Franklin rides his bike to the beach averaging 18mph. He rides home along the same route. What speed must he average on the way home if he wants to average 21 miles per hour for the round trip?

The mean is 66, the median is 75 and the mode is None.

The center or typical value of a dataset is represented by summary statistics known as measures of central tendency. These metrics, such as the mean, median, and mode, are examples. These statistics, often known as the central location of a distribution, show where the majority of values in a distribution fall.

Given,

No. of observations = 5

Mean = Total observations/ no. of observations = 20+73+75+80+82/5 = 66

Median = Middle most observation arranged from smallest to largest = 75

Mode = Observation which occurs at least twice = None

Mean describes the data the best because it takes the average of all the given data.

The distribution of the data set is scattered and the shape of the frequency graph is going upwards.

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Answer:

undefined

Step-by-step explanation:

To find the slope of the line passing through the points (4, 7) and (4, -6), we can use the slope formula:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates of the points (4, 7) and (4, -6) into the formula:

m = (-6 - 7) / (4 - 4)

m = (-13) / (0)

The denominator is zero, which means the line is vertical and parallel to the y-axis. When the denominator is zero, the slope is undefined.

Therefore, the line passing through the points (4, 7) and (4, -6) has an undefined slope.

Answer:

1530 is the sum of 2+1528

Answer:

1,530

Step-by-step explanation:

Answer:

Measure of third angle = 80°

Step-by-step explanation:

Property of an isosceles triangle,

Opposite angles of the equal sides of an isosceles triangle are equal in measure.

Since, base angles of an isosceles triangle are equal,

(3x + 2) = (5x - 30)

5x - 3x = 2 + 30

2x = 32

x = 16

Now measure of the base angles will be = (3×16) + 2 = 50°

Let the measure of third angle = y°

Since, sum of interior angles of a triangle = 180°

50° + 50° + y° = 180°

y + 100 = 180

y = 80°

Therefore, measure of third angle is 80°.

Answer:

The Smart family could paint 110 square feet per hour.

Step-by-step explanation:

Given that while remodeling their living room, the Smart family decided to repaint the walls, and they estimated that they could repaint 55 square feet every half-hour, to determine how many square feet can they paint per hour the following calculation must be performed:

1/2 = 0.5

0.5 = 55

1 = X

55 / 0.5 = X

110 = X

Therefore, the Smart family could paint 110 square feet per hour.

Answer:

equation 15+8=

solution= 23

Step-by-step explanation:

its ez

Answer:

I believe it is false

Step-by-step explanation:

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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x and y have the values 7 and 7√2, respectively.

The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.

We can use this information to determine the values of x and y because the base is specified as being 7.

Let's give the perpendicular side the value of x, and the hypotenuse the value of y.

The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.

Consequently, x = 7.

We can determine that x:y:2x using the ratio of 1:1:2.

When we enter the value of x, we may calculate y:

7:y:√2(7)

Simplifying even more

7:y:7√2

Given that the hypotenuse (y) equals 72, we can write:

y = 7√2

Thus, x and y have the values 7 and 7√2, respectively.

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Answer:

2

Step-by-step explanation:

1 + 1 = 2

Answer:

year 1: 90% × 245000 = 220500

year 2: 90% × 220500 = 198450

year 3: 90% × 198450 = 178605

∴ the car price after 3 years is 178605

explanation:

the value of car decreases 10%. that means the car price is 90%

The price of the car after 3 years will be 178605

We can calculate the value in the following way

Rate of decrease in car's price: 10%

Current price of the car: 245000

Value after 1 year, say value1= current value-10% of current value

\(value1=245000-\frac{10*245000}{100}\)

=245000-24500

=220500

After 1 year, the next decrement in the price will be based on the value of the car in that year. In other words, we calculate the value after the second year by decreasing by 10% of value1.

Value of car after 2 years, say value2= value1- 10% of value1

\(value2=220500- (\frac{10*220500}{100})\)

=220500-22050

=198450

Similarly,

Value of car after 3 years, say value3= value2- 10% of value2

\(value3=198450- (\frac{10*198450}{100})\)

=198450-19845

=178605

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Answer:

17.65%

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/financial/markup-calculator.php?cost=49.50&margin=15&action=solve

Answer:

Step-by-step explanation:

47,57,68

adding 1 to the next number and so on

plus 4, plus 5, plus 6 and so on

The value of the product of the number as given in the task content is; Choice B; 1.

It follows from the task content that the numbers whose product are to be determined are; ¾ and 1⅓.

To effectively multiply, we must convert the mixed number to a fraction as follows;

1⅓ = 4/3.

Hence, the product is; 4/3 × 3/4 = 12/12 = 1.

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The recorded speed in a standing position is faster because 133.69 feet per second is more than 113.6 feet per second

It should be noted that:

1km per hour = 0.911344 foot/second

Therefore, converting 146.7 kilometers per hour to feet per second will be:

= 146.7 × 0.911344

= 133.69 feet per second

Since the fastest recorded speed on inline skates is about 113.6 feet per second, therefore, fastest recorded speed in a standing position is the faster speed.

