A jogger can run 4 laps around the block in 8 minutes. If the jogger runs at a constant rate of speed, how many laps can the they run in 30
minutes?

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer: See image

Step-by-step explanation:

The bases are 5cm times 3cm, meaning that 2 parallel sides have to be 5cm by 3cm, 2 other parallel sides have to 2cm by 3cm, and the 2 other parallel sides have to be 5cm by 2cm.

A producers can maximize their profit if:

By decreasing their marginal cost, producers can lower the amount it costs to produce each additional unit of their product which increases their profit margin. Keeping marginal revenues above marginal costs ensures they generate enough revenue to cover their costs and earning a profit.

While raising prices may increase marginal revenue in short term, it may lead to a decrease in demand which can lower profits. So, it is important for producers to find the right balance between cost and revenue management to maximize their profits.

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Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

9514 1404 393

Answer:

  (d) ∛27 and 3³

Step-by-step explanation:

If f(x) and g(x) are inverse functions, then f(g(x)) = g(f(x)) = x. Here, it looks like we're to assume that the functions are of the form f(x) = root(x) or f(x) = x^power.

  a) these expressions evaluate to 25 and -25, so are additive inverses. We don't believe that is the intention of the question.

  b) f(x) = √x; g(x) = x². f(g(121)) = √(121²) ≠ √121

  c) f(x) = -∛(x); g(x) = (-x)³. f(g(64)) = -∛((-64)³) ≠ -∛64

  d) f(x) = ∛x; g(x) = x³. f(g(3)) = ∛(3³) = ∛27 . . . . . . these are inverse operations

Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

\(w(x)=14\cdot 1.08^{x}\)

w(25) =

\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

Answer:

-22

Step-by-step explanation:

First do r(3) by replacing x with 3 in r:

2*3^2 + 2 = 2*9 + 2 = 18 + 2 = 20

Then replace r(3) with 20 to do q(20):

-20-2 = -22

Answer:

There will be 28 green erasers. I know that the ratio is also 28:20, so there are 20 blu erasers.

Step-by-step explanation:

I time 7 by 4 and 5 by 4 to get the new ratio. I counted the ratios to get to 48.

Step-by-step explanation:

The given line is

y = 3x - 1

3x - y - 1 = 0 .....i)

The line perpendicular to the line I Is

x + 3y + k = 0 .....ii)

The line II) passes through the point (7, 4) so

7 + 3 *4 + k = 0

7 + 12 + k = 0

19 + k = 0

I. e k = - 19

So the required equation is x + 3y - 19 = 0

Hope it will help :)❤

A dataset's quartiles are critical summary statistics that split the data into four equal groups. The first quartile (q1), often known as the lower quartile, splits the data into the bottom 25% and the remainder.

The second quartile (q2), commonly known as the median, splits the data into the lowest and highest 50%. The third quartile (q3), often known as the upper quartile, divides the data into the lowest 75% and the highest 25%. These quartiles give useful information regarding the data distribution and value spread.

The quartiles may also be used to find outliers in the dataset. Understanding the quartiles is an important element of data analysis and may assist inform data-driven decision making.

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The possible lengths of the path are (2,3,5)

Any side of a triangle must be shorter than the other two sides added together. If a side is equal to the other two sides it is not a triangle.

Given here: A 9 mile long triangular path.

In Euclidean geometry, triangle inequlaity theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c.

Thus we have

a) 1+1=2<7 (False)

b)1+2=3<6 (False)

c)2+2=4<5 (False)

d) 2+3=5>4 ( True)

Therefore the possible lengths of the paths are (2,3,5)

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A triangular bike path is exactly  miles long. If each of the three connecting paths is a whole-number of miles long, which could be the lengths of the paths? (1 Point)

1mile,  1mile,  7miles

1 mile, 2 miles, 6 miles

2 miles,  2miles, 5 miles

2 miles,  3miles, 5 miles

The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.

The given tiles in bag-1 = {2, 4, 5, 8, 9}

Total number of tiles in bag-1 = 5

The number of tiles less than number 3 in the bag - 1 = 1

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 1/3

The given tiles in bag-2 = {0, 1, 3, 6, 7}

Total number of tiles in bag-2 = 5

The number of tiles less than number 3 in the bag-2 = 2

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 2/3

From the above analysis, we solved the problem.

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Answer:

11.4

Step-by-step explanation:

10% of 57 is 5.7

5.7 in 1 min

5.7*2 for 2 min

you get 11.4

Hooray! You solved the problem!

Answer:

It's 11.4 Feet

Step-by-step explanation:

If it takes the sub 1 minute to go down 10% of 57 feet, then another minute will be another 10%. So 10% = 5.7 feet, and 10% + 10% = 11.4 feet.

Answer:

It is best to solve a system of equations using substitution when one of the equations isolates one of the variables, or when the coefficient of one of the variables is 1 or -1.

Step-by-step explanation:

This makes it easier to substitute one variable for the other, allowing you to solve for the remaining variable. It is also a good idea to check the solution back in the original equations just to make sure it is a valid solution

Answer:

Answer Below

Step-by-step explanation:

It is best to use substitution if one of the variables is isolated or has a coefficient of 1 or -1.

Answer:

just put like what oh yea put 72

Answer:

100°

Step-by-step explanation:

tThe sum of all arc measures that make up that circle is 360 degrees.

