Which is the equation of a line that is perpendicular to the line represented represented by y = 3/4x - 1/2 ?

Final answer:

The Nautilus traveled a total vertical distance of 55 meters. A red kangaroo traveling at a speed of 40 km/h would take approximately 3 minutes to jump 2 km.

Explanation:

Total Vertical Distance Traveled by the Nautilus

To calculate the total vertical distance the Nautilus traveled, we need to add the distance it descended and the distance it ascended. The Nautilus descended from 75 m BSL to 105 m BSL, which is a distance of 105 m - 75 m = 30 m. Then it ascended from 105 m BSL to 80 m BSL, a distance of 105 m - 80 m = 25 m. So the total vertical distance traveled is 30 m + 25 m = 55 m.

Time for a Red Kangaroo to Jump 2 km

The speed of the kangaroo is 40 km/h. To find the time to jump 2 km, we first convert the speed to km/min: 40 km/h ÷ 60 min/h = 0.6667 km/min. Now, we divide the distance by the speed: 2 km ÷ 0.6667 km/min = 3 min. Thus, it will take the kangaroo approximately 3 minutes to jump 2 km.

Answer:

Option B: Circle [tex]1[/tex] is a dilation of circle  [tex]2[/tex] with a scale factor of  [tex]4[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and is called the scale factor

All circles are similar and the scale factor is equal to the ratio of its radius or the ratio of its diameters or the ratio of its circumferences

Let

z------> the scale factor

A----> the radius of circle 1

B-----> the radius of circle 2

so

[tex]z=\frac{A}{B}[/tex]

we have

[tex]A=8x\ units[/tex]

[tex]B=2x\ units[/tex]

[tex]z=\frac{8x}{2x}=4[/tex]

The dilation is an enlargement because the scale factor is greater than [tex]1[/tex]

Answer: ∠FRO

Step-by-step explanation:

Given : Trapezoid BIRD is dilated to form trapezoid FROG.

As dilation creates similar image as the original .

Thus by the property of similarity ,the corresponding angles are congruent.

Therefore, angle congruent to ∠BIR must be ∠FRO [first three letters of the name of the shapes]

The answer would be 6,900 ft2. The equation to find the area is "a=1/2bx"

a= area b=base h=height. Hope this helps :D

Given that, a town plans to make a triangular park. The triangle has a base of 120 feet and a height of 115 feet.

We know that area of a triangle = [tex] \frac{1}{2} [/tex] x base x height

Given that base of triangle is 120 feet and height is 115 feet. From the given data, we calculate the area of the triangular park.

Area = [tex] \frac{1}{2}*120 *115 = 6900 [/tex]

Hence , Area of triangular park is 6900 square feet.

[tex](6x^2 - 3x^3) - (2x^3 + 4x^2 -5)\\\\=6x^2-3x^3-2x^3-4x^2-(-5)\\\\=6x^2-3x^3-2x^3-4x^2+5\qquad\text{combine like terms}\\\\=(-3x^3-2x^3)+(6x^2-4x^2)+5\\\\=\boxed{-5x^3+2x^2+5}[/tex]

To convert 11 ounces to pounds, divide 11 by 16. The result is 0.6875 pounds, which rounds up to 0.7 pounds.

To convert 11 ounces to pounds, you would divide the number of ounces by the number of ounces in one pound, which is 16.

Since there are 16 ounces in one pound, we can make this conversion by dividing the number of ounces by 16.

11 ounces / 16 ounces/pound = 0.6875 pounds

Rounded to the nearest tenth, this is approximately 0.7 pounds.

Therefore, the correct answer is B. 0.7 pounds.

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To determine the probability that a U.S. resident aged 35-64 with health insurance in 2015 had an income between $50,000 and $79,999.

To calculate the probability that a randomly selected U.S. resident aged 35-64 with health insurance in 2015 had an income between $50,000 and $79,999, we would need specific data from the table mentioned in the question.

The process to find the probability would involve dividing the number of residents aged 35-64 with incomes between $50,000 and $79,999 by the total number of residents aged 35-64 with health insurance. The result would then be converted into a percentage to arrive at the probability.

Final answer:

To find the approximate probability of a U.S. resident with health insurance who was 35-64 in 2015 having an income between $50,000 and $79,999, we divide the number of residents in that category by the total number of residents with health insurance. The approximate probability is 0.1167.

