of a 45° angle is equal to 1. Therefore, all three quantities in the statement are equal to 1.

Overall, in triangle LMN, the length of side NM is represented by x, and both sides NM and LM have a length of 1.

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The sum of the interior angles of a triangle is 180 degrees.

Sure, here's a question related to the Triangle Sum and Exterior Angle Theorem: Consider triangle ABC. The measure of angle A is 60 degrees, and the measure of angle B is 80 degrees. What is the measure of angle C? Using the Triangle Sum Theorem, we know that the sum of the interior angles of a triangle is always 180 degrees.

Additionally, the Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.  

Based on this information, determine the measure of angle C in triangle ABC and provide a step-by-step explanation of how you arrived at your answer.

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Answer:

28(1 + 2t +w)

Step-by-step explanation:

28 + 56t + 28w.

Factor out a 28 from the expression.

28(1 + 2t + w)

The correct representation of 6/1 is in figure A.

Given:

The four figures with shaded regions and unshaded regions.

To find:

The figure with the correct representation of 6/1.

Solution:

In figure A

Fraction of one box =\(\frac{1}{1}\)

There are six individual boxes that will be represented as:

\(\frac{1}{1}+\frac{1}{1}+\frac{1}{1}+\frac{1}{1}+\frac{1}{1}+\frac{1}{1}=\frac{6}{1}\)

In figure B

The number of shaded regions = 5

The total number of regions = 6

The representation will be :

\(\frac{\text{Shaded region}}{\text{Total regions}}=\frac{5}{6}\)

In figure C

Fraction of one box =\(\frac{1}{1}\)

There are five individual boxes that will be represented as:

\(\frac{1}{1}+\frac{1}{1}+\frac{1}{1}+\frac{1}{1}+\frac{1}{1}=\frac{5}{1}\)

In figure D

The number of shaded regions = 1

The total number of regions = 1

The representation will be:

\(\frac{\text{Shaded region}}{\text{Total regions}}=\frac{1}{6}\)

The correct representation of 6/1 is in figure A.

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The distance from the center of dilation, Q, to the image of vertex A will be 4 units.

According to the given rule of dilation, D subscript Q, two-thirds, the triangle ABC will be dilated with a scale factor of two-thirds centered at point Q.

Since point Q is the center of dilation and the distance from triangle ABC to point Q is 6 units, the image of vertex A will be 2/3 times the distance from A to Q. Therefore, the distance from A' (image of A) to Q will be (2/3) x 6 = 4 units.

By applying the scale factor to the distances, we can determine that the length of A'B' is (2/3) x  3 = 2 units, the length of B'C' is (2/3) x 7 = 14/3 units, and the length of A'C' is (2/3) x 8 = 16/3 units.

Thus, the distance from the center of dilation, Q, to the image of vertex A is 4 units.

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Answer:

The area of circle A is 16 times the area of circle B.

Step-by-step explanation:

he area of circle A is three times the area of circle B.

It depends on the value of π.

It depends on the actual diameters of the circles.

The area of circle A is 16 times the area of circle

the circumference of a circle = 2 x pi x r

Let imagine that the radius of B is 2cm

then the circumference of B = 2 x 2 x pi = 4pi

If the circumference of a is 4 times that of B, it means the circumference is 16 and the radius is 8

Area of a circle is pi x r^2

Area of B = pi x 2^2 = 4pi

Area of A = pi x 8^2 = 64pi

64/4 = 16 pi

The equation holds for \($n=k+1$\). The equation holds for all non-negative integers $n$. we have proved that $\sum_{i=0}^n \frac{i}{2^i} = \frac{2^{n+1}-(n+2)}{2^n}$.

Task 1:

**The function $\frac{7}{2}n^2 - 3n - 8 = O(n^2)$,** since we can find constants $c = \frac{15}{4}$ and $n_0 = 1$ that satisfy the definition of big-Oh notation.

To prove this, we need to show that there exist positive constants $c$ and $n_0$ such that for all $n \geq n_0$, $\left|\frac{7}{2}n^2 - 3n - 8\right| \leq c \cdot n^2$.

For $n \geq 1$, we can rewrite the given function as $\frac{7}{2}n^2 - 3n - 8 \leq \frac{15}{4}n^2$. Now, let's prove this inequality:

\begin{align*}

\frac{7}{2}n^2 - 3n - 8 &\leq \frac{15}{4}n^2 \\

\frac{7}{2}n^2 - \frac{15}{4}n^2 - 3n - 8 &\leq 0 \\

-\frac{1}{4}n^2 - 3n - 8 &\leq 0 \\

-\frac{1}{4}n^2 - 3n + 8 &\geq 0 \\

\end{align*}

Now, we can factorize the quadratic expression to determine its roots:

\begin{align*}

-\frac{1}{4}n^2 - 3n + 8 &= -\frac{1}{4}(n+4)(n-8) \\

\end{align*}

From the factorization, we can see that the quadratic is non-positive for $-4 \leq n \leq 8$. Thus, for $n \geq 8$, the inequality holds true.

