Mr. and Mrs. Smith took their children on a trip to the Grand Canyon. When they left home, Mrs. Smith noted the odometer read 5,478.18 miles. When they arrived at the Grand Canyon, she noted that the odometer read 6,010.63. How far had the family-driven?

Answer:

Step-by-step explanation:

When reflecting coordinates about the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same.

So, for the point (4, 6), the new coordinates after reflection about the y-axis would be (-4, 6).

For the point (12, 2), the new coordinates would be (-12, 2).

For the point (-1, 0), the new coordinates would be (1, 0).

Therefore, the new coordinates after reflecting these points about the y-axis are (-4, 6), (-12, 2), and (1, 0).

Answer:

E

Step-by-step explanation:

For Company A, the monthly cost y in dollars can be represented by:

y = 0.12x + 20

where x is the number of minutes used.

For Company B, the monthly cost y in dollars can be represented by:

y = 0.06x + 50

where x is the number of minutes used.

To find the number of minutes of calls where the monthly bills will be the same, we need to set the two equations equal to each other and solve for x:

0.12x + 20 = 0.06x + 50

0.06x = 30

x = 500

Therefore, the monthly bills will be the same for both companies when the number of minutes used is 500.

Answer: (E) 500 minutes

The area of the enlarged map is 75 cm². Answer: (D) 75 cm².

What is scale ?

Scale refers to the ratio of distances or sizes on a map or drawing to the actual distances or sizes of the objects they represent in the real world. It is often expressed as a ratio, such as 1:10,000 or 1/4 inch = 1 foot, and is used to create maps and drawings that accurately represent real-world objects and distances. Scales can be used to enlarge or reduce the size of a map or drawing, making it easier to view and work with.

The original area of Colorado on the map is:

Area = length x width = 4 cm x 3 cm = 12 cm²

To enlarge the map with a scale factor of 2.5, we need to multiply the length and width by 2.5:

New length = 4 cm x 2.5 = 10 cm

New width = 3 cm x 2.5 = 7.5 cm

The area of the enlarged map is:

New area = new length x new width = 10 cm x 7.5 cm = 75 cm²

Therefore, the area of the enlarged map is 75 cm². Answer: (D) 75 cm².

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Answer:

(f-g)(x) = -5x^3 + 8x - 8.

(f-g)(-2) = 16.

Step-by-step explanation:

To find (f-g)(x), we need to subtract g(x) from f(x) and simplify:

(f-g)(x) = f(x) - g(x)

= (-5x^3 - 4x^2 + 8x) - (-4x^2 + 8)

= -5x^3 - 4x^2 + 8x + 4x^2 - 8

= -5x^3 + 8x - 8

Therefore, (f-g)(x) = -5x^3 + 8x - 8.

To find (f-g)(-2), we substitute x = -2 into the expression we just found:

(f-g)(-2) = -5(-2)^3 + 8(-2) - 8

= -5(-8) - 16 - 8

= 40 - 24

= 16

Therefore, (f-g)(-2) = 16.

Answer:

15 miles in 120 minutes

Step-by-step explanation:

We can start by using the unit rate of Alex's running speed:

5 miles / 40 minutes = 0.125 miles per minute

This means that Alex runs at a speed of 0.125 miles per minute.

To find out how many miles he can run in 120 minutes, we can multiply his speed by the number of minutes:

0.125 miles/minute × 120 minutes = 15 miles

Therefore, if Alex runs at the same rate, he can run 15 miles in 120 minutes.

The correct answer is a scatter plot, because it would show the association or relationship between two variables.

A scatter plot is a graph that displays values of two variables on two axes. It is used to show the relationship between the two variables and how one variable affects the other. It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram. The points are plotted on a graph and can be used to identify patterns and trends in the data.

A scatter plot can be used to display the relationship between two variables, such as the weight and height of a manatee. The points on the scatter plot would represent each manatee's weight and height, and the pattern of the points can be used to see the overall relationship between the two variables. A line graph, on the other hand, is used to show how a variable changes over time between each data point given, and would not be suitable for this context as the data collected is not related to time.

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The value of the probability P(A n B) is 0.36

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

A and B are dependent events.

P(A)= 0.4 and P(B)= 0.9

Using the above as a guide, we have the following:

P(A n B) = P(A) * P(B)

Substitute the known values in the above equation, so, we have the following representation

P(A n B) = 0.4 * 0.9

Evaluate

P(A n B) = 0.36

Hence, the solution is 0.36

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Answer:

triangles, we can determine if these triangles can be proven similar by using the SSS Similarity ... use AA Similarity to prove the triangles are similar.