Explanation:

To calculate the approximate probability that a U.S. resident with health insurance who was 35-64 had an income between $50,000 and $79,999 in 2015, we need to find the number of U.S. residents with health insurance in that age group and income category, and divide it by the total number of U.S. residents with health insurance.

From the given table, we can see that there were 32,500 U.S. residents with health insurance who were 35-64 years old and had an income between $50,000 and $79,999.

The total number of U.S. residents with health insurance in 2015, across all age groups, is 278,500.

So, the approximate probability is:

Probability = Number of U.S. residents with health insurance who were 35-64 and had an income between $50,000 and $79,999 / Total number of U.S. residents with health insurance

Approximate Probability = 32,500 / 278,500 = 0.1167

Therefore, the approximate probability that a U.S. resident with health insurance who was 35-64 in 2015 had an income between $50,000 and $79,999 is 0.1167.

As, the values on the x-axis changes, the value of y-axis gets tripled,the rate of change of values of response with respect to the domain is 3. Hence, the multiplicative rate of change of the exponential function is 3.

Given  information:

The graph of an exponential function is having the different rate of change of function with respect to the values of x and y.

The values given for the function are ,

[tex]f(-2)=2/9\\f(-1)=2/3\\f(0)=2\\f(1)=6\\f(2)=6\\f(3)=54\\[/tex]

As, the given function is having a growth on every point which is multiplicative, hence the multiplicative rate of change for the exponential function can be calculated.

According to the points given, the rate of change of values of response with respect to the domain is 3,

Hence, the multiplicative rate of change of the exponential function is 3.

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Answer:

A. [tex]\text{m AB}=49^o[/tex].

B. [tex]\text{m ABC}=253^o[/tex].

C. [tex]\text{m BAC}=156^0[/tex].

D. [tex]\text{m ACB}=311^o[/tex]

Step-by-step explanation:

We have been given a circle and we are asked to find the arc measures of given circle.

Since we know that the measure of an arc that subtends to central angle equals the measure of central angle.

A. We can see from our circle that arc AB subtends to central angle AOB.

[tex]m\angle AOB=49^o[/tex]

[tex]\text{m AB}=49^o[/tex]

Therefore, measure of arc AB will be also 49 degrees.

B. First of all we will have to find the measure of arc BC.

Since we know that the sum of all central angles in a circle is 360°, so we can find the measure of arc BC by subtracting measure of arcs AB and AC from 360 degrees.

[tex]\text{m BC}=360^o-(\text{m AB+m AC})[/tex]

[tex]\text{m BC}=360^o-(49^o+107^o)[/tex]

[tex]\text{m BC}=360^o-156^o[/tex]

[tex]\text{m BC}=204^o[/tex]

We can see that ABC equals arc AB plus arc BC.

[tex]\text{m ABC}=\text{m AB}+\text{m BC}[/tex]

Upon substituting measures of arc AB and BC we will get,

[tex]\text{m ABC}=49^o+204^o[/tex]

[tex]\text{m ABC}=253^o[/tex]

Therefore, measure of arc ABC is 253 degrees.

C. We can see that arc BAC equals arc BA plus arc AC.

[tex]\text{m BAC}=\text{m BA}+\text{m AC}[/tex]

Upon substituting measure of arc BA and AC we will get,

[tex]\text{m BAC}=49^o+107^0[/tex]

[tex]\text{m BAC}=156^0[/tex]

Therefore, measure of arc BAC is 156 degrees.

D. We can see that arc ACB equals arc AC plus arc CB.

[tex]\text{m ACB}=\text{m AC}+\text{m CB}[/tex]

Upon substituting measure of arc AC and CB we will get,

[tex]\text{m ACB}=107^o+204^o[/tex]

[tex]\text{m ACB}=311^o[/tex]

Therefore, the measure of arc ACB is 311 degrees.

Answer:

the answer is 60

Step-by-step explanation:

The answer is option A "Correlation, because time of day doesn't cause a person to run faster or slower." It's completely logic that the time of day doesn't affect the persons speed it's how fit the person that person is would effect his or her speed. Correlation is two data sets that are close together and are connected on a graph.

Hope this helps!