QS + RQ + RS = 360

QS = 360 - 120 - 140 = 100

An arc angle is the degree measurement of that angle inside the circle, opposite the arc

m∠R = arc QS = 100°

Answer:

∠ R = 50°

Step-by-step explanation:

the inscribed angle R is half the measure of its intercepted arc QS

the sum of the arcs on a circle is 360° , that is

RQ + QS + SR = 360°

120° + QS + 140° = 360°

QS + 260° = 360° ( subtract 260° from both sides )

QS = 100°

Then

∠ R = \(\frac{1}{2}\) × 100° = 50°

Answer:

10\(\sqrt{3}\)

Step-by-step explanation:

assumed the radius of the pond was r

∴tan60°=\(\sqrt{3}\)= \(\frac{30}{r}\)

∴r=\(10\sqrt{3}\)

The length of radius of the pond will be 108.76 metres.

Given the values we have,

length of the pole = 30 metres

the angle of elevation of the pole from a point on the circumference = 60°

From this information, we get a right-angled triangle with a perpendicular of 30 m and a base angle of 60°

Therefore we can say that the radius of the pond will be the base of the triangle.

Let the radius of the pond be r

Using the trigonometric ratio of tan, we get,

\(tan \alpha = \frac{perpendicular}{base}\)

\(tan 60 = \frac{30}{r}\)

The value of tan 60° is \(\sqrt{3}\)

\(\sqrt{3}=\frac{30}{r}\)

\(r= \frac{30}{\sqrt{3}}\)

\(r = 17.32\) metres

Therefore the base of the triangle or the radius of the pond is 17.32 metres.

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The circumference of the circle C = 207.24 inches.

The formula for the circumference of circle is,

Assume the value of pi be 3.14.

Substitute 207.24 for C in the formula to determine the radius of circle.

Thus radius of circle is 33 inches.

The point which is on the y-axis and is the y axis and is 7 units from the point (-7, -5) is;

Since the point is on the y-axis, it follows that it's x-coordinate is zero and hence; the point is; (0, y).

The distance is therefore 7 units and hence;

7² = (-7-0)² + (y - (-5))²

49 -49 = (y +5)²

0 = y +5

y = -5

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The figure in number 4 above has three sides and we call such polygon a triangle.

The term polygon refers to a figure that contains a given number of sides. Now there are many kinds of polygon that exists and all the polygons are classified on that basis of the number of sides that they posses. We can know the number of sides by counting it up when we look at the figure as shown in the diagram.

Thus, the figure in number 4 above has three sides and we call such polygon a triangle. The figure in number 6 has six sides and we call such a polygon a hexagon.

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Answer:

this is an identity which is true for all x values

Step-by-step explanation:

Perform the indicated multiplication.  We get:

6x - 1 = 6x -1

and see that this is an identity which is true for all x values.

Answer:

1.66

Step-by-step explanation:

Using the Chi square statistic (χ²) test :

χ² = Σ(Oi - Ei)² / Ei

Expected, Ei :

Freshmen = 30% * 300 = 90

Sophomore =24% * 300 = 72

Junior = 26% * 300 = 78

Senior = 20% * 300 = 60

Observed, Oi :

Freshmen = 83

Sophomore = 68

Junior = 85

Senior = 64

χ² = ((83 - 90)²/90) + ((68 - 72)²/72) + ((85 - 78)²/78) + (64 - 60)²/60)

χ² = 49/90 + 16/72 + 49/78 + 16/60

χ² = 0.544 + 0.222 + 0.628 + 0.267

χ² = 1.661

The test statistic = 1.66

The exact value of sin(pi/3) is √3. By definition, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, sin(pi/3) = √3/1 = √3.

The exact value of sin(pi/3) can be determined using trigonometric properties and identities.

First, we know that pi/3 is equivalent to 60 degrees. In a unit circle, the point corresponding to 60 degrees forms an equilateral triangle with the origin and the x-axis. This triangle has side lengths of 1, 1, and √3.

To find the sine of pi/3, we consider the side opposite the angle (pi/3) in the triangle. In this case, the opposite side has a length of √3. The hypotenuse of the triangle is 1, as it is the radius of the unit circle.

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The common ratio of the resulting sequence is 1.4.

Given that, the three terms are 60, 100 and 180.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Let the same constant is added to the given number is x.

60+x, 100+x and 180+x

Now, the common ratio is

(100+x)/(60+x) = (180+x)/(100+x)

⇒ (100+x)(100+x)=(180+x)(60+x)

⇒ (100+x)²=10800+180x+60x+x²

⇒ 10000+200x+x²=10800+180x+60x+x²

⇒ 10000+200x=10800+180x

⇒ 20x=800

⇒ x=40

The three number are 100, 140 and 220

The common ratio is 140/100 =1.4

Therefore, the common ratio of the resulting sequence is 1.4.

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Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

w = -12

Explanation:

Given the points (6,w) and (15,-3)

Since the slope is 1, we have that:

The value of w is -12.

Answer:

Answer: 25 miles

Step-by-step explanation:

Explanation: He will run 5 hours= 5x5=25

Answer:

25 miles

Step-by-step explanation:

I'll create a set of proportions to figure out the answer (represented by x):

2:10 = 5:x

It looks like our proportion on the left, 2:10, can be simplified by dividing both sides by 2 to get 1:5.

1:5 = 5:x

You can multiply 1 by 5 to get 5, so we should be able to multiply 5 by 5 to get the value of x. 5 times 5 is 25, so the answer to the question is 25 miles.

If you have questions or need clarification on anything, let me know!

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

20%

Step-by-step explanation:

5 divided by 25 multiplied by 100 will give you 20%.

I hope you understand

Answer:

  190 ft deep

Step-by-step explanation:

What the problem doesn't tell you is that "this situation" is the height of the ball relative to the ground level Lisa is standing on. The ball is dropped from a height of 6 feet above that level. The variable 'h' is said to represent the drop height (in feet), so h = 6. Evaluating the expression for t=3.5 will tell the height of the ball relative to ground level after 3.5 seconds.

  -16(3.5)² +6 = -196 +6 = -190

The bottom of the well is 190 feet below ground level.