The graph of the function is added as an attachment

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

g(x) = 6, -7 < x ≤ -2

          2, -2 < x ≤ 3

          -2, 3 < x ≤ 8

The above is a piecewise function that has three linear functions, and three domains

Using the above as a guide, we have the following:

We plot each function in each domain

See attachment for the graph of the function

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Answer:

4) No, It is not a right triangle

Step-by-step explanation:

12 is the hypotenuse which is the longest side of the triangle

6² + 8² = 12² （Pythagoras Theorem）

36 + 64 ≠ 144

Hence it is not a right triangle

Answer:

B. $48

Step-by-step explanation:

Average=sum of the numbers÷number of numbers you added

Average will now be $50+$70+$25+$45+$50= $240÷5= $48

Using the product rule and chain rule, we can find the derivative of y with respect to x as follows:

y = x^4sec(x^9)

y' = (4x^3)(sec(x^9)) + (x^4)(sec(x^9))(d/dx(tan(x^9)))

We can simplify the derivative using the identity d/dx(tan(u)) = sec^2(u)(du/dx), where u = x^9:

y' = (4x^3)(sec(x^9)) + (x^4)(sec(x^9))(sec^2(x^9))(9x^8)

Simplifying further, we get:

y' = 4x^3sec(x^9) + 9x^12sec(x^9)

Therefore, the derivative of y with respect to x is 4x^3sec(x^9) + 9x^12sec(x^9).

The distinguishing feature of the distance between the foci and a point on the ellipse is that it is constant for all points on the ellipse.

What is an Ellipse?

In mathematics, an ellipse is a closed curve that is symmetrical about two perpendicular lines, called the major and minor axes.

The distinguishing feature of the distance between the foci and a point on the ellipse is that it is constant for all points on the ellipse. This distance is known as the focal length or eccentricity, and it is a measure of how much the ellipse deviates from a perfect circle. The sum of the distances from any point on the ellipse to the two foci is always equal to this constant distance, which can be calculated using the equation c² = a² - b², where c is the distance between the foci, and a and b are the lengths of the major and minor axes of the ellipse, respectively.

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Answer:

Step-by-step explanation:

The sum of the distances between the foci and any point on an ellipse is a constant sum. This sum is equal to the length of the major axis.

An ellipse is a set of all points in a plane so that the sum of the distances from two fixed points, called the foci, is constant. d1 + d2 = 2a = constant. An ellipse is what we commonly call an oval and looks like a squashed or flattened circle. In fact, a circle is a special kind of ellipse where the foci are located at the center of the circle. Two fixed points on the interior of an ellipse are given by (0, c) and (0, -c) for an ellipse with a vertical orientation and by (c, 0) and (-c, 0) for an ellipse with a horizontal orientation. The larger denominator is the major axis; therefore, if the larger denominator is under the x2, the ellipse will have a horizontal orientation. If the larger denominator is under the y2, the ellipse will be oriented vertically. Because both the vertices and foci lie on the major axis, they will both have the same y-coordinate (if the major axis is horizontal) or the same x-coordinate (if the major axis is vertical).

Answer:

Step-by-step explanation: true

Answer:

a = 75

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

2(1)*(1-(1))²=0

plug in 0 for everywhere you see x

The Required explanation of triangle inequality theorem has been done.

In mathematics, inequalities specify the connection between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol ()" to indicate that two values are not equivalent. But various inequalities are used to compare the values, whether it is less than or larger than.

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides is always greater than the length of the third side. Mathematically, if a, b, and c are the lengths of the sides of a triangle, then a + b > c, b + c > a, and c + a > b.

This theorem is a fundamental principle in geometry and can be used to prove many other theorems related to triangles.

It is also used in everyday life, such as in designing bridges, ensuring the stability of buildings, and determining the shortest distance between two points.

The triangle inequality theorem is a powerful tool in mathematics and is a key concept for anyone studying geometry.

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According to the graphs, the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia (option A).

To select an appropriate conclusion that matches the information in the graphs we must carefully analyze the information in the graphs. Additionally, we can read each of the options and check them with the trends shown in the graphs.

In accordance with the above procedure, we can infer that the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia because the Residential real estate graph shows that In 2010 housing was more expensive in Australia than in Spain.

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Answer:

Results

Interest Rate -61.911%

Total of 36 Monthly Payment of $8,100.00

Total Interest Paid $-16,900.00

Step-by-step explanation:

Answer:R= 3%/year

Step-by-step explanation:

r = 225 / (2500 x 3) = 0.03

r= 0.03

converting r decimal to a percentage

R = 0.03 * 100 = 3%/year

The interest rate required to accumulate simple interest of $225.00 from a principle of $2,500.00 over 3 years is 3% per year.

Answer:

64 Ounces

Step-by-step explanation:

There are 64 ounces in 4 1/2.

4 1/2 = 4.5

4.5 x 16 = 72

72 ounces - 8 ounces = 64 ounces

Answer:64

Step-by-step explanation:

Answer:

a. Since we know the mean and median of the wingspans, we can assume that the data is approximately normally distributed. We also know the range, which is the difference between the maximum and minimum values. From this information, we can set up two equations:

Mean = (Wingspan1 + Wingspan2 + Wingspan3)/3 = 6 1/4

Median = 6

We can use the second equation to eliminate one of the variables. If the median is 6, then the middle value must be 6 as well. Let's assume that Wingspan2 = 6. Then we have:

(Wingspan1 + 6 + Wingspan3)/3 = 6 1/4

Multiplying both sides by 3 and simplifying:

Wingspan1 + Wingspan3 = 18 3/4

We also know that the range is 1 3/4, so:

Wingspan3 - Wingspan1 = 1 3/4

Solving for Wingspan3 in terms of Wingspan1:

Wingspan3 = Wingspan1 + 1 3/4

Substituting this into the previous equation:

Wingspan1 + (Wingspan1 + 1 3/4) = 18 3/4

2Wingspan1 + 1 3/4 = 18 3/4

2Wingspan1 = 17

Wingspan1 = 8 1/2

Therefore, Wingspan3 = 10 1/4. So the three bald eagles have wingspans of 8 1/2 feet, 6 feet, and 10 1/4 feet.

b. Since the mean and median of the weights are the same, we can assume that the data is exactly normally distributed. We also know the range, which is the difference between the maximum and minimum values. From this information, we can set up two equations:

Mean = (Weight1 + Weight2 + Weight3)/3 = 12.75

Median = 12.75

We can use the second equation to eliminate one of the variables. If the median is 12.75, then the middle value must be 12.75 as well. Let's assume that Weight2 = 12.75. Then we have:

(Weight1 + 12.75 + Weight3)/3 = 12.75

Multiplying both sides by 3 and simplifying:

Weight1 + Weight3 = 38.25

We also know that the range is 5 pounds, so:

Weight3 - Weight1 = 5

Solving for Weight3 in terms of Weight1:

Weight3 = Weight1 + 5

Substituting this into the previous equation:

Weight1 + (Weight1 + 5) = 38.25

2Weight1 + 5 = 38.25

2Weight1 = 33.25

Weight1 = 16.625

Therefore, Weight3 = 21.625. So the three bald eagles have weights of 16.625 pounds, 12.75 pounds, and 21.625 pounds.

Answer:

[tex]2304[/tex][tex]\pi[/tex]

Step-by-step explanation:

V = [tex]\frac{4}{3} \pi r^{3}[/tex]

V = [tex]\frac{4}{3} *\pi * 12*12*12[/tex]

Use 3 to divide one of the 12 which will be equal to 4

V = [tex]4 *\pi *4*12*12[/tex]

V = [tex]2304\pi[/tex]

c. 39

Step-by-step explanation:

the answer is 39

Answer:

7 x 3 1/4 = 91/4 or 22 3/4

Step-by-step explanation:

To calculate 7 x 3 1/4, we can first convert the mixed number 3 1/4 to an improper fraction:

3 1/4 = (3 x 4 + 1) / 4 = 13/4

Then, we can multiply 7 by 13/4 as follows:

7 x 13/4 = (7 x 13) / 4 = 91/4

Therefore, 7 x 3 1/4 = 91/4 or 22 3/4 (if we want to express the answer as a mixed number).

Answer:

22 3/4

Step-by-step explanation:

There are plenty of ways of solving this question. The improper fraction of 3 1/4 is 13/4.

7 · 3 1/4

[tex]\frac{7}{1}[/tex] x [tex]\frac{13}{4}[/tex] = [tex]\frac{91}{4}[/tex]

[tex]\frac{91}{4}[/tex] = 22.75 = 22 3/4

(21)⁹ . (15)⁹ is the equivalent expression using the same bases.

What are power and exponent?

One can represent extremely big or extremely small numbers in a more straightforward fashion by using exponents and powers. For instance, we can write 3 x 3 x 3 x 3 as 34, where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner.

                            It is claimed that the entire statement 34 possesses power. How many times you should multiply a number depends on its power. Other names for powers include exponents and indices.

using (a.b )ⁿ = (a)ⁿ . (b)ⁿ

 ( 21.15)⁹ = (21)⁹ . (15)⁹

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Using the Pythagorean theorem we can see that x = 9.3

Think of a right triangle with a hypotenuse of 16, a cathetus of 18 - 5 =13, and the other cathetus is x (we are ignoring the right part of the figure, only look at the triangle in the left)

Then we can use the Pythagorean theorem (the sum of the squares of the legs is equal to the square of the hypotenuse) to find the value of x.

x = √(16² - 13²) = 9.3

That is the value of x.

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Answer:

$85.00

Step-by-step explanation:

Let's first subtract the cost of the parts from the total to find the cost of the labor:

Cost of labor = Total cost - Cost of parts

Cost of labor = $576.50 - $109

Cost of labor = $467.50

We know that the technician worked for 5.5 hours, so we can find the cost of labor per hour by dividing the cost of labor by the number of hours:

Cost of labor per hour = Cost of labor / Number of hours

Cost of labor per hour = $467.50 / 5.5

Cost of labor per hour = $85

Therefore, the cost of labor per hour is $85.

Answer: 1/2

Step-by-step explanation:

Kim ate 2/5 which is also equal to 4/10 and Courtney has eaten 1/10

4/10 + 1/10 = 5/10 = 1/2