Answer:

A. Correlation, because time of day doesn't cause a person to run faster or slower

Step-by-step explanation:

Marcus notices that he runs faster in the mornings rather than the evenings.This is a correlation because it tells us about the relationship of Marcus's running speed with respect to the time of day. The causation is not possible because there is no definite mention for the increase in speed.

Hence, option A is the answer.

We are given points on trig graph as

[tex](0,-4)[/tex]

[tex](\frac{\pi}{2} ,0)[/tex]

[tex](\pi ,4)[/tex]

[tex](\frac{3\pi}{2} ,0)[/tex]

[tex](2\pi ,-4)[/tex]

now, we can find rate of change from x = π to x = 2π

so, we will select two points

[tex](\pi ,4)[/tex]  and [tex](2\pi ,-4)[/tex]

we can also write as

[tex]a=\pi , f(a)=4[/tex]

[tex]b=2\pi , f(b)=-4[/tex]

now, we can use average rate of change formula

[tex]A=\frac{f(b)-f(a)}{b-a}[/tex]

now, we can plug values

and we get

[tex]A=\frac{-4-4}{2\pi -\pi}[/tex]

[tex]A=\frac{-8}{\pi }[/tex]

so, option-C.............Answer

Answer:

hes saysing its "a" the first brand g

Step-by-step explanation:

Brand G will end up costing $159.48 less than Brand F.

The correct option is a.

To determine which grill is cheaper over a fifteen-year period, we need to compare the total cost of buying and paying off each grill.

Brand F: The grill costs $650, and we will pay it off in five years of monthly payments, which is 60 payments.

The monthly payment required to pay off a $650 loan with a 13.01% annual interest rate, compounded monthly, over five years is:

PMT = (r x P) / (1 - (1 + r)⁻ⁿ

   = (0.1301/12  x 650) / (1 - (1 + 0.1301/12)⁻⁶⁰

   = $14.79

Therefore, the total cost of a Brand F grill, including interest, is:

Total Cost = 650 + 60(14.79) = $1537.4

Brand G: The grill costs $200, but we will need to buy three of them over fifteen years.

Each grill will be paid off in three years of monthly payments, which is 36 payments.

The monthly payment required to pay off a $200 loan with a 13.01% annual interest rate, compounded monthly, over three years is:

PMT = (0.1301/12 x 200) / (1 - (1 + 0.1301/12)⁻³⁶

   = $6.74

Therefore, the total cost of three Brand G grills, including interest, is:

Total Cost = 3 * (200 + 36 * 6.74) = $1327.92

The difference in cost is: $159.48.

Therefore, over a fifteen-year period, buying three Brand G grills instead of one Brand F grill will save you $159.48.

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Answer:

cos(a+b)≈0.507

Step-by-step explanation:

Hi there, in Quadrant I both sine and cosine functions are positive.

This cos (a+b) being a Classical Trigonometrical Identity, the product of the sum between two cosines equals the product of two cosines minus the product of two sines.

But we need to find the value of a and b, so that we can go on. Calculate the arccosine and arcsine function respectively is mandatory

[tex]cos(a+b)=cosa*cosb-sena*senb\\ cos(a+b)=cosa*\frac{5}{13} -\frac{4}{5}*senb\\ a=arcsin(\frac{5}{13})\\a=22.61\\b=arccos(\frac{4}{5})\\b=36.86\\ 5/13=0.38\\4/5=0.8\\cos(a+b)=cos(22.61)*cos(36.86) -sen(22.61)*sen(36.86)\\ cos (a+b)=0.507[/tex]

The trigonometric ratio for sin z is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.

The trigonometric ratio for sin z is defined as the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle. In other words, if we have a right triangle with angle z, sin z is equal to the length of the side opposite to angle z divided by the length of the hypotenuse.

Mathematically, sin z = opposite/hypotenuse.

For example, if we have a right triangle with angle z, and the length of the opposite side is 3 units and the length of the hypotenuse is 5 units, then sin z = 3/5.

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The graph attached shows the point of intersection of a linear and exponential function.

Given is a linear function and a exponential function.

We can write the equations as -

y = ax + b

y = eˣ

For the points of intersection -

ax + b = eˣ

Refer to the graph attached. It shows the point of intersection of a linear and exponential function.

Therefore, the graph attached shows the point of intersection of a linear and exponential function.

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Answer:

y = 3/2x + 1

Step-by-step explanation: