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a air balloon is at a height of 2,520 feet. it begins to descend at the rate of 140 feet per minute.
2. Find the expression for 2,5,8,10,15 minutes

Answer:

B

Step-by-step explanation:

Complementary angles sum to 90° then the other angle is

90° - 52° = 38°

Answer:

B 38°

Step-by-step explanation:

complementary angles are two angles that up to 90°, since we know one is 52°, 90-52=38, so your answer is 38

Answer:

Step-by-step explanation:

        In 7 hours he drove                     210 miles

So,    In 1 hour   he drove                     \(210/7\) miles

                                                              = 30 miles

The value of a in the expression 8 - i/3 - 2i is 8.

To find the value of a, we need to simplify the expression by combining like terms.

First, let's deal with the complex numbers. We have -i/3 - 2i. To combine these terms, we can factor out the common factor of i:

-i/3 - 2i = i(-1/3 - 2)

Next, we can simplify the real numbers. -1/3 - 2 can be combined to give -7/3.

So, we have i(-7/3).

Finally, we can simplify the expression by multiplying i with -7/3:

i(-7/3) = -7i/3.

Therefore, the expression 8 - i/3 - 2i simplifies to 8 - 7i/3.

From this expression, we can see that the real part, a, is 8.

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since the population standard deviations (σ1 and σ2) are not provided, we cannot calculate the exact test statistic Z.

To test the null hypothesis H0: (μ1 - μ2) = 0 versus the alternative hypothesis Ha: (μ1 - μ2) ≠ 0, we can use a two-sample z-test. The test statistic is calculated as:

Z = (x bar1 - x bar2) / sqrt((σ1^2 / n1) + (σ2^2 / n2))

Where:
X bar1 and x bar2 are the sample means of the two groups,
σ1 and σ2 are the population standard deviations of the two groups,
n1 and n2 are the sample sizes of the two groups.

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The minimum number of sets of knives Gabriel should buy will be 10sets.

A chef's knife, a paring knife, and a serrated knife are the only three knives that are essential in a kitchen. Any more knives are a luxury; while they can facilitate cooking and enhance the experience, they are not required.

Given the least number of knives needed = 587 knives

Amount currently available on ground = 387knives

The remaining amount of knives needed = 587 - 387

The remaining amount of knives needed = 200 knives

If each set on sale contains 20 knives, the number of sets Isabella will need will be:

The number of sets of knives=200/20 =10

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.

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Answer:

1814.85 N

Step-by-step explanation:

Weight = mass * acceleration of gravity

Jayden's weight = 185 * 9.81 = 1814.85 N

The claim we need to check is that 16 is the 50% of 36.

Recall that if we add 50% and 50%, we should end up with 100%. In our case, we have that our 100% is 36. So, if it was true that 16 is the 50% of 36, then it should happen that if we add 16 with itself, we should get 36.

Note that

Since 16+16 is not 36, it is not true that 16 is the 50% of 36.

Answer:

y = - \(\frac{5}{2}\) x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line

m = \(\frac{-2-3}{0-(-2)}\) = \(\frac{-5}{0+2}\) = - \(\frac{5}{2}\)

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = - \(\frac{5}{2}\) x - 2 ← equation of line

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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The book sold 38,100 copies in its first month of release. then approximately 537,324 copies have been sold to date.

What is the percentage?

A percentage is a ratio, fraction, or portion of a whole which is represented as 100.

Let "x" be the total number of copies sold to date.

According to the problem, 38,100 is 7.1% of x, which can be written as:

38,100 = 0.071x

To find x, we can solve for it by dividing both sides of the equation by 0.071:

x = 38,100 / 0.071

x = 537,323.94 (rounded to the nearest whole number)

Therefore, approximately 537,324 copies have been sold to date.

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the line first find the slope

Slope of the line using points

(-2,2)and(-3,-9) is

\(m = \frac{ - 9 - 2}{ - 3 + 2} = \frac{ - 11}{ - 1} = 11\)

Then use the formula

y - y1 = m(x - x1)

where

m is the slope

( x1 , y1) can be any of the points

Equation of the line using point (-2,2) and slope 11 is

y - 2 = 11 ( x + 2)

y - 2 = 11x + 22

11x - y = - 2 - 22

We have the final answer as

Hope this helps you

The solution to the given inequality is:

b≥4 or b≤-5.

We can also write this as the interval notation:

(-∞, -5] ∪ [4, ∞)

A connection between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics. The inequality can be resolved by adding the same amount to each side, subtracting the same amount from each side, multiplying or dividing each side by the same positive integer, and more. If you multiply or divide either side by a negative value, you must flip the inequality sign.

We need to solve the inequality -10b+3≤-37 or 3b - 10 ≤-25.

First, let's solve the first inequality, -10b+3≤-37:

-10b+3≤-37

Subtracting 3 from both sides, we get:

-10b≤-40

Dividing both sides by -10,

b≥4

So the first solution is b≥4.

Now, let's solve the second inequality, 3b - 10 ≤-25.

3b - 10 ≤-25

Adding 10 to both sides, we get:

3b≤-15

Dividing both sides by 3, we get:

b≤-5

So the second solution is b≤-5.

Therefore, the solution to the given inequality is:

b≥4 or b≤-5.

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The complete question:

What is the solution of the composite inequality -10b+3≤-37 or 3b - 10 ≤-25?

Also, write in the interval notation.

The required values of x and y that allows these two triangles to be similar are x=(32±√239)/5, y=(19±2√239)/5.

Let the first triangle be called ABC where A(-1, 4), B(-3, 5) and C(-6, 1).

Let the second triangle be called LMN where L(-2, 8), M(-6, 10) and N(x, y)

Now if the 2 triangles are similar then the ratio of the lengths of corresponding sides will also be equal.

AB: BC= \(\sqrt{(-1+3)^{2}+(4-5)^{2} }\):\(\sqrt{(-1+6)^{2}+(5-1)^{2} }\) = √5:√41

AC: BC= \(\sqrt{(-1+6)^{2}+(4-1)^{2} }\): \(\sqrt{(-1+6)^{2}+(5-1)^{2} }\)=√34:√41

Now,

LM: MN= \(\sqrt{(-2+6)^{2}+(8-10)^{2} }\):\(\sqrt{(x+6)^{2}+(y-10)^{2} }\)

=2√5:\(\sqrt{(x+6)^{2}+(y-10)^{2} }\)

Comparing LM: MN to AB: BC we get \(\sqrt{(x+6)^{2}+(y-10)^{2} }\)=2√41

∴ \((x+6)^{2}+(y-10)^{2}\) = 164...... (1)

Again, LN: MN= \(\sqrt{(x+2)^{2}+(y-8)^{2} }\) : \(\sqrt{(x+6)^{2}+(y-10)^{2} }\)= AC: BC= √34:√41

Applying (1) to this rati we get: \(\sqrt{(x+2)^{2}+(y-8)^{2} }\)=2√34....(2)

Solving (1) and (2) we get: 8x-4y=32-68=-36

∴ 2x-y=9

Substituting y=2x-9 in (1) we get: \((x+6)^{2}+(2x-9)^{2}\)=164

Solving we get x=(32±√239)/5, y=(19±2√239)/5

Hence we get the required answers.

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The system of equations y = 3x - 7 and 6x - 2y = 12 has no solution. That is the lines of the equation is parallel.

To solve a system of equations, you can use substitution or elimination.

One method to find the solution for this system of equations is substitution. To use this method, you can solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation.

Solving for y in the first equation:

y = 3x - 7

Then substitute the result in the second equation:

6x - 2(3x - 7) = 12

6x - 6x + 14 = 12

14 = 12

That clearly is not true and this system of equations has no solution.

--The question is incomplete, answering to the question below--

"What is the solution to the system y = 3x - 7 and 6x - 2y = 12?

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The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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The gardener used 40.5 gallons of gasoline in his lawn mowers in the one month.

Let's say the amount of gasoline used in the lawn mowers is x gallons.

Then, the rest of the gasoline (61.5 - x) would have been used for other purposes.

Since the total amount of gasoline used is 61.5 gallons, we can set up an equation:

x + (61.5 - x) = 61.5

Simplifying this equation, we get:

x + 61.5 - x = 61.5

Combining like terms, we get:

61.5 = 61.5

This equation is true, so we know that our assumption that x is the amount of gasoline used in the lawn mowers is correct.

Therefore, the gardener used x = 40.5 gallons of gasoline in his lawn mowers in the one month.

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The experiment type of research study is being used.

What is an experiment ?

A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law

In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.

As opposed to option A, where the participants are being observed in their natural context, this is not a naturalistic observation example.

The lack of a relationship means that it is neither a correlation research, as in option C, nor a survey, as in option D.

Option B is the appropriate response, thus.

So, the experiment  type of research study is being used.

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Answer:

$7.80

Step-by-step explanation:

130*6=7.80

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

The measure of the other leg of right angled triangle is 15.5cm

The Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

According to the question

In a right angled triangle

Hypotenuse = 16 cm

Base = 4 cm

measure of the other leg or perpendicular is

Now ,

By applying  Pythagoras theorem

\(Hypotenuse^{2} = Base^{2} + Perpendicular^{2}\)

substituting the values

\(16^{2} = 4^{2} + Perpendicular^{2}\)

256 = 16 \(+ Perpendicular^{2}\)

240 =  \(Perpendicular^{2}\)

applying square root both side

Perpendicular = 15.5 cm

Hence, the measure of the other leg of right angled triangle is 15.5cm

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Answer:

adult $8.00

child $5.50

Step-by-step explanation:

Let the price of 1 adult ticket = x.

Let the price of 1 child ticket = y.

2x + 4y = 38

3x + 3y = 40.5

Multiply the first equation by 3. Multiply the second equation by -2. Then add them.

         6x + 12y = 114

(+)      -6x - 6y = -81

-----------------------------

                  6y = 33

y = 33/6

y = 5.5

2x + 4y = 38

2x + 4(5.5) = 38

2x + 22 = 38

2x = 16

x = 8

Answer:

adult $8.00

child $5.50

Answer:

An adult ticket is $8.00 and a child's ticket is $5.50.

Step-by-step explanation:

We form a system of 2 equations and solve them.

Let a be the price of adult ticket and c the price of a child's.

2a + 4c = 38         (A)

3a + 3c = 40.5      (B)

Multiply equation A by 3 and equation B by -2:

6a + 12c = 114

-6a - 6c = -81        Adding these 2 equations:

0 + 6c = 33

c = 33/6 = 5.5.

Now we substitute for c in equation A:

2a + 4(5.5) = 38

2a = 38 - 22

2a = 16

a = 6.

Let's now check these results by substitution in equation B:

3a + 3c = 40.5

3(8) + 3(5.5) = 24.0 + 16.5 = 40.5

- so it checks out.

Answer:

what-

Step-by-step explanation:

The approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches is 0.6

To find the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches, we will first calculate the surface area (SA) and volume (V) of the ball, and then divide the surface area by the volume.

Step 1: Calculate the surface area (SA) using the formula for the surface area of a sphere:

\(SA = 4 πr^2\)
\(SA = 4 π5^2\)
\(SA = 4 π(25)\)
\(SA=100π\)

Step 2: Calculate the volume (V) using the formula for the volume of a sphere:

\(V = \frac{4}{3} π (r)^{3}\)
\(V = \frac{4}{3} π (5)^{3}\)
\(V = \frac{4}{3} π (125)\)
V = 166.67 π cubic inches

Step 3: Calculate the surface-area-to-volume ratio (SA/V)
\(\frac{SA}{V} = \frac{100}{166.67}\)
\(\frac{SA}{V}=\frac{100}{166.67}\)

\(\frac{SA}{V}= 0.6\)

So the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches is 0.6. The best answer from the choices provided is A.

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In a randomized controlled experiment, there is a control group and a treatment group.

This statement is i.e. option d is correct.

Randomized controlled experiments are commonly used in scientific research, particularly in medicine and psychology.

They are used to determine whether a treatment or intervention is effective or not.

In a randomized controlled experiment, the participants are randomly assigned to either the control group or the treatment group.

The control group is used as a comparison group and does not receive the treatment or intervention.

The treatment group, on the other hand, receives the treatment or intervention being studied.

There are several ways that a randomized controlled experiment can be designed to minimize the potential for bias. For example, in a randomized controlled experiment, random assignment of participants to groups helps to ensure that the two groups are similar at the outset of the study.

This reduces the likelihood that differences between the groups will be due to factors other than the treatment or intervention being studied.

Other ways that a randomized controlled experiment can be designed to minimize bias include blinding and use of placebos.

Blinding refers to the practice of keeping certain participants, such as those administering the treatment, unaware of which group a participant is in.

This helps to ensure that any differences between the two groups are not due to the expectations of the researchers or participants.

Use of placebos is another way to reduce bias in a randomized controlled experiment.

Placebos are inactive substances that are given to the control group to mimic the treatment group, ensuring that any differences between the groups are due to the treatment being studied and not other factors.

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Answer:

The answer is 17.

Step-by-step explanation:

Multiply (8x8) + (15x15) = 289

Next you find the square root of 289.

√289 + 17

Answer:

38.5 mm^2

Have a nice day!

Step-by-step explanation:

Area = πr^2

Area = π(3.5^2)

Area = π(12.25)

Area = 38.48451...

Area = 38.5