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Answer:

A

Step-by-step explanation:

Answer:

plane EBG

Step-by-step explanation:

plane C is also named plane EBG

\(\\ \sf\longmapsto Plane\:EBG\)

Answer:

90

Step-by-step explanation:

since mean = sum of terms / number of terms, we can find the total sum of the tests currently to see how much it needs to be raised

76 * 6 = 456

x = score of the new test

(456 + x)/7 = 78

x =90

The statement that is true regarding the function f(x) = (x-4)(x + 1) is that the function is increasing for all real values of x where x < -1 and where x > 4. So, the option is: O The function is increasing for all real values of x where x < -1 and where x > 4.

Explanation: Given function is:f(x) = (x - 4) (x + 1). The graph of the given function is shown below: As it is visible from the graph, the function is decreasing for all real values of x where x lies between -1 and 4 (inclusive).

The turning point of the function is x = -0.5, which is the x-coordinate of the vertex of the parabola. Also, we see that the vertex is the minimum point of the parabola and the y-coordinate of the vertex is -4.25. This means that f(x) ≥ -4.25 for all x. The function is increasing for all real values of x where x < -1 and where x > 4.

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The sum of the first 10 terms of the geometric sequence is given by: 1,048,575.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

The sum of the first n terms is given by:

\(S_n = \frac{a_1(1 - q^n)}{1 - q}, q \neq 1\)

For this problem, the parameters are given as follows:

a1 = 3, q = 4, n = 10.

Hence the sum is given by:

\(S_{10} = 3\frac{1 - 4^10}{1 - 4} = 1,048,575\)

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Answer:

Where is the question?

Step-by-step explanation:

In the given congruent triangles, measure of ∠CED = 70° and the measure of  ∠BCE = 134°.

Angle is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.

According To SAS rule of congruency the given two triangle are Congruent

Therefore by CPCT,

∠CED = ∠CAB

∠ABC = ∠CDE

That is,

9z - 2 = 3y + 10

and

64° = 8z

z = 64/8

z = 8

Putting the value of z in 9z - 2 = 3y + 10 we get

9(8) - 2 = 3y + 10

72 - 2 = 3y + 10

70 = 3y + 10

70 - 10 = 3y

3y = 60

y = 60/3

y = 20

Then

∠CED = 9(8) - 2

= 70°

And

∠BCE = 7(20) - 6

= 134°

Thus, In the given congruent triangles, measure of ∠CED = 70° and the measure of  ∠BCE = 134°.

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Answer:

c = 45 and e = 30

Step-by-step explanation:

Since we know that A = 45, B = 90, we can calculate C knowing that the total angle of a triangle is 180, so you do 180-45-90 = 45

Finding the angle C helps us find F by subtracting 45 from 180, since a straight line is 180 degrees, which is 135.

We know that E = 15, and what was said earlier about how the toal angle is 180 in a triangle, we can subtract 15 and 135 from 180, which is 30.

Hope that answers your question

To calculate the distance between two points:

We apply the following formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute data and solve:

\(\bf{d=\sqrt{(6-(-3))^2+(-8-8(-8))^2 } }\\ \\ \bf{ d=\sqrt{9^2+0^2}=\sqrt{81+0} }\\ \\ \bf{d=\sqrt{81}=9 }\)

The distance between the points (−3,− 8), (6, – 8) is 9.

Answer:

The equation is:

\(L=3\,\,d^2\\\)

and a beam with 10 in diagonal will support 300 lb

Step-by-step explanation:

The mathematical expression that represents the statement:

"The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. "

can be written as:

\(L=k\,\,d^2\)

where k is the constant of proportionality

To find the constant we use the data they provide: "A beam with diagonal 6 in will support a maximum load of 108 lb.":

\(L=k\,\,d^2\\108 = k\,\,(6)^2\\k=\frac{108}{36} \,\,\frac{lb}{in^2}\\ k = 3\,\,\frac{lb}{in^2}\)

Now we can use the proportionality found above to find the maximum load for a 10 in diagonal beam:

\(L=3\,\,d^2\\L=3\,\,(10)^2\\L=300 \,\,lb\)

Answer:

L=3d^2 the beam will support 300 pounds

Step-by-step explanation:

108=k x 6^2

Dividing by 6^2=36 gives k=3, so an equation that relates L and d is

L=3d^2 d=10 yields

3(10)^2=300

So a beam with a 10in diagonal will support a 300lb load.

Answer:

Rewrite the division problem as -9/2 (4,3)

 the quotient: -6

Step-by-step explanation:

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

If m<5 =115 then

m<1 =115

because they are corresponding angles

Answer:

d

Step-by-step explanation:

678 is between 5 and 9

u should not count 5 and 9