Now, let's consider the case when $1 \leq n < 8$. We can observe that $\frac{7}{2}n^2 - 3n - 8 \leq \frac{7}{2}n^2 \leq \frac{15}{4}n^2$. Therefore, the inequality holds for this range as well.

Hence, we have found $c = \frac{15}{4}$ and $n_0 = 1$ that satisfy the definition of big-Oh notation, proving that $\frac{7}{2}n^2 - 3n - 8 = O(n^2)$.

Task 2:

The statement "$f(n) = O(g(n))$ if and only if $g(n) = \boldsymbol{\Omega}(f(n))$" is **true**.

To prove this, we need to show that $f(n) = O(g(n))$ implies $g(n) = \Omega(f(n))$, and vice versa.

First, let's assume that $f(n) = O(g(n))$. By the definition of big-Oh notation, this means there exist positive constants $c$ and $n_0$ such that for all $n \geq n_0$, $|f(n)| \leq c \cdot g(n)$.

Now, we can rewrite the inequality as $c' \cdot g(n) \geq |f(n)|$, where $c' = \frac{1}{c}$. This implies that $g(n) = \Omega(f(n))$, satisfying the definition of big-Omega notation.

Next, let

's assume that $g(n) = \Omega(f(n))$. This means there exist positive constants $c'$ and $n_0'$ such that for all $n \geq n_0'$, $c' \cdot f(n) \leq |g(n)|$.

By multiplying both sides of the inequality by $\frac{1}{c'}$, we get $\frac{1}{c'} \cdot f(n) \leq \frac{1}{c'} \cdot |g(n)|$. This implies that $f(n) = O(g(n))$, satisfying the definition of big-Oh notation.

Therefore, we have proved that $f(n) = O(g(n))$ if and only if $g(n) = \Omega(f(n))$.

Task 3:

Using mathematical induction, we can prove that $\sum_{i=0}^n \frac{i}{2^i} = \frac{2^{n+1}-(n+2)}{2^n}$.

Base case: For $n=0$, the left-hand side (LHS) is $\frac{0}{2^0} = 0$, and the right-hand side (RHS) is $\frac{2^{0+1}-(0+2)}{2^0} = \frac{2-2}{1} = 0$. Therefore, the equation holds true for the base case.

Inductive step: Assume the equation holds for $n=k$, where $k\geq0$. We need to prove that it holds for $n=k+1$.

Starting with the LHS:

\begin{align*}

\sum_{i=0}^{k+1} \frac{i}{2^i} &= \sum_{i=0}^k \frac{i}{2^i} + \frac{k+1}{2^{k+1}} \\

&= \frac{2^{k+1}-(k+2)}{2^k} + \frac{k+1}{2^{k+1}} \quad \text{(by the induction hypothesis)} \\

&= \frac{2^{k+1} - (k+2) + (k+1)}{2^{k+1}} \\

&= \frac{2^{k+1} + k + 1 - k - 2}{2^{k+1}} \\

&= \frac{2^{k+2} - (k+2)}{2^{k+1}} \\

&= \frac{2^{(k+1)+1} - ((k+1)+2)}{2^{k+1}} \\

&= \frac{2^{(k+1)+1} - ((k+1)+2)}{2^{(k+1)+1}}

\end{align*}

Thus, the equation holds for $n=k+1$.

By the principle of mathematical induction, the equation holds for all non-negative integers $n$. Therefore, we have proved that $\sum_{i=0}^n \frac{i}{2^i} = \frac{2^{n+1}-(n+2)}{2^n}$.

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In 6 days 285 miles can be travelled.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

190  miles cover in 4 days.

let x miles travelled in 6 days

So, using proportion

190/4 = x/6

190 x 6 = 4x

4x= 1440

x= 285 miles.

Hence, in 6 days 285 miles can be travelled.

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Here is the answer to your question.Q1: Using MATLAB instruction:\(\[ z_1=[2+5 i 3+7 i ; 6+13 i 9+11 i], z_2=\left[\begin{array}{lll} 7+2 i & 6+8 i ; 4+4 s q r t(3) i & 6+s q r t(7) i \end{array}\right] \] i.\) Find z1z2 and display the result in rectangular form.

Since the sizes of z1 and z2 are compatible, we can multiply them. The MATLAB code for multiplying z1 and z2 is shown below:>>z1

=\([2+5i 3+7i; 6+13i 9+11i]; > > z2=[7+2i 6+8i; 4+4*sqrt(3)*i 6+sqrt(7)*i]; > > z1z2=z1*z2 The result of z1z2 is:z1z2\)

=  -39.0000 + 189.0000i  -50.0000 - 97.0000i -152.0000 - 50.0000i  -42.0000 +154.0000iTo represent the result in rectangular form, we need to use the real() and imag() functions to get the real and imaginary parts of the product. .

Then, we can combine these parts using the complex() function to get the result in rectangular form. The MATLAB code for this is shown below:>>rectangular_result

= complex(real(z1z2), imag(z1z2))

=  -39.0000 + 189.0000i  -50.0000 - 97.0000i -152.0000 - 50.0000i  -42.0000 +154.0000i

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The sequence's numbers are all multiples of 30. Every number can be divided by 30.

If two integers are divided equally, leaving no remainder, then we say that one integer divides the other (we sometimes say, "with no remainder," but that is not technically correct). Mathematicians express this more explicitly as follows: If a and b are integers (with a not zero), then a divides b if c is an integer such that b = ac. Sequence: 1 51, 2 52,....., n 5n,....n 5n=n(n 4 1)=n(n1)(n1)(n+1)(n 2 +1)

At n=1, n 5, n=0, n=1, 2, 3, etc. Not attainable

Atn=2,n 5 −n=30 ∴ The sequence's numbers are all multiples of 30. Every number can be divided by 30.

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3 because 6x3 +2 =20 and -3+23=20

Answer:

AC=20

Step-by-step explanation:

6y+2 = -y+23

move y to one side

7y+2=23

move 2 to the other side

7y=21

divide by 7 on both sides to isolate y

y=3

Substitute y in

-3+23=20

Check your work,18+2=20

Answer:20 cups flour’s

Step-by-step explanation:

the correct answer is a. likely to be due to true differences between the groups.

If we say we have statistically significant results, it means that the results are likely to be due to true differences between the groups. Statistical significance is a term used in hypothesis testing to determine if the observed differences between groups are likely to be real and not due to chance.

When conducting a statistical analysis, researchers compare the data from different groups or samples to see if there is a significant difference between them. This involves calculating a p-value, which represents the probability of obtaining the observed results if there were no true differences between the groups.

If the p-value is less than a predetermined threshold, typically 0.05, then the results are considered statistically significant. This means that the likelihood of obtaining the observed results by chance alone is very low, and it is more likely that the differences between the groups are due to a real effect.

For example, let's say we conduct a study to compare the effectiveness of two different treatments for a medical condition. If we find that the p-value is less than 0.05, we can conclude that there is a statistically significant difference between the treatments, and the observed improvement in one group is likely to be due to the treatment itself rather than random chance.

In summary, when we say we have statistically significant results, it means that the observed differences between groups are likely to be due to true differences rather than chance. This provides evidence for the presence of a real effect or relationship between the variables being studied.

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Answer:

(2x+1)(x−3)(x−2)

Step-by-step explanation:

Test the hypothesis step of the scientific method is he performing.

Making conjectures (hypothetical explanations) is a step in the scientific method. Predictions are then derived from the hypotheses as logical conclusions, and experiments or actual observations are conducted based on those predictions.

Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science. Since one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.

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Answer:

Between 0 and 3: decreasing

Between 3 and 4: constant (stays the same)

Between 4 and 8: decreasing

Step-by-step explanation:

3x(2x - 5) = (3x - 4)(2x + 1)

6x² - 15x = 6x² + 3x - 8x - 4

6x² - 15x - 6x² - 3x + 8x = -4

-10x = -4 / : (-10)

x = 0,4

Step-by-step explanation:

Pam and Erin want the gardens to be proportional.

proprtional- equal

Pams garden has a length of 16 and width of 12. To find the area of Pam's garden multiply the length by the width.

16×12= 192

Now that we know the area of Pam's garden, we can set up and equation for Erin's garden. Since they have to be equal we know that Erin's garden should equal 192. Thus we solve for the length by dividing the width from the total.

192÷21=9.14

Answer:

answer is in the graph

Step-by-step explanation:

label your y axis miles (horizontal axis) with intervals of 10

label your x axis hours (right to left axis) with intervals of 1

for every 1 hour (x axis) your graph increases by 10 miles (y axis)

so your points are

(1, 10) and (2, 20) and (3, 30) and so on

your equation for the line is  y=10x

see attached graph

To find the length of the curve given by r(t) = cos(7t) i + sin(7t) j + 7 ln(cos(t)) k, 0 ≤ t ≤ π/4, we need to use the formula for arc length:

L = ∫[a,b] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt

In this case, we have:

dx/dt = -7 sin(7t)
dy/dt = 7 cos(7t)
dz/dt = -7 sin(t) / cos(t)

So,

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 sin^2(7t) + 49 cos^2(7t) + 49 sin^2(t) / cos^2(t)
= 49 [sin^2(7t) + cos^2(7t) + sin^2(t) / cos^2(t)]
= 49 [1 + sin^2(t) / cos^2(t)]

Now, using the identity sin^2(t) + cos^2(t) = 1, we can rewrite this as:

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 cos^2(t)

Therefore, the length of the curve is:

L = ∫[0,π/4] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt
= ∫[0,π/4] 7 cos(t) dt
= 7 [sin(t)]|[0,π/4]
= 7 sin(π/4) - 7 sin(0)
= 7 (√2/2)
= 7√2/2

So the length of the curve is 7√2/2.

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